{"id":1650,"date":"2013-08-19T12:13:00","date_gmt":"2013-08-19T03:13:00","guid":{"rendered":"http:\/\/yoonhada.com\/?p=1650"},"modified":"2023-12-29T11:39:35","modified_gmt":"2023-12-29T02:39:35","slug":"fast-fourier-transform","status":"publish","type":"post","link":"http:\/\/yoonhada.com\/?p=1650","title":{"rendered":"Fourier Transform"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><br><strong>1. Fourier transform \uc9c1\uad00\uc801 \uc774\ud574<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\ubaa8\ub4e0 \uacf5\ubd80\uc758 \uc2dc\uc791\uc740 \ud575\uc2ec \uac1c\ub150\uc744 \uc815\ud655\ud788 \uc774\ud574\ud558\ub294\ub370 \uc788\ub2e4. \uadf8\ub9ac\uace0 \uadf8 \uc774\ud574\ub294 \uac00\uae09\uc801 \uc9c1\uad00\uc801\uc77c\uc218\ub85d \uc88b\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 \uc9c1\uad00\uc801\uc73c\ub85c \uc124\uba85\ud558\uba74 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740&nbsp;\uc784\uc758\uc758 \uc785\ub825 \uc2e0\ud638\ub97c \ub2e4\uc591\ud55c \uc8fc\ud30c\uc218\ub97c \uac16\ub294 \uc8fc\uae30\ud568\uc218\ub4e4\uc758 \ud569\uc73c\ub85c \ubd84\ud574\ud558\uc5ec \ud45c\ud604\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc880\ub354 \ub4e4\uc5b4\uac00\uba74, \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uc8fc\uae30\ud568\uc218\ub294 sin, cos \uc0bc\uac01\ud568\uc218\uc774\uba70 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740 \uace0\uc8fc\ud30c\ubd80\ud130 \uc800\uc8fc\ud30c\uae4c\uc9c0 \ub2e4\uc591\ud55c \uc8fc\ud30c\uc218 \ub300\uc5ed\uc758 sin, cos \ud568\uc218\ub4e4\ub85c \uc6d0\ubcf8 \uc2e0\ud638\ub97c \ubd84\ud574\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc544\ub798 \uadf8\ub9bc(\uadf8\ub9bc 1)\uc758 \uc608\ub97c \ubcf4\uc790. \ub9e8 \uc55e\uc758 \ubd89\uc740 \uc0c9 \uc2e0\ud638\ub294 \uc785\ub825 \uc2e0\ud638\uc774\uace0 \ub4a4\uc758 \ud30c\ub780\uc0c9 \uc2e0\ud638\ub4e4\uc740 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 \ud1b5\ud574 \uc5bb\uc5b4\uc9c4 (\uc6d0\ubcf8 \uc2e0\ud638\ub97c \uad6c\uc131\ud558\ub294) \uc8fc\uae30\ud568\uc218 \uc131\ubd84\ub4e4\uc774\ub2e4. \uac01\uac01\uc758 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\ub4e4\uc740 \uace0\uc720\uc758 \uc8fc\ud30c\uc218(frequency)\uc640 \uac15\ub3c4(amplitude)\ub97c \uac00\uc9c0\uace0 \uc788\uc73c\uba70&nbsp;<strong>\uc774\ub4e4\uc744 \ubaa8\ub450 \ud569\uce58\uba74 \uc6d0\ubcf8 \ubd89\uc740\uc0c9 \uc2e0\ud638<\/strong>\uac00 \ub41c\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/yoonhada.com\/wp-content\/uploads\/2023\/01\/9967FA3359B63D8122.png\" alt=\"\" class=\"wp-image-1667\" width=\"622\" height=\"286\" srcset=\"http:\/\/yoonhada.com\/wp-content\/uploads\/2023\/01\/9967FA3359B63D8122.png 470w, http:\/\/yoonhada.com\/wp-content\/uploads\/2023\/01\/9967FA3359B63D8122-300x138.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 1. \ud478\ub9ac\uc5d0 \ubcc0\ud658 (\uadf8\ub9bc\ucd9c\ucc98:&nbsp;<a href=\"https:\/\/en.wikipedia.org\/wiki\/Fourier_transform\" target=\"_blank\" rel=\"noreferrer noopener\">\uc704\ud0a4\ud53c\ub514\uc544<\/a>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5ec\uae30\uc11c \uc785\ub825 \uc2e0\ud638\ub294 \uc804\ud30c, \uc74c\uc131 \uc2e0\ud638 \ub4f1\uacfc \uac19\uc774 \uc2dc\uac04\ucd95(time)\uc5d0 \ub300\ud574 \uc815\uc758\ub41c \uc2e0\ud638\uc77c \uc218\ub3c4 \uc788\uace0 \uc774\ubbf8\uc9c0(image) \ub4f1\uacfc \uac19\uc774 \uacf5\uac04\ucd95\uc5d0 \ub300\ud574 \uc815\uc758\ub41c \uc2e0\ud638\uc77c \uc218\ub3c4 \uc788\ub2e4. \ud1b5\uc2e0 \ubd84\uc57c\uc5d0\uc11c\ub294 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 time domain\uc5d0\uc11c frequency domain\uc73c\ub85c\uc758 \ubcc0\ud658\uc774\ub77c\uace0 \ud558\uace0, \ucef4\ud4e8\ud130 \ube44\uc804(computer vision), \uc601\uc0c1\ucc98\ub9ac \ucabd\uc5d0\uc11c\ub294 spatial domain\uc5d0\uc11c frequency domain\uc73c\ub85c\uc758 \ubcc0\ud658\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uba85\uce6d\uc774\uc57c \uc5b4\uca0c\ub4e0 \uadf8 \ud575\uc2ec\uc740 \uc785\ub825 \uc2e0\ud638\ub97c sin, cos\uc758 \uc8fc\uae30\uc131\ubd84\uc73c\ub85c \ubd84\ud574\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc758 \ub300\ub2e8\ud55c \uc810\uc740 \uc785\ub825 \uc2e0\ud638\uac00 \uc5b4\ub5a4 \uc2e0\ud638\uc774\ub4e0\uc9c0 \uad00\uacc4\uc5c6\uc774 \uc784\uc758\uc758 \uc785\ub825 \uc2e0\ud638\ub97c sin, cos \uc8fc\uae30\ud568\uc218\ub4e4\uc758 \ud569\uc73c\ub85c \ud56d\uc0c1 \ubd84\ud574\ud560 \uc218 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4. \uadf8\ub9ac\uace0 \uadf8 \uacfc\uc815\uc744 \uc218\uc2dd\uc73c\ub85c \ud45c\ud604\ud55c \uac83\uc774 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc2dd\uc774\ub2e4.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Fourier transform \uc218\uc2dd\uc801 \uc774\ud574<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5b4\ub5a4 \uac1c\ub150\uc744 \uc9c1\uad00\uc801\uc73c\ub85c \uc774\ud574\ud588\ub2e4\uba74 \uadf8 \uac1c\ub150\uc5d0 \ub300\ud55c \uc218\uc2dd\uc801 \uc774\ud574\ub294 \uadf8 \uac1c\ub150\uc744 \ud55c\uce35 \ud48d\uc131\ud558\uace0 \uae4a\uc774\uc788\uac8c \uc774\ud574\ud558\uac8c \ud574 \uc900\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc740 \ud504\ub791\uc2a4\uc758 \uc218\ud559\uc790 Joseph Fourier (1768 ~ 1830)\uac00 \uc81c\uc548\ud55c \ubc29\ubc95\uc73c\ub85c\uc11c \uc218\ud559\uc0ac(\ud574\uc11d\ud559)\uc758 \uc5ed\uc0ac\uac00 \uc0c8\ub85c \uc50c\uc5ec\uc9c8 \uc815\ub3c4\ub85c \ub300\ub2e8\ud55c \ubc1c\uacac\uc774\uc5c8\ub2e4\uace0 \ud55c\ub2e4. \uadf8 \uc720\uba85\ud55c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uc218\uc2dd\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$f(x) = \\int^\\infty_{-\\infty}{F(u)e^{j2\\pi ux} du}\\qquad&#8212; (1)$$<br>$$F(u) = \\int^\\infty_{-\\infty}{f(x)e^{-j2\\pi ux} dx}\\qquad&#8212; (2)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5ec\uae30\uc11c&nbsp;[latex]j[\/latex]\ub294 \ud5c8\uc218\ub2e8\uc704&nbsp;[latex]j=\\sqrt{-1}[\/latex],&nbsp;[latex]f(x)[\/latex]\ub294 \uc6d0\ubcf8 \uc785\ub825 \uc2e0\ud638, [latex]e^{j2\\pi ux}[\/latex]\ub294 \uc8fc\ud30c\uc218 [latex]u[\/latex]\uc778 \uc8fc\uae30\ud568\uc218 \uc131\ubd84, [latex]F(u)[\/latex]\ub294 \ud574\ub2f9 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc758 \uacc4\uc218(coefficient)\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc77c\ub2e8 \uc2dd\uc744 \uc788\ub294 \uadf8\ub300\ub85c \ud574\uc11d\ud558\uba74 \uc2dd (1)\uc740&nbsp;\uc785\ub825\uc2e0\ud638 [latex]f(x)[\/latex]\uac00 [latex]e^{j2\\pi ux}[\/latex]\ub4e4\uc758 \ud569\uc73c\ub85c \ud45c\ud604(\ubd84\ud574)\ub41c\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4 (<a rel=\"noreferrer noopener\" href=\"http:\/\/darkpgmr.tistory.com\/45\" target=\"_blank\">\uc801\ubd84\uc740 \ud569\ud55c\ub2e4\ub294 \uc758\ubbf8\ub97c \uac16\ub294\ub2e4<\/a>). \uadf8\ub9ac\uace0 \uc2dd (2)\ub294 [latex]f(x)[\/latex]\ub97c \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc73c\ub85c \ubd84\ud574\ud588\uc744 \ub54c\uc758 \uacc4\uc218(coefficient) [latex]F(u)[\/latex]\uac00 \uc2dd (2)\ub85c \uc8fc\uc5b4\uc9c4\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4. \uc55e\uc11c \uadf8\ub9bc 1\uacfc \uc5f0\uad00\ud574 \ubcf4\uba74 [latex]e^{j2\\pi ux}[\/latex]\ub294 [latex]f(x)[\/latex]\ub97c \uad6c\uc131\ud558\ub294 (\ud30c\ub780\uc0c9\uc758 \uc8fc\ud30c\uc218 u\uc778) \uc8fc\uae30\ud568\uc218 \uc131\ubd84\ub4e4\uc774\uace0 [latex]F(u)[\/latex]\ub294 \ud574\ub2f9 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc758 \uac15\ub3c4(amplitude)\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0 \ub300\ud55c \uc77c\ubc18\uc801\uc778 \uc124\uba85 \ubc29\uc2dd\uc740 \ub450\ubc88\uc9f8 \uc2dd (2)\ub97c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc774\ub77c\uace0 \uc815\uc758\ud558\uace0 \uccab\ubc88\uc9f8 \uc2dd (1)\uc744 \ud478\ub9ac\uc5d0 \uc5ed\ubcc0\ud658(inverse Fourier transform)\uc774\ub77c\uace0 \uc815\uc758\ud558\ub294 \uac83\uc774\ub2e4. \uadf8\ub9ac\uace0 \ud478\ub9ac\uc5d0&nbsp;\uc5ed\ubcc0\ud658\uc744 \ud558\uba74 \ub2e4\uc2dc \uc6d0\ub798\uc758 \ud568\uc218\ub85c \ub3cc\uc544\uc628\ub2e4\uace0 \ud55c\ub2e4. \ud558\uc9c0\ub9cc \uc774\ub7ec\ud55c&nbsp;\uae30\uacc4\uc801\uc778 \uc774\ud574(\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \uc5b4\ub514 \ud558\ub298\uc5d0\uc11c \ub69d \ub5a8\uc5b4\uc9c4 \uc815\uc758\ub85c\ub9cc \ubc1b\uc544\ub4e4\uc774\ub294 \uac83)\ub294&nbsp;\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \ubcf8\uc9c8\uc744 \uc774\ud574\ud558\ub294\ub370 \ubcc4 \ub3c4\uc6c0\uc774 \ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc81c \uc2dd\uc73c\ub85c \uc880\ub354 \ub4e4\uc5b4\uac00 \ubcf4\uc790. \uc77c\ub2e8, \uc2dd \uc790\uccb4\ub294 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \ub300\ub2e8\ud568\uc5d0 \ube44\ucd94\uc5b4 \ub9e4\uc6b0 \ub2e8\uc21c\ud558\ub2e4 (Simple is the best!!). \ub2e4\ub9cc \ud55c \uac00\uc9c0 [latex]e^{j2\\pi ux}[\/latex]\uc758 \uc758\ubbf8\ub9cc \uc774\ud574\ud558\uba74 \ub41c\ub2e4. \uadf8\ub9ac\uace0 \uc774\ub97c \uc704\ud574\uc11c\ub294 \uc624\uc77c\ub7ec \uacf5\uc2dd(Euler&#8217;s formula)\uc774 \ud544\uc694\ud558\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc624\uc77c\ub7ec \uacf5\uc2dd(Euler&#8217;s formula)\uc740 \ubcf5\uc18c\uc9c0\uc218\ud568\uc218\ub97c \uc0bc\uac01\ud568\uc218\ub85c \ubcc0\ud658\ud560 \uc218 \uc788\ub3c4\ub85d \ud558\ub294 \uc720\uba85\ud55c \uc2dd\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$e^{j\\theta} = \\cos\\theta+ j\\sin\\theta\\qquad&#8212; (3)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc2dd (3)\uc740 \uc99d\uba85 \uac00\ub2a5\ud55c \uc2dd\uc774\uba70 \uadf8 \uc99d\uba85\uc740&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/ko.wikipedia.org\/wiki\/%EC%98%A4%EC%9D%BC%EB%9F%AC%EC%9D%98_%EA%B3%B5%EC%8B%9D\" target=\"_blank\">\uc778\ud130\ub137\uc5d0\uc11c \uc5b4\ub835\uc9c0 \uc54a\uac8c \ucc3e\uc744 \uc218 \uc788\ub2e4<\/a>. \uc5b4\uca0c\ub4e0&nbsp;\uc624\uc77c\ub7ec \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uba74 \uc2dd (1)\uc758 [latex]e^{j2\\pi ux}[\/latex]\ub294 \uc2e4\uc218\ubd80\uac00 [latex]\\cos(2\\pi ux)[\/latex], \ud5c8\uc218\ubd80\uac00 [latex]\\sin(2\\pi ux)[\/latex]\uc778 \uc8fc\uae30\ud568\uc218\uc784\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$e^{j2\\pi ux} = \\cos2\\pi ux + j\\sin 2 \\pi ux\\qquad&#8212; (4)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5ec\uae30\uc11c  [latex]\\cos(2\\pi ux)[\/latex], [latex]\\sin(2\\pi ux)[\/latex] \ubaa8\ub450 \uc8fc\uae30(period)\uac00 [latex]\\frac{1}{u}[\/latex], \uc8fc\ud30c\uc218(frequency) [latex]u[\/latex]\uc778 \uc8fc\uae30\ud568\uc218\uc774\ubbc0\ub85c \uacb0\uad6d&nbsp;[latex]e^{j2\\pi ux}[\/latex]\ub294 \uc8fc\ud30c\uc218 [latex]u[\/latex]\uc778 \uc815\ud604\ud30c(sinusoidal wave)\uc758 \ubcf5\uc18c\uc9c0\uc218\ud568\uc218 \ud45c\ud604\uc784\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uc8fc\uae30: \ud30c\ub3d9\uc774 \ud55c\ubc88 \uc9c4\ub3d9\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04, \ub610\ub294 \uadf8 \uae38\uc774<\/li>\n\n\n\n<li>\uc8fc\ud30c\uc218: 1\ucd08 \ub3d9\uc548\uc758 \uc9c4\ub3d9 \ud69f\uc218. \uc8fc\ud30c\uc218\uc640 \uc8fc\uae30\ub294 \uc11c\ub85c \uc5ed\uc218 \uad00\uacc4 (\uc8fc\ud30c\uc218 = 1\/\uc8fc\uae30)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \uc815\ud604\ud30c(sinusoidal wave)\ub294 \ud30c\ud615\uc774 sin \ub610\ub294 cos&nbsp;\ud568\uc218\uc778 \ud30c\ub3d9(wave)\uc744 \ub9d0\ud55c\ub2e4. \uadf8\ub7f0\ub370, \uc5ec\uae30\uc11c \uc65c \uac11\uc790\uae30 \ubcf5\uc18c\uc218\uac00 \ub098\uc624\uace0 \ub610 \uc8fc\uae30\ud568\uc218\ub97c \uc800\ub807\uac8c \ud45c\ud604\ud558\ub290\ub0d0\uace0 \ub530\uc9c8 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc \uc5ec\uae30\uc11c\ub294 \uadf8\ub0e5 \ubcf5\uc218\uc9c0\uc218\ud568\uc218\ub294 \uc815\ud604\ud30c(sinusoidal wave)\ub97c \ud45c\ud604\ud558\ub294 \ubc29\ubc95 \uc911 \ud558\ub098\ub77c\ub294 \uc815\ub3c4\ub85c\ub9cc \uc54c\uc544\ub450\uc790. \uc815\ud604\ud30c \ubc0f \ubcf5\uc218\uc9c0\uc218\ud568\uc218 \ud45c\ud604\uc5d0 \ub300\ud55c \ubcf4\ub2e4 \uc790\uc138\ud55c \ub0b4\uc6a9\uc740 <a href=\"https:\/\/angeloyeo.github.io\/2019\/06\/18\/phasor.html\" target=\"_blank\" rel=\"noreferrer noopener\">\ud398\uc774\uc800(phasor)\uc5d0 \ub300\ud55c \uc124\uba85\uae00<\/a>\uc744 \ucc38\uace0\ud558\uae30 \ubc14\ub780\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc81c \ub2e4\uc2dc \uc6d0\ub798\uc758 \uc2dd (1), (2)\ub85c \ub3cc\uc544\uac00 \ubcf4\uc790.&nbsp;\uc2dd (1)\uc740 \ud568\uc218 [latex]f(x)[\/latex]\ub97c \ubaa8\ub4e0 \uac00\ub2a5\ud55c \uc8fc\ud30c\uc218([latex]u[\/latex])\uc758 \uc8fc\uae30\ud568\uc218\ub4e4([latex]e^{j2\\pi ux}[\/latex])\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ud45c\ud604\ud55c \uac83\uc774\ub2e4. \uadf8\ub9ac\uace0 \uadf8 \uc77c\ucc28\uacb0\ud569 \uacc4\uc218 [latex]F(u)[\/latex]\ub294 \uc2dd (2)\ub85c \ud56d\uc0c1 \uc8fc\uc5b4\uc9c8 \uc218 \uc788\ub2e4\ub294 \uac83\uc774 \uc694\uc9c0\uc774\ub2e4. \uc774\uc640 \uac19\uc774 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc2dd\uc744 \ubcfc \uc218 \uc788\ub2e4\uba74 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \ud575\uc2ec\uc744 \uc774\ud574\ud55c \uac83\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \uc2dd (1), (2)\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc2dd\uc740 \uc5b8\ub73b \ubcf4\uba74 \uc815\uc758(definition)\ub85c \ubcf4\uc774\uc9c0\ub9cc \uc0ac\uc2e4\uc740 \uc99d\uba85\ud574\uc57c \ud560&nbsp;\uc815\ub9ac(theorem)\uc774\ub2e4. \uc989, \uc2dd (2)\uc758 [latex]F(u)[\/latex]\ub97c \uc2dd (1)\uc5d0 \ub300\uc785\ud558\uba74 \ud56d\uc0c1 [latex]f(x)[\/latex]\uac00 \ub098\uc634\uc744 \uc99d\uba85\ud574\uc57c \ud55c\ub2e4. \uc774\uac83\uc774 \uc99d\uba85\ub418\uba74 \ubaa8\ub4e0 \uc784\uc758\uc758 \uc2e0\ud638\ud568\uc218\ub294 \ud56d\uc0c1 \uc8fc\uae30\ud568\uc218\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ubd84\ud574\ub420 \uc218 \uc788\uc74c\uc774 \uc99d\uba85\ub418\ub294 \uac83\uc774\ub2e4 (<a rel=\"noreferrer noopener\" href=\"https:\/\/ghebook.blogspot.kr\/2012\/07\/fourier-series.html\" target=\"_blank\">\uc99d\uba85\uc740 \uc774\uacf3 \ucc38\uc870<\/a>).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub9c8\uc9c0\ub9c9\uc73c\ub85c, (\uc99d\uba85\uc740 \uc544\ub2c8\uc9c0\ub9cc) \uc65c \uc77c\ucc28\uacb0\ud569\uc758 \uacc4\uc218 [latex]F(u)[\/latex]\uac00 \uc2dd (2)\ub85c \uc8fc\uc5b4\uc9c0\ub294\uc9c0\ub97c \uc120\ud615\ub300\uc218\ud559\uacfc \uc5f0\uad00\uc9c0\uc5b4 \uc9c1\uad00\uc801\uc73c\ub85c \uc774\ud574\ud574 \ubcf4\uc790. \uc2dd (1)\uc5d0\uc11c [latex]e^{j2\\pi ux}[\/latex], u = 0, \u00b11, \u00b12, &#8230;\uc740 \ubaa8\ub4e0 \uc2e0\ud638\ub97c \uc0dd\uc131\ud560 \uc218 \uc788\ub294 \uc9c1\uad50(orthogonal) \uae30\uc800(basis) \ud568\uc218\ub4e4\ub85c \ubcfc \uc218 \uc788\ub2e4 (\ud3b8\uc758\uc0c1\u00a0u\ub97c \uc815\uc218 \ubc94\uc704\ub85c \ud45c\uae30\ud588\uc73c\ub098 u\ub294 \uc2e4\uc218 \uc804\uccb4 \ubc94\uc704\uc784). \uadf8\ub7ec\uba74\u00a0\uc785\ub825 \uc2e0\ud638 f(x)\ub97c \uc774\ub4e4 \uae30\uc800\ud568\uc218\ub4e4\ub85c \ubd84\ud574\ud588\uc744 \ub54c\uc758 \uacc4\uc218 [latex]F(u)[\/latex]\ub294 f(x)\uc640 \uae30\uc800\ud568\uc218\uc758 \ub0b4\uc801(dot product)\uc73c\ub85c \uacc4\uc0b0\ub420 \uc218 \uc788\ub2e4 (\uc544\ub798\uc758 \u261e\uc120\ud615\ub300\uc218\ud559 \uad00\ub828 \uc124\uba85 \ucc38\uc870). \uc2dd (2)\ub294 f(x)\uc640 [latex]e^{j2\\pi ux}[\/latex]\uc758 \ud568\uc218 \ub0b4\uc801\uc774\uae30 \ub54c\ubb38\uc5d0 \uadf8 \uacb0\uacfc\ub294 f(x)\ub97c [latex]e^{j2\\pi ux}[\/latex]\ub4e4\ub85c \ubd84\ud574\ud588\uc744 \ub54c\uc758 \uacc4\uc218\uac00 \ub41c\ub2e4. \ub530\ub77c\uc11c, F(u)[latex]F(u)[\/latex]\uac00 \uc2dd (2)\ub85c \uc8fc\uc5b4\uc9c0\ub294 \uc774\uc720\uac00 \uc124\uba85\uc774 \ub418\uc5c8\ub2e4. \ucc38\uace0\ub85c, \uc2dd (2)\uc5d0\uc11c j \uc55e\uc5d0 -\uac00 \ubd99\uc740 \uc774\uc720\ub294 \ubcf5\uc18c\uc218\uc5d0\uc11c\uc758 \ub0b4\uc801\uc740 \uc5b4\ub290 \ud55c\ucabd\uc5d0 \ucf24\ub808(conjugate) \ubcf5\uc18c\uc218\ub97c \ucde8\ud55c \ud6c4 \uacc4\uc0b0\ub418\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \uc120\ud615\ub300\uc218\ud559(linear algebra)\uc5d0\uc11c\ub294 \uc5b4\ub5a4 \ubca1\ud130 \uacf5\uac04\uc744 \uc0dd\uc131\ud560 \uc218 \uc788\ub294 \uc77c\ucc28\ub3c5\ub9bd\uc778 \ubca1\ud130\ub4e4\uc758 \uc9d1\ud569\uc744 \uae30\uc800(basis)\ub77c\uace0 \ud55c\ub2e4. \ub9cc\uc77c \uae30\uc800(basis) \ubca1\ud130\ub4e4\uc774 v1, v2, &#8230;, vn\ub77c \ud558\uba74 \uc774 \ubca1\ud130\uacf5\uac04\uc5d0 \uc18d\ud558\ub294 \uc784\uc758\uc758 \ubca1\ud130 v\ub294 v = a1v1 + a2v2 + &#8230; + anvn (ai\ub294 \uc0c1\uc218)\uc640 \uac19\uc774 \uae30\uc800 \ubca1\ud130\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ud45c\ud604\ub420 \uc218 \uc788\ub2e4 (\uc65c\ub0d0\ud558\uba74 vi\ub4e4\uc774 \uc774 \ubca1\ud130\uacf5\uac04\uc758 \ubaa8\ub4e0 \ubca1\ud130\ub4e4\uc744 \uc0dd\uc131\ud560 \uc218 \uc788\uc73c\ub2c8\uae4c). \uadf8\ub7f0\ub370 \ub9cc\uc77c \uae30\uc800\ubca1\ud130\ub4e4\uc774 \uc11c\ub85c \uc218\uc9c1(vi\u00b7vj = 0)\uc778 \ub2e8\uc704\ubca1\ud130\ub77c\uba74 \uc77c\ucc28\uacb0\ud569 \uacc4\uc218 ai\ub294 \ub0b4\uc801\uc744 \uc774\uc6a9\ud558\uc5ec ai = v\u00b7vi\ub85c \uc190\uc27d\uac8c \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4 (\u2235 v\u00b7vi = (a1v1 + &#8230; + anvn)\u00b7vi = ai*(vi\u00b7vi) = ai). \uc5b4\ub5a4 \ubca1\ud130\uc640 \uae30\uc800(basis) \ubca1\ud130\ub97c \ub0b4\uc801\ud558\uba74 \uc774 \ubca1\ud130\uc5d0 \ud3ec\ud568\ub41c \uae30\uc800 \uc131\ubd84\uc758 \uacc4\uc218\uac00 \uc5bb\uc5b4\uc9c4\ub2e4\ub294 \uac83\uc740 \uc120\ud615\ub300\uc218\ud559\uc5d0\uc11c \ub9e4\uc6b0 \uc720\uc6a9\ud55c \uc131\uc9c8\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e [latex]F(u)[\/latex]\uac00 \uc2dd (2)\ub85c \uc8fc\uc5b4\uc9c0\ub294 \uc774\uc720\uc5d0 \ub300\ud55c&nbsp;\uc120\ud615\ub300\uc218\ud559\uc801 \uc124\uba85\uc740 \uac1c\uc778\uc801 \uc774\ud574 \ubc29\uc2dd\uc774\ub77c\uc11c \uc99d\uba85\uc774 \uc788\uac70\ub098 \uadfc\uac70 \ubb38\ud5cc\uc774 \uc788\ub294 \ub0b4\uc6a9\uc740 \uc544\ub2d9\ub2c8\ub2e4. \uadf8\ub0e5 \uadf8\ub7f0 \uc2dd\uc73c\ub85c \uc774\ud574\ud560 \uc218\ub3c4 \uc788\uad6c\ub098 \ud558\uace0 \ucc38\uace0\ub9cc \ud558\uae30 \ubc14\ub78d\ub2c8\ub2e4. \uc815\ub9d0 \uadf8\ub7f0\uc9c0 \uc218\ud559\uc801\uc73c\ub85c \uc99d\uba85\ud574 \ubd10\ub77c \ud558\uba74 \uace8\uce58\uc544\ud515\ub2c8\ub2e4..<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. \uc774\ubbf8\uc9c0(\uc601\uc0c1\uc2e0\ud638)\uc5d0\uc11c\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 \uc601\uc0c1\ucc98\ub9ac\uc5d0 \uc801\uc6a9\ud558\uae30 \uc704\ud574\uc11c\ub294 \uc774\ubbf8\uc9c0(\uc601\uc0c1\uc2e0\ud638)\uac00 \uac00\uc9c0\uace0 \uc788\ub294 \uba87 \uac00\uc9c0 \ucc28\uc774\uc810\uc744 \uc778\uc9c0\ud574\uc57c \ud55c\ub2e4. \uba3c\uc800, \uc774\ubbf8\uc9c0\ub294 2\ucc28\uc6d0\uc758(x\ucd95 \ubc29\ud5a5\uc758 \ubcc0\ud654\uc640 y\ucd95 \ubc29\ud5a5\uc758 \ubcc0\ud654\uac00 \ub3d9\uc2dc\uc5d0 \ud3ec\ud568\ub41c) \uc2e0\ud638\uc774\uae30 \ub54c\ubb38\uc5d0 2\ucc28\uc6d0\uc5d0\uc11c \uc815\uc758\ub418\ub294 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc774 \ud544\uc694\ud558\ub2e4. 2\ucc28\uc6d0 \uc2e0\ud638\uc5d0 \ub300\ud55c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/993B073359B875CE36\" width=\"270\" height=\"37\">,&nbsp;&#8212; (5)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/998C953359B876000F\" width=\"274\" height=\"37\">. &#8212; (6)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e8, \uc5ec\uae30\uc11c F(u, v)\ub294 x\ucd95 \ubc29\ud5a5\uc73c\ub85c \uc8fc\ud30c\uc218(frequency) u, y\ucd95 \ubc29\ud5a5\uc73c\ub85c v\uc778 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc758 \uacc4\uc218\uc774\ub2e4. \uadf8\ub9ac\uace0 \uadf8 \uac12\uc740 \uc2dd (6)\uc5d0 \uc758\ud574 \uacc4\uc0b0\ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub7f0\ub370 \uc774\ubbf8\uc9c0\ub294 \uc5f0\uc18d(continuous)\uc774 \uc544\ub2cc \uc774\uc0b0(discrete) \uc2e0\ud638\uc774\ub2e4. \uadf8\ub9ac\uace0 \ud55c\uc815\ub41c \uc720\ud55c(finite) \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub418\ub294 \uc2e0\ud638\uc774\ub2e4. \ub530\ub77c\uc11c, \uc774\uc0b0 \ub370\uc774\ud130\uc5d0\uc11c \uc815\uc758\ub418\ub294 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc774 \ud544\uc694\ud558\ub2e4. W x H \ud06c\uae30\uc758 \uc774\ubbf8\uc9c0 f(x, y)\uc5d0 \ub300\ud55c \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658(discrete Fourier transform)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99FE293359BF6B7B28\" width=\"256\" height=\"56\">,&nbsp;&#8212;(7)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99B2BF3359BF6B610F\" width=\"307\" height=\"56\">.&nbsp;&#8212;(8)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e8, x = 0, 1, &#8230;, W-1, y = 0, 1, &#8230;, H-1\uc774\uace0 u = 0, 1, &#8230;, W-1, v = 0, 1, &#8230;, H-1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc2dd (7)\uc5d0\uc11c e<sup>j2\u03c0(ux\/W+vy\/H)<\/sup>\ub294&nbsp;x\ucd95 \ubc29\ud5a5\uc73c\ub85c \uc8fc\ud30c\uc218\uac00 u\/W, y\ucd95 \ubc29\ud5a5\uc73c\ub85c \uc8fc\ud30c\uc218\uac00 v\/H\uc778 sinusoidal \uc8fc\uae30\ud568\uc218\uc774\ub2e4 (by \uc624\uc77c\ub7ec \uacf5\uc2dd). \uc77c\ubc18\uc801\uc778 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc2dd\uacfc\ub294 \ub2ec\ub9ac&nbsp;W\uc640 H\ub85c\uc758 \ub098\ub204\uae30\uac00 \ub4e4\uc5b4\uc788\uc74c\uc5d0 \uc720\uc758\ud574\uc57c \ud558\uba70 \uc774\ub294 \ub370\uc774\ud130\uac00 \uc815\uc758\ub41c \uad6c\uac04\uc744 \ud558\ub098\uc758 \ub2e8\uc704 \uc8fc\uae30(unit period)\ub85c \ub9cc\ub4dc\ub294 \ud6a8\uacfc\uac00 \uc788\ub2e4. \uc77c\uc885\uc758 \uc815\uaddc\ud654 \ud329\ud130(normalization factor)\ub77c\uace0 \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5ec\uae30\uc11c 2D \uc774\ubbf8\uc9c0\ub97c \uc5b4\ub5bb\uac8c \uc2e0\ud638\ub85c \ud574\uc11d\ud560 \uc218 \uc788\ub294\uc9c0, \uadf8\ub9ac\uace0 2D \uc815\ud604\ud30c(sinusoidal wave) e<sup>j2\u03c0(ux\/W+vy\/H)<\/sup>\uac00 \ub3c4\ub300\uccb4 \uc5b4\ub5a4 \ubaa8\uc2b5\uc77c\uc9c0 \uc544\ub9c8\ub3c4 \uc758\uc544\ud574\ud560 \uc218 \uc788\ub2e4. \uccab\uc9f8, \uc774\ubbf8\uc9c0\ub97c \uc2e0\ud638\ub85c \ud574\uc11d\ud558\ub294 \ubb38\uc81c\ub294 x \ub610\ub294 y\ucd95\uc744 \uc2dc\uac04\ucd95\uc73c\ub85c \ub193\uace0 \uc88c\ud45c\uc758 \ubcc0\ud654\uc5d0 \ub530\ub77c \ubcc0\ud558\ub294 \uc774\ubbf8\uc9c0 \ud53d\uc140\uc758 \ubc1d\uae30 \ubcc0\ud654\ub97c \uc2e0\ud638\ub85c \uc0dd\uac01\ud558\uba74 \uc27d\uac8c \uc774\ud574\ud560 \uc218 \uc788\ub2e4. \ub2e4\uc74c\uc73c\ub85c, 2D\uc5d0\uc11c \uc815\uc758\ub418\ub294 \uc815\ud604\ud30c(sinusoidal wave)\uc758 \ubaa8\uc2b5\uc740 \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc774 \ubaa8\ub4e0 \ubc29\ud5a5\uc73c\ub85c\uc758 \ub2e8\uba74\uc774 sinusoidal\uc774 \ub418\ub294 \ubb3c\uacb0 \ud615\ud0dc\uc758 \ud30c\ub3d9\uc744 \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/9906EE3359BF835C18\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 2. 2D\uc5d0\uc11c\uc758 sinusoidal wave<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc55e\uc11c \uadf8\ub9bc 1\uc758 1D \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uacbd\uc6b0\uc640 \uc720\uc0ac\ud558\uac8c \uc0dd\uac01\ud574 \ubcf4\uba74, \uc774\ubbf8\uc9c0\uc5d0 \ub300\ud55c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc740 \uadf8\ub9bc 2\uc640 \uac19\uc740 \ud615\ud0dc\uc758 \ub2e4\uc591\ud55c&nbsp;2D \uc815\ud604\ud30c\ub4e4\uc758 \ud569\uc73c\ub85c \uc774\ubbf8\uc9c0\ub97c \ubd84\ud574\ud558\uc5ec \ud45c\ud604\ud558\ub294 \uac83\uc73c\ub85c \uc774\ud574\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\ubbf8\uc9c0\uc5d0 \ub300\ud55c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc5d0\uc11c \ud55c \uac00\uc9c0 \uc8fc\uc758\ud574\uc57c \ud560 \uac83\uc740 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uacc4\uc218 F(u, v)\uac00 e<sup>j2\u03c0(ux+vy)<\/sup>\uc758 \uacc4\uc218\uac00 \uc544\ub2c8\ub77c e<sup>j2\u03c0(ux\/W+vy\/H)<\/sup>\uc758 \uacc4\uc218\ub77c\ub294 \uc810\uc774\ub2e4. \uc989,&nbsp;\uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c F(u, v)\ub294 \uc8fc\ud30c\uc218 u, v \uc131\ubd84\uc774 \uc544\ub2c8\ub77c \uc8fc\ud30c\uc218 u\/W, v\/H \uc131\ubd84\uc5d0 \ub300\ud55c \uacc4\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">W \u00d7 H \uc774\ubbf8\uc9c0\uc5d0 \ub300\ud55c \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c F(u, v)\ub294<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; x\ucd95 \uc8fc\ud30c\uc218 u\/W, y\ucd95 \uc8fc\ud30c\uc218 v\/H\uc778 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc5d0 \ub300\uc751<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; \uc8fc\uae30\ub85c\ub294 x\ucd95 \ubc29\ud5a5 W\/u \ud53d\uc140, y\ucd95 \ubc29\ud5a5 H\/v \ud53d\uc140\uc778 \uc8fc\uae30\uc131\ubd84\uc744 \ub098\ud0c0\ub0c4 (\uc8fc\uae30 = 1\/\uc8fc\ud30c\uc218)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \ubc14\ub85c \uc774 \ubd80\ubd84\uc774 \uac1c\uc778\uc801\uc73c\ub85c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0 \ub300\ud574\uc11c \ud63c\ub3d9\uc2a4\ub7ec\uc6e0\ub358 \ubd80\ubd84 \uc911 \ud558\ub098\uc774\ub2e4. W x H \uc774\ubbf8\uc9c0\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c F(u, v)\ub294 \uc8fc\ud30c\uc218 u, v\uc758 \uc131\ubd84\uc774 \uc544\ub2c8\ub77c \uc8fc\ud30c\uc218 u\/W, v\/H \uc131\ubd84\uc774\ub2e4. \ub530\ub77c\uc11c, \uc8fc\ud30c\uc218 \uacf5\uac04\uc5d0\uc11c \ud2b9\uc815 F(u, v) \uac12\uc774 \ub192\uac8c \ub098\ud0c0\ub0ac\ub2e4\uba74 \uc6d0\ub798\uc758 \uc774\ubbf8\uc9c0 \uacf5\uac04\uc5d0\uc11c\ub294 x\ucd95 \ubc29\ud5a5\uc73c\ub85c \uc8fc\uae30\uac00 W\/u \ud53d\uc140, y\ucd95 \ubc29\ud5a5 \uc8fc\uae30\uac00 H\/v \ud53d\uc140\uc778 \uc8fc\uae30\uc131 \uc131\ubd84\uc774 \uc874\uc7ac\ud55c\ub2e4\ub294 \uc758\ubbf8\uac00 \ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ucc38\uace0\ub85c, 1\ucc28\uc6d0\uc5d0\uc11c\uc758 \ud568\uc218 f(x), x = 0, 1, 2, &#8230;, W-1\uc5d0 \ub300\ud55c \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658(discrete Fourier transform)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99C04C3359B87BDE17\" width=\"281\" height=\"56\">&nbsp;&#8212; (9)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99BDEE3359B87C061C\" width=\"323\" height=\"56\">&nbsp;&#8212; (10)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e 1\ucc28\uc6d0 \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658(discrete Fourier transform)\uc2dd\uc740 \uc2e4\uc81c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \ucef4\ud4e8\ud130\ub85c \uad6c\ud604\ud558\ub294\ub370 \uc788\uc5b4\uc11c \uac00\uc7a5 \uae30\ubcf8\uc774 \ub418\ub294 \uc2dd\uc774\ub2e4. \uc65c\ub0d0\ud558\uba74 \ud30c\ub3d9\uacfc \uac19\uc740 \uc5f0\uc18d \uc2e0\ud638\ub77c \ud560\uc9c0\ub77c\ub3c4 \uc2e4\uc81c \ubd84\uc11d\uc5d0 \uc788\uc5b4\uc11c\ub294 \uc0d8\ud50c\ub9c1\ub41c \uc774\uc0b0 \ub370\uc774\ud130\ub97c \uc774\uc6a9\ud574\uc57c \ud558\uace0 2\ucc28\uc6d0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0 \ub300\ud55c \uad6c\ud604\ub3c4 \ub0b4\ubd80\uc801\uc73c\ub85c\ub294 1\ucc28\uc6d0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \uc774\uc6a9\ud558\uc5ec \uad6c\ud604\ub418\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(spectrum)\uacfc \ud398\uc774\uc988(phase)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc81c \uc2e4\uc81c\ub85c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 \ud1b5\ud574 \uc5bb\uc5b4\uc9c0\ub294 F(u, v) \uac12\ub4e4\uc774 \uc5b4\ub5a4 \uc758\ubbf8\ub97c \uac00\uc9c0\uba70 \uc5b4\ub5a4 \ud615\ud0dc(visualization)\ub97c \uac16\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \ud1b5\ud574 \uc5bb\uc5b4\uc9c0\ub294 F(u, v)\ub294 \ubcf5\uc18c\uc218(complex number)\uc774\uba70 \uc2e4\uc218\ubd80(Real)\uc640 \ud5c8\uc218\ubd80(Imaginary)\ub85c \uad6c\uc131\ub41c\ub2e4 (1\ucc28\uc6d0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uacbd\uc6b0\ub3c4 \ub9c8\ucc2c\uac00\uc9c0\uc774\ub2e4).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/9942343359C0D24E30\" width=\"168\" height=\"21\">&nbsp;&#8212; (11)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774 \ub54c, \ubcf5\uc18c\uc218 F(u, v)\uc758 \ud06c\uae30 |F(u, v)|\ub97c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 spectrum(\uc2a4\ud399\ud2b8\ub7fc) \ub610\ub294 magnitude\ub77c\uace0 \ubd80\ub974\uace0, F(u, v)\uc758 \uac01\ub3c4 \u03a6\ub97c phase(\ud398\uc774\uc988) angle \ub610\ub294 phase spectrum\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99A76F3359C0D4870A\" width=\"228\" height=\"25\">&nbsp;&#8212; (12)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/997C8E3359C0D4E932\" width=\"195\" height=\"50\">&nbsp;&#8212; (13)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(Fourier spectrum)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uba3c\uc800, \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(Fourier spectrum)\uc5d0 \ub300\ud574 \uc0b4\ud3b4\ubcf4\uc790. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc740 \ud574\ub2f9 \uc8fc\ud30c\uc218 \uc131\ubd84\uc774 \uc6d0 \uc2e0\ud638(\uc774\ubbf8\uc9c0)\uc5d0 \uc5bc\ub9c8\ub098 \uac15\ud558\uac8c \ud3ec\ud568\ub418\uc5b4 \uc788\ub294\uc9c0\ub97c \ub098\ud0c0\ub0b8\ub2e4. W x H \uc774\ubbf8\uc9c0\ub97c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\ud558\uba74 \uc2dd (7), (8)\uc5d0 \uc758\ud574&nbsp;W x H\uc758 F(u, v), u = 0, &#8230;, W-1, v = 0, &#8230;, H-1 \uac00 \uc5bb\uc5b4\uc9c4\ub2e4. \ub530\ub77c\uc11c, |F(u, v)|\ub97c \ud53d\uc140\uac12\uc73c\ub85c \uc7a1\uc73c\uba74 \uc544\ub798 \uc608\uc640 \uac19\uc774 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc744 \uc6d0\ubcf8 \uc774\ubbf8\uc9c0\uc640 \ub3d9\uc77c\ud55c \ud06c\uae30\uc758 \uc774\ubbf8\uc9c0\ub85c \uc2dc\uac01\ud654\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/993C0C3359C8493E0D\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 3. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(spectrum)\uacfc \uc88c\ud45c\uacc4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a) \uc785\ub825 \uc774\ubbf8\uc9c0, (b) \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc, (c) shifted \uc2a4\ud399\ud2b8\ub7fc<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(Fourier spectrum)\uc744 \uc774\ubbf8\uc9c0\ub85c \uc2dc\uac01\ud654\ud558\ub294 \ub370\uc5d0\ub294 2\uac00\uc9c0 \ubb38\uc81c\uc810\uc774 \uc788\ub2e4. \uba3c\uc800, \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc740 \uc800\uc8fc\ud30c \uc601\uc5ed\uc740 \ub9e4\uc6b0 \ud070 \uac12\uc744 \uac16\ub294 \ubc18\uba74\uc5d0 \ub300\ubd80\ubd84\uc758 \ub2e4\ub978 \uc601\uc5ed\uc740 0\uc5d0 \uac00\uae4c\uc6b4 \uac12\uc744 \uac16\ub294\ub2e4. \ub530\ub77c\uc11c \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc744 \uadf8\ub300\ub85c \uc774\ubbf8\uc9c0\ub85c \uc2dc\uac01\ud654\ud558\uba74 \uac80\uc740 \ubc14\ud0d5 \uc704\uc5d0 \ud770\uc810 \ud558\ub098\ub9cc \uc874\uc7ac\ud558\ub294 \ud615\ud0dc\uac00 \ub41c\ub2e4. \uc774\ub7ec\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574\uc11c \uc2a4\ud399\ud2b8\ub7fc\uc744 \uc774\ubbf8\uc9c0\ub85c \ud45c\ud604\ud560 \ub54c\uc5d0\ub294 \uadf8\ub9bc 3(b)\ucc98\ub7fc \uc2a4\ud399\ud2b8\ub7fc\uc5d0 log\ub97c \ucde8\ud558\ub294 \uac83\uc774 \uc77c\ubc18\uc801\uc774\ub2e4. \ub2e4\uc74c\uc73c\ub85c, \uc6d0\ub798\uc758 \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub294 \uadf8\ub9bc 3(b)\ucc98\ub7fc \ubaa8\uc11c\ub9ac\ub85c \uac08\uc218\ub85d \uac12\uc774 \ub192\uc544\uc9c0\uae30 \ub54c\ubb38\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc758 \ud615\ud0dc\ub97c \ud30c\uc545\ud558\uae30 \ud798\ub4e4\ub2e4. \ub530\ub77c\uc11c \uc774\ub7ec\ud55c \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc704\ud574 \uadf8\ub9bc 3(c)\ucc98\ub7fc \uc6d0\uc810\uc774 \uc911\uc2ec(center)\uc5d0 \uc624\ub3c4\ub85d \uc2a4\ud399\ud2b8\ub7fc\uc758 \uc704\uce58\ub97c \uc774\ub3d9\uc2dc\ud0a8(shift) \ud615\ud0dc\uc758&nbsp;\uc774\ubbf8\uc9c0\ub97c \uc0ac\uc6a9\ud558\ub294 \uac83\uc774 \uc77c\ubc18\uc801\uc774\ub2e4 (\uc544\ub798 \u261e\uc124\uba85 \ucc38\uc870). \uc55e\uc73c\ub85c \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub77c \ud558\uba74 \uadf8\ub9bc 3(c)\uc640 \uac19\uc740 shifted \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub97c \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \uadf8\ub9bc 3(c)\uc640 \uac19\uc740 shift\uac00 \uac00\ub2a5\ud55c \uc774\uc720\ub294 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc774 \uc6d0\uc810\ub300\uce6d\uc778 \uc8fc\uae30\ud568\uc218\uc774\uae30 \ub54c\ubb38\uc774\ub2e4. \uc0ac\uc2e4 \uc2dd (9), (10)\ub85c \uc8fc\uc5b4\uc9c0\ub294&nbsp;\uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658(discrete Fourier transform)\uc2dd\uc740 f(x)\uac00 \uc8fc\uae30\ud568\uc218\uc77c \ub54c\uc5d0\ub9cc \uc131\ub9bd\ud558\ub294 \uc2dd\uc774\ub2e4. \uc6d0\ub798\uc758 \uc785\ub825\uc2e0\ud638 f(x)\ub294 x = 0, 1, &#8230;, W-1\uc758 \uc720\ud55c \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub41c \ud568\uc218\uc774\ub2e4. \uc6b0\ub9ac\uac00 \uad00\uc2ec\uc788\ub294 \ubd80\ubd84\uc740 0 ~ W-1 \uad6c\uac04\uc5d0\uc11c\uc758 \ud2b9\uc131\uc774\ubbc0\ub85c \uadf8 \uc678\uc758 \uad6c\uac04\uc5d0 \ub300\ud574\uc11c\ub294 \ud568\uc218\ub97c \uc5b4\ub5bb\uac8c \uc815\uc758\ud574\ub3c4 \ubb34\ubc29\ud558\ub2e4. \ub530\ub77c\uc11c, \ud478\ub9ac\uc5d0 \ubcc0\ud658 \uc801\uc6a9\uc744 \uc704\ud574 \uc774 \ud568\uc218\ub97c \ud655\uc7a5\ud558\uc5ec f(x + W) = f(x)\uc778 \uc8fc\uae30\ud568\uc218(0 ~ W-1\uc5d0\uc11c\uc758 \ud568\uc218\uac12\uc774 \ub2e4\ub978 \uad6c\uac04\uc5d0\uc11c\ub3c4 \uacc4\uc18d \ubc18\ubcf5)\ub85c \uac00\uc815\ud558\uace0 \uc2dd\uc744 \uc138\uc6b4 \uac83\uc774 \uc2dd (9), (10)\uc774\ub2e4. \uc774 \ub54c, [latex]F(u)[\/latex] \ub610\ud55c f(x)\uc640 \ub3d9\uc77c\ud55c \uc8fc\uae30(W)\uc758 \uc8fc\uae30\ud568\uc218\uac00 \ub41c\ub2e4. \uc989. F(u) = F(u + W). \ub610\ud55c \uc2dd (10)\uc5d0\uc11c |F(u)| = |F(-u)|\uc784\ub3c4 \uc27d\uac8c \uc54c \uc218 \uc788\ub2e4. \uc989, \uc774\uc0b0 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc740 \uc6d0\uc810\ub300\uce6d\uc774\uba74\uc11c W\ub97c \uc8fc\uae30\ub85c \ud558\ub294 \uc8fc\uae30\ud568\uc218 \ud615\ud0dc\uc784\uc744 \uc54c \uc218 \uc788\ub2e4. 2\ucc28\uc6d0\uc758 \uacbd\uc6b0\ub3c4 \ub9c8\ucc2c\uac00\uc9c0\uc774\uba70 F(u, v) = F(u + W, v) = F(u, v+ H) = F(u + W, v + h), |F(u, v)| = |F(-u, -v)|\uc778 \uc8fc\uae30\ud568\uc218\uac00 \ub41c\ub2e4. \uadf8\ub9ac\uace0 \uc774\ub7ec\ud55c \uc6d0\uc810 \ub300\uce6d\uc131\uacfc \uc8fc\uae30\uc131\uc73c\ub85c \uc778\ud574 \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub97c \uadf8\ub9bc 3(c)\uc640 \uac19\uc774 shift\ud558\uc5ec \ud45c\ud604\ud558\ub294 \uac83\uc774 \uac00\ub2a5\ud574\uc9c4\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">shifted \uc2a4\ud399\ud2b8\ub7fc\uc744 \uc774\ud574\ud558\uae30 \uc704\ud574 \ud55c \uc608\ub85c \uc544\ub798 \uadf8\ub9bc 4\uc758 \uc67c\ucabd\uacfc \uac19\uc740 \ud615\ud0dc\uc758 \uc2a4\ud399\ud2b8\ub7fc \uc2e0\ud638\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790. \uadf8\ub7f0\ub370 \ub9cc\uc77c \uc2a4\ud399\ud2b8\ub7fc\uc774 \uc6d0\uc810\ub300\uce6d\uc774\uace0 W\ub97c \uc8fc\uae30\ub85c \ubc18\ubcf5\ub41c\ub2e4\uba74 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc740 \uc624\ub978\ucabd\uacfc \uac19\uc740 \ud615\ud0dc\uac00 \ub420 \uc218\ubc16\uc5d0 \uc5c6\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4. \uc6d0\ub798\uc758 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc758 \ud615\ud0dc\ub294&nbsp;\uad6c\uac04 0 ~ W\uc758 \ud615\ud0dc(\uadf8\ub9bc 3b)\uc774\uc9c0\ub9cc (\uc5b4\ucc28\ud53c \uc815\ubcf4\uac00 \ubc18\ubcf5\ub418\uae30 \ub54c\ubb38\uc5d0) \uc774\ub97c \uad6c\uac04 -W\/2 ~ W\/2 \ud615\ud0dc(\uadf8\ub9bc 3c)\ub85c shift\ud558\uc5ec \ud45c\ud604\ud55c \uac83\uc774 shifted \uc2a4\ud399\ud2b8\ub7fc\uc774\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/9930183359C85EB809\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 4. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc758 \uc8fc\uae30 \ud2b9\uc9d5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc758 \ud574\uc11d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc55e\uc11c \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(Fourier spectrum)\uc740 \ud574\ub2f9\ub418\ub294 \uc8fc\ud30c\uc218 \uc131\ubd84\uc758 \uac15\ub3c4\ub97c \ub098\ud0c0\ub09c\ub2e4\uace0 \ud588\ub294\ub370, \uc815\ub9d0 \uadf8\ub7f0\uc9c0 \uadf8\ub9ac\uace0 \uc774 \uac12\uc774 \uc774\ubbf8\uc9c0 \ub3c4\uba54\uc778\uc5d0\uc11c \uc5b4\ub5bb\uac8c \ud574\uc11d\ub420 \uc218 \uc788\ub294\uc9c0 \uc2e4\uc81c&nbsp;\uc608\ub97c \ud1b5\ud574\uc11c \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc544\ub798 \uc608\ub294 \uc774\ubbf8\uc9c0\uc5d0 \uc778\uc704\uc801\uc73c\ub85c \uc8fc\uae30\uc131\ubd84\uc744 \ucd94\uac00\ud558\uc600\uc744 \ub54c \uc8fc\ud30c\uc218 \uacf5\uac04\uc5d0\uc11c\uc758 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc774 \uc5b4\ub5bb\uac8c \ubcc0\ud558\ub294\uc9c0\ub97c \ubcf4\uc5ec\uc900\ub2e4. \uc6d0\ubcf8 \uc774\ubbf8\uc9c0\uc758 \ud574\uc0c1\ub3c4\ub294 205&nbsp;\u00d7 205 \ud53d\uc140\uc774\uba70(W = 205, H = 205) \ub530\ub77c\uc11c \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub3c4 205 x 205 \ud574\uc0c1\ub3c4\ub97c \uac16\ub294\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99F19E3359C8A2EB0D\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 5. \uc8fc\uae30\uc131\ubd84 \ucd94\uac00\uc5d0 \ub530\ub978 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc758 \ubcc0\ud654<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uba3c\uc800, \uadf8\ub9bc 5(a)\ub294 \uc6d0\ubcf8 \uc774\ubbf8\uc9c0 \ubc0f \ub300\uc751\ub418\ub294 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub97c \ubcf4\uc5ec\uc900\ub2e4. \uadf8\ub9bc\uc758 \uc608\uc640 \uac19\uc774 \uc77c\ubc18\uc801\uc778 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc \uc774\ubbf8\uc9c0\ub294 \uc6d0\uc810 F(0, 0) \uc8fc\ubcc0\uc758 \uc800\uc8fc\ud30c \uc601\uc5ed\uc5d0\uc11c \uac15\ud55c \ud53c\ud06c(peak)\uac00 \ub098\ud0c0\ub098\uace0 \uc6d0\uc810\uc5d0\uc11c \uba40\uc5b4\uc9c8\uc218\ub85d \uc989, \uace0\uc8fc\ud30c \uc601\uc5ed\uc73c\ub85c \uac08\uc218\ub85d \uac12\uc774 \uae09\uaca9\ud788 \uc791\uc544\uc9c0\ub294 \ud615\ud0dc\ub97c \uac16\ub294\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 5(b)\ub294 (a)\uc758 \uc774\ubbf8\uc9c0\uc5d0 5 \ud53d\uc140(pixel)&nbsp;\uac04\uaca9\uc758 \uc218\ud3c9\uc120\uc744 \uc778\uc704\uc801\uc73c\ub85c \ucd94\uac00\ud55c \uacbd\uc6b0\uc774\ub2e4. \uadf8\ub7ec\uba74 \uc8fc\ud30c\uc218 \uacf5\uac04\uc5d0\uc11c\ub294 \uadf8\ub9bc\uacfc \uac19\uc774 F(0, 41), F(0,82)\uc5d0 \uac15\ud55c \ud53c\ud06c(peak)\uac00 \ub098\ud0c0\ub09c\ub2e4. \uc55e\uc11c \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c F(u, v)\ub294 x\ucd95 \uc8fc\uae30&nbsp;W\/u \ud53d\uc140, y\ucd95 \uc8fc\uae30&nbsp;H\/v \ud53d\uc140\uc778 \uc8fc\uae30\uc131\ubd84\uc758 \uacc4\uc218\ub77c \ud588\ub2e4. \uadf8\ub7ec\uba74, F(0, 41)\uc740 \uc8fc\uae30\uac00 x\ucd95 \ubc29\ud5a5 205\/0 =&nbsp;\u221e, y\ucd95 \ubc29\ud5a5 205\/41 = 5 \ud53d\uc140\uc778 \uc8fc\uae30\uc131\ubd84\uc5d0 \ub300\uc751\ub41c\ub2e4. \uadf8\ub9ac\uace0 \uc774\uac83\uc740 \uadf8\ub9bc 5(b)\ub97c \ub9cc\ub4e4 \ub54c \uc0ac\uc6a9\ud55c \uc218\ud3c9\uc120\uc758 \uc8fc\uae30(\uc138\ub85c\ubc29\ud5a5 5\ud53d\uc140)\uc640 \uc815\ud655\ud788 \uc77c\uce58\ud55c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e F(0, 82)\uc5d0\ub3c4 \ud53c\ud06c(peak)\uac00 \ub098\ud0c0\ub098\ub294 \uac83\uc740 y\ucd95 \ubc29\ud5a5\uc73c\ub85c 205\/82 = 2.5 \ud53d\uc140 \uac04\uaca9\uc758 \uc8fc\uae30 \uc131\ubd84\uc774 \uc785\ub825 \uc774\ubbf8\uc9c0\uc5d0 \uc788\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4. \uc774\ub294 \uc774\ubbf8\uc9c0\uc5d0 \ucd94\uac00\ud55c \uc218\ud3c9\uc120\uc774 \uc815\ud604\ud30c(sinusoidal wave)\uac00 \uc544\ub2c8\ub77c \uacc4\ub2e8 \ud615\ud0dc\uc774\uae30 \ub54c\ubb38\uc5d0 5 \ud53d\uc140 \uc8fc\uae30\uc758 \uc815\ud604\ud30c\uc640 2.5 \ud53d\uc140 \uc8fc\uae30\uc758 \uc815\ud604\ud30c\ub97c \ud569\uccd0\uc11c \uadf8\ub7ec\ud55c \uacc4\ub2e8 \ud615\ud0dc\ub97c \uadfc\uc0ac\ud588\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e4\uc74c\uc73c\ub85c, \uc774\ubc88\uc5d0\ub294 \uadf8\ub9bc 5(c)\uc640 \uac19\uc774 \ub300\uac01\uc120 \ubc29\ud5a5\uc758 \uc815\ud604\ud30c\ub97c (a)\uc758 \uc774\ubbf8\uc9c0\uc5d0 \ucd94\uac00\ud574 \ubcf4\uc790. \ucd94\uac00\ud55c \uc815\ud604\ud30c\ub294 x\ucd95 \ubc29\ud5a5 \uc8fc\uae30 20 pixel, y\ucd95 \ubc29\ud5a5 \uc8fc\uae30 10 \ud53d\uc140\uc778 2D sin \ud568\uc218\ub97c \uc774\uc6a9\ud588\ub2e4. \uc774 \ub54c, \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc5d0\ub294 F(10, 20.5)\uc5d0 \uac15\ud55c \ud53c\ud06c(peak)\uac00 \uc0dd\uc131\ub428\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4. \uc989, x\ucd95 \ubc29\ud5a5\uc73c\ub85c\ub294 W\/u = 205\/10 = 20.5 \ud53d\uc140, y\ucd95 \ubc29\ud5a5\uc73c\ub85c\ub294 H\/v = 205\/20.5 = 10 \ud53d\uc140\uc758 \uc8fc\uae30 \uc131\ubd84\uc774 \uc785\ub825 \uc774\ubbf8\uc9c0\uc5d0 \uc788\uc74c\uc744 \uc758\ubbf8\ud55c\ub2e4. \uadf8\ub9ac\uace0 \uc774\ub294 \uc2e4\uc81c \uc785\ub825 \uc774\ubbf8\uc9c0\uc5d0 \ucd94\uac00\ub41c \uc8fc\uae30 \uc131\ubd84\uacfc \uc815\ud655\ud788 \uc77c\uce58\ud55c\ub2e4 (\uc18c\uc218\uc810 \uc624\ucc28\ub294 u, v\uc88c\ud45c\ub97c \uc815\uc218\ub85c \ud45c\ud604\ud568\uc5d0 \uc758\ud55c \uac83\uc774\ub2e4).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc0c1\uc73c\ub85c \uc8fc\ud30c\uc218 \uacf5\uac04\uc5d0\uc11c\uc758 F(u, v)\uac00 \uc785\ub825 \uc774\ubbf8\uc9c0 \uacf5\uac04\uc5d0\uc11c \uc5b4\ub5bb\uac8c \uc5f0\uad00\ub418\uc5b4 \ud574\uc11d\ub420 \uc218 \uc788\ub294\uc9c0\ub97c \uc2e4\uc81c \uc608\ub97c \ud1b5\ud574\uc11c \uc0b4\ud3b4\ubcf4\uc558\ub2e4. \ub9c8\uc9c0\ub9c9\uc73c\ub85c \uc55e\uc11c \uadf8\ub9bc 5(b), (c)\uc5d0\uc11c \uc2a4\ud399\ud2b8\ub7fc\uc758 \ud53c\ud06c(peak) \uc601\uc5ed\uc744 \uc9c0\uc6b4 \ud6c4 \ud478\ub9ac\uc5d0 \uc5ed\ubcc0\ud658(inverse Fourier transform)\ud558\uba74 \uc544\ub798\uc640 \uac19\uc740 \uc7ac\ubbf8\uc788\ub294 \uacb0\uacfc\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4 (\uc9c0\uc6b4\ub2e4\ub294 \uc758\ubbf8\ub294 \ud574\ub2f9\ub418\ub294 F(u, v) \uac12\ub4e4\uc744 0\uc73c\ub85c \ub9cc\ub4e0\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/991D913359C89CBB1C\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 6. \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \uc774\uc6a9\ud55c \uc8fc\uae30 \uc131\ubd84 \uc81c\uac70<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e&nbsp;<a href=\"http:\/\/darkpgmr.tistory.com\/14\" target=\"_blank\" rel=\"noreferrer noopener\">[\uac1c\ubc1c\ud55c \uac83\ub4e4] &#8211; FFT\uc640 \ubaa8\uc544\ub808 \uc81c\uac70 \ud504\ub85c\uadf8\ub7a8<\/a>\uc744 \uc774\uc6a9\ud558\uba74 \uc774\ubbf8\uc9c0\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658, \ud2b9\uc815 \uc2a4\ud399\ud2b8\ub7fc \uc0ad\uc81c \ubc0f \uc5ed\ubcc0\ud658\uc744 \uc9c1\uc811 \ud14c\uc2a4\ud2b8\ud574 \ubcfc \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758&nbsp;<strong>\ud398\uc774\uc988(phase)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc5d0\uc11c \uc2a4\ud399\ud2b8\ub7fc(spectrum)\uc740 \uc798 \uc54c\ub824\uc9c4 \ubc18\uba74 \ud398\uc774\uc988(phase)\ub294 \uc0c1\ub300\uc801\uc73c\ub85c \uc798 \uc54c\ub824\uc838 \uc788\uc9c0 \uc54a\ub2e4. \ud558\uc9c0\ub9cc \ud398\uc774\uc988(phase)\uc5d0\ub3c4 \uc2a4\ud399\ud2b8\ub7fc(spectrum) \ubabb\uc9c0 \uc54a\uc740 \uc911\uc694\ud55c \uc815\ubcf4\uac00 \ub2f4\uaca8 \uc788\ub2e4\uace0 \ud55c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud398\uc774\uc988(phase)\ub97c \uc6b0\ub9ac\ub9d0\ub85c \ubc88\uc5ed\ud558\uba74 &#8216;\ub2e8\uacc4&#8217;\uac00 \ub418\uace0 \uc804\ubb38\uc6a9\uc5b4\ub85c\ub294 &#8216;\uc704\uc0c1&#8217;\uc774 \ub41c\ub2e4. \uc704\ud0a4\ud53c\ub514\uc544\uc5d0\ub294\ud398\uc774\uc988(phase, \uc704\uc0c1)\ub97c &#8216;\ubc18\ubcf5\ub418\ub294 \ud30c\ud615\uc758 \ud55c \uc8fc\uae30\uc5d0\uc11c \uccab \uc2dc\uc791\uc810\uc758 \uac01\ub3c4 \ud639\uc740 \uc5b4\ub290 \ud55c \uc21c\uac04\uc758 \uc704\uce58&#8217;\ub77c\uace0 \uc815\uc758\ud55c\ub2e4. \uc989, \ud30c\ud615(wave)\uc758 \uc2dc\uc810\uc774 \uc5b4\ub514\uc778\uc9c0\uac00 \ud398\uc774\uc988(phase)\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, sin \ud30c\uc640 cos \ud30c\ub294&nbsp;90\ub3c4\uc758 \ud398\uc774\uc988(phase, \uc704\uc0c1) \ucc28\uc774\uac00 \uc874\uc7ac\ud558\ub294 \ub3d9\uc77c\ud55c \ud30c\ud615\uc73c\ub85c \ubcfc \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uad00\uc810\uc5d0\uc11c \ubcf4\uba74&nbsp;\ud398\uc774\uc988(phase)\ub294 \uc6d0\ubcf8 \uc2e0\ud638\ub97c \uc8fc\uae30 \uc2e0\ud638\ub85c \ubd84\ud574\ud588\uc744 \ub54c \uac01 \uc8fc\uae30\uc131\ubd84\uc758 \uc2dc\uc810\uc774 \uc5b4\ub518\uc778\uc9c0(\uc989, \uac01 \uc8fc\uae30\uc131\ubd84\ub4e4\uc774&nbsp;\uc5b4\ub5bb\uac8c \uc904\uc744 \ub9de\ucdb0\uc11c \uc6d0\ubcf8 \uc2e0\ud638\ub97c \uc0dd\uc131\ud588\ub294\uc9c0)\ub97c \ub098\ud0c0\ub0b4\ub294 \uc694\uc18c\uac00 \ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc544\ub798 \uadf8\ub9bc\uc740 \ud398\uc774\uc988(phase)\uc758 \uc601\ud5a5\uc744 \ubcf4\uc5ec\uc8fc\ub294 \uc608\ub85c\uc11c \ud30c\ub780\uc0c9 \uc8fc\uae30\uc131\ubd84 \uc2e0\ud638\ub4e4\uc744 \ud569\uccd0\uc11c \ube68\uac04\uc0c9 \uc2e0\ud638\uac00 \uc0dd\uc131\ub418\ub294 \uc608\ub97c \ubcf4\uc5ec\uc900\ub2e4. \uc67c\ucabd, \uc624\ub978\ucabd \uacbd\uc6b0 \ubaa8\ub450 \ub3d9\uc77c\ud55c \uc8fc\ud30c\uc218\uc758 \uc8fc\uae30\uc131\ubd84\ub4e4\uc744 \ud569\ucce4\uc9c0\ub9cc \uac01 \uc131\ubd84\uc758 \ud398\uc774\uc988(phase) \ucc28\uc774\ub85c \uc778\ud558\uc5ec \uc804\ud600 \ub2e4\ub978 \uc2e0\ud638\uac00 \uc0dd\uc131\ub428\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99987F3359C8B75D15\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 7. \ud398\uc774\uc988(phase) \ucc28\uc774\uc5d0 \ub530\ub978 \uc2e0\ud638 \uc0dd\uc131\uc758 \ucc28\uc774<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e4\uc74c\uc73c\ub85c \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \ud398\uc774\uc988(phase)\uac00 \uc5b4\ub5bb\uac8c \uc218\uc2dd\uc73c\ub85c \ud45c\ud604\ub418\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uc790. (1\ucc28\uc6d0) \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uacc4\uc218 [latex]F(u)[\/latex]\ub294 \uc2dd (12), (13) \ubc0f \uc624\uc77c\ub7ec \uacf5\uc2dd\uc5d0 \uc758\ud574 \ub2e4\uc74c\uacfc \uac19\uc774 \uadf9\uc88c\ud45c(polar coordinate) \ud615\ud0dc\ub85c \ud45c\ud604\ub420 \uc218 \uc788\ub2e4 (\uc124\uba85\uc758 \ud3b8\uc758\uc0c1 1\ucc28\uc6d0\uc758 \uacbd\uc6b0\ub97c \uc608\ub85c \ub4e0\ub2e4).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/992DA83359C992C005\" width=\"220\" height=\"23\">&nbsp;&#8212; (14)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u261e \uc2e4\uc218\ucd95\uc774 x\ucd95, \ud5c8\uc218\ucd95\uc774 y\ucd95\uc778 \ubcf5\uc18c\ud3c9\uba74\uc5d0\uc11c [latex]F(u)[\/latex]\ub294 x\ucd95\uacfc \uc774\ub8e8\ub294 \uac01\uc774 \u03a6\uc778 \ub9c9\ub300\uae30\uc758 \ub05d\uc810 (R, I)\uc5d0 \ub300\uc751\ub41c\ub2e4. \uc774 \ub54c, R = |F|cos\u03a6, I = |F|sin\u03a6\uc774\ubbc0\ub85c F = |F|cos\u03a6 + j|F|sin\u03a6 = |F|e<sup>j\u03a6<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc81c \uc2dd (14)\ub97c \uc2dd (1)\uc5d0 \ub300\uc785\ud558\uba74,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99E97E3359C998A815\" width=\"188\" height=\"117\">. &#8212; (15)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc640 \uac19\uc774 \ud398\uc774\uc988(phase) \ud140\uc774 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc758 \uc2dc\uc810\uc744 \uc870\uc808\ud558\ub294 \ud140\uc774 \ub41c\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc989, \ud478\ub9ac\uc5d0 \uacc4\uc218 [latex]F(u)[\/latex]\uc5d0\ub294 \ub300\uc751\ub418\ub294 \uc8fc\uae30\ud568\uc218 \uc131\ubd84\uc758 \uac15\ub3c4(amplitude)\ub97c \ub098\ud0c0\ub0b4\ub294&nbsp;\uc2a4\ud399\ud2b8\ub7fc \uc815\ubcf4&nbsp;|F(u)|\uc640 \uc2dc\uc810\uc744 \uc870\uc808\ud558\ub294 \ud398\uc774\uc988(phase) \uc815\ubcf4&nbsp;\u03a6(u)\uac00 \ud568\uaed8 \ud3ec\ud568\ub418\uc5b4 \uc788\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ucc38\uace0\ub85c, \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc(spectrum)\uacfc \ud398\uc774\uc988(phase)\uc5d0 \uad00\ud55c \uc7ac\ubbf8\uc788\ub294 \ube44\uad50 \uacb0\uacfc\ub97c \ud558\ub098 \uc18c\uac1c\ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc 8\uc5d0\uc11c (a)\ub294 \uc6d0\ubcf8 \uc774\ubbf8\uc9c0, (b)\ub294 \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uc744 \ubcf4\uc874\ud558\uace0 \ud398\uc774\uc988(phase)\ub97c \ub79c\ub364(random)\ud558\uac8c \ud588\uc744 \ub54c\uc758 \uc5ed\ubcc0\ud658 \uacb0\uacfc, (c)\ub294 \ud398\uc774\uc988(phase)\ub97c \ubcf4\uc874\ud558\uace0 \uc2a4\ud399\ud2b8\ub7fc\uc744 \ub79c\ub364\ud558\uac8c \ud588\uc744 \ub54c\uc758 \uc5ed\ubcc0\ud658 \uacb0\uacfc\uc774\ub2e4. \uacb0\uacfc\ub97c \ubcf4\uba74 \uc774\ubbf8\uc9c0\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c \uc2a4\ud399\ud2b8\ub7fc(spectrum)\ubcf4\ub2e4 \ud398\uc774\uc988(phase)\uc5d0 \ubcf4\ub2e4 \ub354 \uc911\uc694\ud55c \uc815\ubcf4\uac00 \ud3ec\ud568\ub418\uc5b4 \uc788\uc74c\uc744 \ud655\uc778\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99B75F3359CB147629\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc 8. \ud478\ub9ac\uc5d0 \uc2a4\ud399\ud2b8\ub7fc\uacfc \ud398\uc774\uc988\uc758 \uc911\uc694\ub3c4 \ube44\uad50<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uc720\uc6a9\ud55c \uc131\uc9c8\ub4e4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc5d0 \ub300\ud55c \uba87 \uac00\uc9c0 \uc720\uc6a9\ud55c \uc131\uc9c8\ub4e4\uc744 \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; \uc8fc\ud30c\uc218 \uacf5\uac04\uc758 \uc6d0\uc810 F(0, 0)\uc758 \uac12\uc740 \uc774\ubbf8\uc9c0\uc758 \ud3c9\uade0\uac12\uacfc \uc77c\uce58<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/996B493359CB18022D\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; Impulse \ud568\uc218(<a href=\"https:\/\/en.wikipedia.org\/wiki\/Dirac_delta_function\" target=\"_blank\" rel=\"noreferrer noopener\">Dirac delta \ud568\uc218<\/a>)\uc5d0 \ub300\ud55c \ud478\ub9ac\uc5d0 \ubcc0\ud658\/\uc5ed\ubcc0\ud658\uc740 \uc720\ub2c8\ud3fc(uniform) \ud568\uc218 (\uc544\ub798 \uc2dd\uc5d0\uc11c \ud478\ub9ac\uc5d0 \ubcc0\ud658\/\uc5ed\ubcc0\ud658 \uad00\uacc4\ub97c&nbsp;\u21d4 \ub85c \ud45c\uae30).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99C11D3359CB196237\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211; \uac00\uc6b0\uc2dc\uc5b8(Gaussian) \ud568\uc218\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658\/\uc5ed\ubcc0\ud658\uc740 \uac00\uc6b0\uc2dc\uc5b8 \ud568\uc218\uac00 \ub428<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/t1.daumcdn.net\/cfile\/tistory\/99C4923359CB1ACE0E\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>6. \ub9fa\uc74c\ub9d0<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc0c1\uc73c\ub85c \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc5d0 \ub300\ud55c \uc815\ub9ac\ub97c \ub9c8\uce69\ub2c8\ub2e4. \uc6d0\ub798\ub294 \uc774\ub807\uac8c\uae4c\uc9c0 \uae38\uac8c \uc4f8 \uc0dd\uac01\uc740 \uc544\ub2c8\uc5c6\ub294\ub370 \uc4f0\ub2e4 \ubcf4\ub2c8 \uae00\uc774 \uae38\uc5b4\uc84c\ub124\uc694.. ^^<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\ucc38\uace0\uc790\ub8cc \ubc0f \uc720\uc6a9\ud55c \uad00\ub828 \uae00 \ub9c1\ud06c<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/www.incodom.kr\/%ED%91%B8%EB%A6%AC%EC%97%90_%EB%B3%80%ED%99%98\" target=\"_blank\" rel=\"noreferrer noopener\">\ud478\ub9ac\uc5d0 \ubcc0\ud658<\/a>&nbsp;by jipark<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/ghebook.blogspot.kr\/2012\/07\/fourier-series.html\" target=\"_blank\" rel=\"noreferrer noopener\">\ud478\ub9ac\uc5d0 \uae09\uc218\uc758 \uc2dc\uc791<\/a>&nbsp;by \uc804\ud30c\uac70\ubd81\uc774<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/ghebook.blogspot.kr\/2012\/08\/fourier-transform.html\" target=\"_blank\" rel=\"noreferrer noopener\">\ud478\ub9ac\uc5d0 \ubcc0\ud658<\/a>&nbsp;by \uc804\ud30c\uac70\ubd81\uc774<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/wikidocs.net\/4175\" target=\"_blank\" rel=\"noreferrer noopener\">\ud398\uc774\uc800(phasor)<\/a>&nbsp;by AngeloYeo<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/wikidocs.net\/4030\" target=\"_blank\" rel=\"noreferrer noopener\">\ud5c8\uc218\uc758 \uc874\uc7ac \uc758\ubbf8\uc5d0 \ub300\ud558\uc5ec<\/a>&nbsp;by AngeloYeo<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/www.comm.utoronto.ca\/~dkundur\/course_info\/signals\/notes\/Kundur_FourierMagPhase.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Magnitude and Phase<\/a>&nbsp;by Deepa Kundur (\ud1a0\ub860\ud1a0 \ub300\ud559)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.researchgate.net\/post\/What_information_is_contained_in_the_phase_spectrum_of_a_signal2\" target=\"_blank\" rel=\"noreferrer noopener\">What information is contained in the phase spectrum of a signal?<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>FFT<\/strong>\uc758 \uac04\ub2e8\ud55c \uc815\uc758<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Continuous Fourier Transform\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$X(f) = \\int^\\infty_{-\\infty}{x(t)e^{-i2\\pi ft} dt}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub807\uc9c0\ub9cc \ub514\uc9c0\ud138 \uac1c\ub150\uc73c\ub85c \ubc14\ub00c\uac8c \ub418\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \uc815\uc758\ub97c \ud560 \uc218\uac00 \uc788\uac8c \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$X(m) = \\sum^{N-1}_{n=0} x(n)e^{-j\\pi nm\/N}$$<br>$$X(m) = \\sum^{N-1}_{n=0} x(n)[\\cos(2\\pi nm\/N-j\\sin(2\\pi nm\/N]$$<\/p>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">\uc5ec\uae30\uc11c \uac01\uac01\uc758 \uc6a9\uc5b4\ub4e4\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Sampling frequency (rate) : [latex]f_s[\/latex]<br>Analysis frequency : [latex]\\frac{mf_s}{N}[\/latex]<br>Nyquist frequency : [latex]2\\times f_{max}[\/latex]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc608\ub97c \ub4e4\uc5b4\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.\ub2e4\uc74c\uacfc \uac19\uc740 \uc2e0\ud638\uac00 \uc788\ub2e4\uac00 \ud569\uc2dc\ub2e4. \ub9cc\uc57d\uc5d0 &nbsp;N=8,&nbsp;fs=8000&nbsp;samples\/s&nbsp;\ub77c\uace0 \ud55c\ub2e4\uba74&nbsp;<br>Analysis Frequency\ub294&nbsp;m*fs\/N = 1000*m&nbsp;\uc774 \ub429\ub2c8\ub2e4.<br>\uacb0\uad6d&nbsp;index\uc5d0 1000 \uc744 \uacf1\ud55c \uac12\uc774 \ub418\ub294 \uac81\ub2c8\ub2e4.<br><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles3.naver.net\/data6\/2005\/4\/5\/242\/Snap4-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub7fc \uc774 \uc0c1\ud0dc\uc5d0\uc11c&nbsp;<strong>FFT<\/strong>\ub97c \uc218\ud589\ud558\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles15.naver.net\/data5\/2005\/4\/5\/174\/Snap14-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">X(1)\uacfc&nbsp;X(2)\ub294 \uac01\uac01 1kHz\uc640 2kHz\uc774\ubbc0\ub85c \uac12\uc774 \ub098\uc640\uc57c \ud569\ub2c8\ub2e4. \uadf8\ub7f0\ub370&nbsp;X(6)\uacfc&nbsp;X(7)\uc5d0\uc11c\ub3c4 \uc131\ubd84\uc774\ub728\ub294 \uac83\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4. \ubb54\uac00 \uc774\uc0c1\ud558\ub2e4\uac00 \uc0dd\uac01\ud560 \uc218\ub3c4 \uc788\uc9c0\ub9cc&nbsp;<strong>FFT<\/strong>\uac00&nbsp;N\/2 \uc9c0\uc810\uc744 \uae30\uc900\uc73c\ub85c \ub300\uce6d\uc774\ub77c\ub294 \uac83\ub9cc \uc544\uc2e0\ub2e4\uba74 \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uacb0\uacfc\ub77c\ub294 \uac83\uc744 \uc54c \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles10.naver.net\/data6\/2005\/4\/5\/25\/Snap15-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub7f0\ub370 \uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c\ub3c4 \ubcf4\uc5ec\uc9c0\ub4ef\uc774 \uc6d0\ub798\ub294 1\uacfc 0.5\uc758 \ud06c\uae30\uac00 \ub5a0\uc57c \ud560\uac83\uc774 4\uc640 2\uc758 \ud06c\uae30\ub85c \uc0dd\uacbc\uc74c\uc744 \uc54c \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\uac83\uc740&nbsp;<strong>FFT<\/strong>\uac00 \uc6d0\ub798 \ud06c\uae30\uc5d0&nbsp;N\/2\ub97c \uacf1\ud55c \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc790, \uc774\ucbe4\uc5d0\uc11c&nbsp;<strong>Matlab\u2122<\/strong>\uc744 \uc774\uc6a9\ud574&nbsp;<strong>FFT<\/strong>\ub97c \uc9c1\uc811 \uad6c\ud604\ud574 \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<strong>Matlab Coding<\/strong><strong><\/strong>&nbsp;N=8;fs=8000;ts=1\/fs;for&nbsp;n=1:1:N&nbsp;x(n)=sin(2*pi*1000*(n-1)*ts)+0.5*sin(2*pi*2000*(n-1)*ts+3*pi\/4);endfor&nbsp;m=1:1:N&nbsp;temp=0;&nbsp;X=0;&nbsp;for&nbsp;n=1:1:N&nbsp;X=x(n)*(cos(2*pi*(n-1)*(m-1)\/N)-j*sin(2*pi*(n-1)*(m-1)\/N));&nbsp;X=X+temp;&nbsp;temp=X;&nbsp;endXX(m)=X;endm=0:1:N-1;subplot(2,2,1)stem(m,abs(XX));subplot(2,2,2)stem(m,phase(XX)*180\/pi);<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Matlab Internal function(fft)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N=8;fs=8000;ts=1\/fs;for&nbsp;n=1:1:N&nbsp;x(n)=sin(2*pi*1000*(n-1)*ts)+0.5*sin(2*pi*2000*(n-1)*ts+3*pi\/4);endXX=fft(x);&nbsp;&nbsp;&nbsp;&nbsp;%% or, XX=fft(x,N);m=0:1:N-1;subplot(2,2,3)stem(m,abs(XX));subplot(2,2,4)stem(m,phase(XX)*180\/pi);&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles10.naver.net\/data6\/2005\/4\/5\/201\/Snap7-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc704\uc5d0\uc11c\ub3c4 \ubcf4\uc5ec\uc9c0\ub4ef\uc774&nbsp;<strong>Matlab\u2122&nbsp;<\/strong>\uc5d0\uc11c \uc81c\uacf5\ud558\ub294&nbsp;fft\ub77c\ub294 \ud568\uc218\ub97c \uc774\uc6a9\ud558\uba74 \ucf54\ub4dc\uac00 \ud6e8\uc52c \uac04\ub2e8\ud574\uc9c0\ub294 \uac83\uc744 \ubcf4\uc2e4 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.(\ucc38\uace0\ub85c \ud504\ub85c\uadf8\ub7a8\uc774 \uc81c\ub300\ub85c \uc2e4\ud589 \uc548\ub418\uc2dc\ub294 \ubd84\ub4e4\uc740 \uc218\uc815 \ud30c\uc77c\uc744 \ucca8\ubd80\ud588\uc73c\ub2c8 \ucc38\uc870\ud558\uc154\uc11c \uc2e4\ud589\ud574\ubcf4\uc2dc\uae30 \ubc14\ub78d\ub2c8\ub2e4.) \uc774\uc81c \ubcf8\uaca9\uc801\uc73c\ub85c&nbsp;<strong>FFT<\/strong>\uc758 \ud2b9\uc131\uc744 \uc2dc\ubbac\ub808\uc774\uc158\uc744 \ud1b5\ud574\uc11c \ud655\uc778\ud574 \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4. \uc2e0\ud638\uc640 \uc870\uac74\uc740 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles1.naver.net\/data5\/2005\/4\/5\/192\/Snap8-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\uba3c\uc800&nbsp;<strong>Sampling Frequency<\/strong>&nbsp;\uc758 \uc911\uc694\uc131\uc744 \uc54c\uc544\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<br>\uc6b0\uc120&nbsp;&nbsp;Sampling Frequency&nbsp;\uac00&nbsp;Nyquist Frequency&nbsp;\ubcf4\ub2e4 \uc791\uc740 99\uc77c \ub54c\ub97c \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.\ucc98\uc74c \uadf8\ub9bc\uc740<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc6d0\ub798 \uc2e0\ud638\uc774\uba70 \ub450\ubc88\uc9f8 \uadf8\ub9bc\uc740&nbsp;<strong>FFT<\/strong>\ud55c \uadf8\ub9bc, \uc138\ubc88\uc9f8 \uadf8\ub9bc\uc740&nbsp;<strong>FFT<\/strong>\ud55c \uc2e0\ud638\ub97c \ub2e4\uc2dc&nbsp;<strong>IFFT<\/strong>\ub97c \ud1b5\ud558\uc5ec \ub418\ub3cc\ub9b0\uadf8\ub9bc\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles15.naver.net\/data5\/2005\/4\/5\/14\/Snap9-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5c9\ub6b1\ud558\uac8c\ub3c4 50Hz \uc5d0 \ub5a0\uc57c \ud560 \uc131\ubd84\uc774 49Hz \uc5d0\uc11c \ub72c \uac83\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e4\uc74c\uc740&nbsp;Sampling Frequency&nbsp;\uac00&nbsp;Nyquist Frequency&nbsp;\uc640 \uac19\uc740 100\uc77c \ub54c\ub97c \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles9.naver.net\/data5\/2005\/4\/5\/24\/Snap10-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\ubc88\uc5d4 50Hz\uc758 \uc131\ubd84 \ud06c\uae30\uac00 \ub450\ubc30\uac00 \ub418\uc5b4 \ubc84\ub838\uc2b5\ub2c8\ub2e4. \uadf8 \uc6d0\uc778\uc740 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\uc774 \uc804\uccb4\uc801\uc778 \uc8fc\ud30c\uc218 \ud2b9\uc131\uc774&nbsp;Nyquist Frequency\/2&nbsp;\uc9c0\uc810\uc744 \uae30\uc900\uc73c\ub85c \ub300\uce6d\uc774\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles10.naver.net\/data6\/2005\/4\/5\/105\/Snap11-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\ub2e4\uc74c\uc740&nbsp;Sampling Frequency&nbsp;\uac00&nbsp;Nyquist Frequency&nbsp;\ubcf4\ub2e4 \ud070 101\uc77c \ub54c\ub97c \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles2.naver.net\/data5\/2005\/4\/5\/289\/Snap12-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc62c\ubc14\ub978 \uac12\uc774 \ub098\uc628 \uac83\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.Sampling Frequency&nbsp;\uac00 102\uc77c \ub54c\ub3c4 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\uc774 \uc62c\ubc14\ub978 \uac12\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles10.naver.net\/data5\/2005\/4\/5\/201\/Snap13-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774\uc81c\ub294 \uc8fc\uae30 \uc77c\uce58\uc758 \uc911\uc694\uc131\uc744 \uc54c\uc544\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.\uc2e0\ud638\ub97c \uc880\ub354 \ubd84\uba85\ud558\uac8c \ubcf4\uae30 \uc704\ud558\uc5ec&nbsp;Sampling Frequency\ub97c 1000\uc73c\ub85c \ub193\uace0 \uc2dc\ubbac\ub808\uc774\uc158\uc744 \ud558\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.\uc774\ubc88\uc5d0\ub294 \uc8fc\uae30\ub97c 1\uc8fc\uae30,2\uc8fc\uae30,10\uc8fc\uae30\uae4c\uc9c0 \uc8fc\uc5b4\uac00\uba70 \ud655\uc778\ud574 \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1 Cycle<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles13.naver.net\/data5\/2005\/4\/5\/124\/Snap16-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2&nbsp;Cycles<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles3.naver.net\/data5\/2005\/4\/5\/2\/Snap17-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>10 Cycles<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles6.naver.net\/data5\/2005\/4\/5\/229\/Snap19-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc717 \uadf8\ub9bc\uc5d0\uc11c&nbsp; \uc8fc\uae30\uac00 \ub298\uc5b4\ub0a0 \uc218\ub85d \uad00\uc2ec \uc8fc\ud30c\uc218\uac00 \uc544\ub2cc \uacf3\uc758 \ud3ec\uc778\ud2b8 \uc218\uac00 \uc810\uc810 \ub298\uc5b4\ub098\ub294 \uac83\uc744 \ud655\uc778\ud574 \ubcfc \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.\uc5ec\uae30\uae4c\uc9c0\ub294 \ubcc4\ub2e4\ub978 \ubb38\uc81c\uac00 \uc5c6\uc5b4 \ubcf4\uc785\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc8fc\uae30\uac00 4.4\uc778 \uacbd\uc6b0\ub97c \uc0b4\ud3b4\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles11.naver.net\/data5\/2005\/4\/5\/90\/Snap20-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc\uc5d0\uc11c\ub3c4 \ubcf4\uc5ec\uc9c0\ub4ef\uc774 \uc815\ud655\ud55c \uac12\uc744 \uc5bb\ub294\ub370 \uc2e4\ud328\ud558\uc600\uace0 \ub2e4\ub978 \uc131\ubd84\ub4e4\ub3c4 \ud280\uc5b4\ub098\uc624\ub294 \uac83\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4. \ucc38\uc73c\ub85c \ub09c\uac10\ud55c \uc77c\uc774 \uc544\ub2d0 \uc218 \uc5c6\uc2b5\ub2c8\ub2e4. \uc774\ub807\uac8c \uc8fc\uae30\ub97c \uc77c\uce58 \uc2dc\ucf1c\uc904 \uc218 \uc5c6\uc744 \ub54c\uc5d0&nbsp; \ubb38\uc81c\ub4e4\uc744 \ud574\uacb0\ud558\uae30 \uc704\ud55c \uba87\uac00\uc9c0 \ubc29\ubc95\uc774 \uc788\uc2b5\ub2c8\ub2e4. \uccab\ubc88\uc9f8\ub294&nbsp;<strong>Windowing<\/strong>\uc774\ub77c\ub294 \uae30\ubc95\uc774\uba70 \ub450\ubc88\uc9f8\ub294&nbsp;<strong>Zero padding<\/strong>&nbsp;\uae30\ubc95\uc785\ub2c8\ub2e4. \uba3c\uc800&nbsp;<strong>Windowing<\/strong>&nbsp;\uae30\ubc95\uc744 \uc0b4\ud3b4\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.&nbsp;<strong>Windowing&nbsp;<\/strong>\uc740 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\uc740 \uc2e0\ud638 \ubcc0\ud615\uc744 \uc6d0\uc2e0\ud638\uc5d0 \uac00\ud558\uac8c \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles3.naver.net\/data5\/2005\/4\/5\/242\/Snap21-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Windowing&nbsp;<\/strong>\uc774 \uc774\ubc88 \uc608\uc81c\uc5d0 \uc4f0\uc778 \uacbd\uc6b0\uc640 \ub2e4\ub978 \uc2e0\ud638\uc5d0 \uc4f0\uc778 \uacbd\uc6b0\ub97c \ube44\uad50\ud574\ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles14.naver.net\/data5\/2005\/4\/5\/285\/Snap22-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>CDMA2000<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles13.naver.net\/data5\/2005\/4\/5\/108\/Snap29-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles16.naver.net\/data6\/2005\/4\/5\/95\/Snap30-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uadf8\ub9bc\uc5d0\uc11c \ubcfc \uc218 \uc788\ub4ef\uc774 \uae30\ubcf8\uc801\uc73c\ub85c&nbsp;<strong>Windowing<\/strong>\uc740&nbsp;<strong>CDMA2000<\/strong>&nbsp;\uc2e0\ud638\uc640 \uac19\uc774 \ub300\uc5ed\ud3ed\uc744 \uc9c0\ub2c8\ub294 \uc2e0\ud638\uc5d0 \uc801\ud569\ud569\ub2c8\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ubcf8 \uc608\uc81c\uc5d0\ub294 \uc801\ud569\ud558\uc9c0 \uc54a\uc740 \ubc29\uc2dd\uc785\ub2c8\ub2e4.\uadf8\ub7ec\uba74 \uc774\uc81c&nbsp;<strong>Zero padding&nbsp;<\/strong>\uae30\ubc95\uc744 \ubcf4\ub3c4\ub85d \ud558\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles7.naver.net\/data5\/2005\/4\/5\/230\/Snap23-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\uae30\ubcf8\uc801\uc73c\ub85c \uc704\uc640 \uac19\uc740 \ubc29\uc2dd\uc774&nbsp;<strong>Zero padding&nbsp;<\/strong>\uc785\ub2c8\ub2e4.<strong>Zero padding&nbsp;<\/strong>\uc740&nbsp;<strong>Matlab\u2122&nbsp;<\/strong>\uc5d0\uc11c&nbsp;fft(x,N);\uc774\ub77c\ub294&nbsp;\uba85\ub839\uc5b4\ub85c \uad6c\ud604\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.&nbsp;\uc5ec\uae30\uc11c&nbsp;N\uc5d0&nbsp;Signal length\ubcf4\ub2e4 \ud070 \uac12\uc744 \uc8fc\uac8c \ub418\uba74 \uadf8\uac8c \ubc14\ub85c&nbsp;<strong>Zero padding&nbsp;<\/strong>\uc758&nbsp;\ud6a8\uacfc\ub97c \uc8fc\uac8c \ub429\ub2c8\ub2e4.<strong>Zero padding<\/strong>&nbsp;\uc758 \uae38\uc774\ub97c \ub298\ub824\uc90c\uc5d0 \ub530\ub77c \uacb0\uacfc\uac00 \uc544\ub798\uc640 \uac19\uc774 \ub098\uc624\uac8c \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>N&nbsp;= 2*Signal length<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles9.naver.net\/data5\/2005\/4\/5\/88\/Snap24-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>N= 3*Signal length<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles15.naver.net\/data6\/2005\/4\/5\/62\/Snap25-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>N&nbsp;= 10*Signal length<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles10.naver.net\/data5\/2005\/4\/5\/249\/Snap26-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc8fc\ud30c\uc218 \uc131\ubd84\uc740 \uc798 \ubf51\uc544 \ub0b4\uc5c8\uc9c0\ub9cc&nbsp;<strong>Zero padding&nbsp;<\/strong>\uc758 \uae38\uc774\uac00 \ub298\uc5b4\ub0a8\uc5d0 \ub530\ub77c \ud544\uc694\uc5c6\ub294 \ub300\uc5ed\uc774 \uc0dd\uaca8\ub0ac\uc74c\uc744 \ud655\uc778\ud560 \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub7f4 \ub54c\ub294 \ub2e4\uc74c \uadf8\ub9bc\uacfc \uac19\uc774 \uc8fc\uae30\ub97c \ub298\ub824\uc8fc\uba74 \uc62c\ubc14\ub978&nbsp; \uacb0\uacfc\ub97c \uc5bb\uac8c \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/postfiles16.naver.net\/data6\/2005\/4\/5\/223\/Snap27-horgan.jpg?type=w3\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/postfiles1.naver.net\/data6\/2005\/4\/5\/160\/Snap28-horgan.jpg?type=w3\" alt=\"\" width=\"550\" height=\"198\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><br>\uacb0\ub860\uc801\uc73c\ub85c \uc62c\ubc14\ub978 fft\ub97c \uc704\ud574\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uaddc\uce59\uc744 \uc9c0\ucf1c\uc918\uc57c \ud55c\ub2e4\ub294 \uac83\uc744 \uc54c \uc218\uac00 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1.Sampling Frequency\ub294&nbsp;Maximum Frequency\ubcf4\ub2e4 \ucd5c\uc18c\ud55c 2\ubc30\uc774\uc0c1\uc744 \uc7a1\uc544\uc8fc\uc5b4\uc57c \ud569\ub2c8\ub2e4.<br>2.\uc8fc\uae30\ub97c \ub418\ub3c4\ub85d\uc774\uba74 \ub9de\ucd94\uc5b4 \uc8fc\uc154\uc57c \ud569\ub2c8\ub2e4.<br>3.\uc8fc\uae30\ub97c \ub9ce\uc774 \uc8fc\uc2e4\uc218\ub85d \uc88b\uc2b5\ub2c8\ub2e4.<br>4.\uc8fc\uae30\ub97c \ubabb \ub9de\ucd94\uc5c8\uc744\ub54c\uc5d0\ub294&nbsp;<strong>Zero padding&nbsp;<\/strong>\uc744 \uc774\uc6a9\ud558\uc2dc\uba74 \ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[\ucd9c\ucc98]<\/strong>&nbsp;<a href=\"http:\/\/blog.naver.com\/horgan\/40011894016\" target=\"_blank\" rel=\"noreferrer noopener\">Matlab\uc744 \uc774\uc6a9\ud55c FFT\uc758 \uc62c\ubc14\ub978 \uc774\ud574<\/a>|<strong>\uc791\uc131\uc790<\/strong>&nbsp;<a href=\"http:\/\/blog.naver.com\/horgan\" target=\"_blank\" rel=\"noreferrer noopener\">\uc77c\ud3b8\ub2e8\uc2ec<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Fourier transform \uc9c1\uad00\uc801 \uc774\ud574 \ubaa8\ub4e0 \uacf5\ubd80\uc758 \uc2dc\uc791\uc740 \ud575\uc2ec \uac1c\ub150\uc744 \uc815\ud655\ud788 \uc774\ud574\ud558\ub294\ub370 \uc788\ub2e4. \uadf8\ub9ac\uace0 \uadf8 \uc774\ud574\ub294 \uac00\uae09\uc801 \uc9c1\uad00\uc801\uc77c\uc218\ub85d \uc88b\ub2e4. \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier transform)\uc744 \uc9c1\uad00\uc801\uc73c\ub85c \uc124\uba85\ud558\uba74 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740&nbsp;\uc784\uc758\uc758 \uc785\ub825 \uc2e0\ud638\ub97c \ub2e4\uc591\ud55c \uc8fc\ud30c\uc218\ub97c \uac16\ub294 \uc8fc\uae30\ud568\uc218\ub4e4\uc758 \ud569\uc73c\ub85c \ubd84\ud574\ud558\uc5ec \ud45c\ud604\ud558\ub294 \uac83\uc774\ub2e4. \uc880\ub354 \ub4e4\uc5b4\uac00\uba74, \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uc8fc\uae30\ud568\uc218\ub294 sin, cos \uc0bc\uac01\ud568\uc218\uc774\uba70 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740 \uace0\uc8fc\ud30c\ubd80\ud130 \uc800\uc8fc\ud30c\uae4c\uc9c0 \ub2e4\uc591\ud55c \uc8fc\ud30c\uc218 \ub300\uc5ed\uc758 sin, cos \ud568\uc218\ub4e4\ub85c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[83],"tags":[29],"class_list":["post-1650","post","type-post","status-publish","format-standard","hentry","category-archive","tag-mathematics"],"_links":{"self":[{"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/posts\/1650","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/yoonhada.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1650"}],"version-history":[{"count":21,"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/posts\/1650\/revisions"}],"predecessor-version":[{"id":1681,"href":"http:\/\/yoonhada.com\/index.php?rest_route=\/wp\/v2\/posts\/1650\/revisions\/1681"}],"wp:attachment":[{"href":"http:\/\/yoonhada.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1650"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/yoonhada.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1650"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/yoonhada.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}