{"id":7665,"date":"2007-10-08T03:44:00","date_gmt":"2007-10-08T03:44:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=7665"},"modified":"2007-10-08T03:44:00","modified_gmt":"2007-10-08T03:44:00","slug":"%ed%91%b8%eb%a6%ac%ec%97%90-%eb%b3%80%ed%99%98fourier-transformation-4","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=7665","title":{"rendered":"\ud478\ub9ac\uc5d0 \ubcc0\ud658(Fourier Transformation) #4"},"content":{"rendered":"
\n *\uc2e4\uc81c \uacc4\uc0b0\uc5d0\uc11c\ub294 \uc801\ubd84\uc774\ub098 \uc9c0\uc218\ud568\uc218\uc5d0 $2\\pi$\ub9cc\ud07c\uc774 \uacf1\ud574\uc9c0\uac70\ub098 \ub098\ub220\uc9c0\uac70\ub098 \ub4f1\ub4f1\uc758 \uc77c\uc774 \uc77c\uc5b4\ub098\ubbc0\ub85c, \uc815\ud655\ud55c \uacf5\uc2dd\uc740 \ucc45\uc744 \ucc3e\uc544\ubcf4\uace0 \uc0c1\ud669\uc5d0 \uc801\ud569\ud55c \uac83\uc744 \uc0ac\uc6a9\ud560 \uac83\uc744 \uad8c\ud55c\ub2e4. \uc544\ub798\uc758 \uc124\uba85 \ubc0f \uc774 \ube14\ub85c\uadf8\uc5d0\uc11c\uc758 \uc124\uba85\uc740 \ubaa8\ub450 \uc815\uaddc\ud654(Normalization)\uc744 \ud558\uc9c0 \uc54a\uc740 \uac1c\ub150 \uc774\ud574\ub97c \uc704\ud55c \uc124\uba85\uc77c \ubfd0\uc774\ub2e4.<\/p>\n

*\uc774 \uae00\uc758 \ub313\uae00\uc744 \ucc38\uace0\ud558\uc5ec \ub17c\ub9ac\uc801\/\uc218\ud559\uc801\uc778 \uc624\ub958\uac00 \ub0b4\ud3ec\ub418\uc5b4 \uc788\uc744 \uc218 \uc788\uc74c\uc744 \uacbd\uace0\ud574 \ub450\ub294 \ubc14\uc774\ub2e4. \uc804\uccb4\uc801\uc778 \ub9e5\ub77d\uc758 \uc774\ud574\uc5d0\uc11c\ub294 \ub9de\uc9c0\ub9cc, \uc5ec\uae30 \ub098\uc628 \uacf5\uc2dd\ub4e4\uc744 \uadf8\ub300\ub85c \uc801\uc6a9\ud558\ub824\uace0 \ud560 \ub54c\ub294 \ubb38\uc81c\uac00 \ubc1c\uc0dd\ud560 \uc218 \uc788\uc73c\ubbc0\ub85c \ub2e4\ub978 \uc88b\uc740 \ucc45\ub4e4\uc744 \ucc38\uace0\ud560 \uac83\uc744 \uac15\ub825\ud788 \uad8c\uc7a5\ud55c\ub2e4.<\/p>\n

\uc6d0\ub798\ub294 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uc2e4\uc81c \uacc4\uc0b0\ub4e4\uc744 \ud574\ubcf4\ub824\uace0 \ud588\uc73c\ub098, \uc0ac\uc2e4 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \uacc4\uc0b0\ud55c\ub2e4\ub294 \uac83\uc774 $e^{ikx}$\ub97c \uacf1\ud574\uc11c \uc798 \uc801\ubd84\ud558\uba74 \ub05d\ub098\ub294 \uac83\uc778\uc9c0\ub77c \uc774\uac74 \uc624\ud788\ub824 \uc801\ubd84 \uae30\uc220\uc5d0 \uac00\uae4c\uc6cc\uc11c \uadf8\ub9cc \ub450\uc5c8\ub2e4. \uc5b4\ub5a4 \ud568\uc218\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc774 \uad81\uae08\ud558\uba74 \uc801\ubd84\uc744 \uc798 \ud574\ubcf4\uc2dc\uae30\ub97c. \ubd80\ubd84\uc801\ubd84\uacfc \uce58\ud658\uc801\ubd84\uc744 \uc5ec\ub7ec\ubc88 \uc798 \uc0ac\uc6a9\ud574\uc57c \ud55c\ub2e4. \uadf8\ub9ac\uace0 \uc778\ud130\ub137 \uac80\uc0c9\ud558\uba74 \ub300\ud45c\uc801\uc778 \ud568\uc218\ub4e4\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658 \ud45c\uac00 \uc788\uc73c\ub2c8\uae4c \ucc38\uace0\ud574\ub3c4 \uc88b\ub2e4. \uc774\ubcf4\ub2e4 \uc5b4\ub824\uc6b4 \ubb38\uc81c\ub294 \ubcf4\ud1b5 \ub354 \ub9ce\uc740 \ud568\uc218\ub4e4\uc758 \ud478\ub9ac\uc5d0 \ubcc0\ud658 \ud45c\ub97c \ucc3e\uc544\ubcf4\uac70\ub098, Maple \uc774\ub098 Mathematica \ub4f1\uc758 \uc218\ud559 \ud504\ub85c\uadf8\ub7a8\uc744 \uc4f0\uba74 \ub41c\ub2e4. \uadf8\uac83\ub3c4 \uc5c6\uc73c\uba74 \uace7 \ub2e4\uc74c \ubb38\ub2e8\uc5d0\uc11c \uc18c\uac1c\ud560 DFT\ub97c \uc774\uc6a9\ud558\uba74 \ub41c\ub2e4.
\n
\n
\n http:\/\/ipml.ee.duth.gr\/~papamark\/circuits\/Table%20of%20Fourier%20Transforms.htm
\n <\/a>
\n
\n<\/p>\n

FourierTransformPairs.pdf\uc5d0 \uc561\uc138\uc2a4\ud558\ub824\uba74 \ud074\ub9ad\ud558\uc138\uc694.<\/a><\/p>\n

<\/a><\/p>\n

\uc774\ubc88 \uc2dc\uac04\uc5d0\ub294 \uc774\uc0b0 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Discrete Fourier Transform=DFT)\uc5d0 \ub300\ud574\uc11c \uc54c\uc544\ubcf4\ub3c4\ub85d \ud558\uaca0\ub2e4.
\n
\n \uc0ac\uc2e4 DFT \uc790\uccb4\ub294 \uadf8\ub2e4\uc9c0 \ud6a8\uc6a9\uc774 \uc5c6\ub2e4. \ud558\uc9c0\ub9cc \uc774\uac78 \uc751\uc6a9\ud558\uba74 \ube60\ub978 \ud478\ub9ac\uc5d0 \ubcc0\ud658(Fast Fourier Transform=FFT)\uc774 \uac00\ub2a5\ud558\uace0, FFT\ub294 \ud604\ub300 \ud1b5\uc2e0 \uae30\uc220\uc758 \uc911\uc694\ud55c \ubc29\ubc95\ub860 \uc911\uc758 \ud558\ub098\uc774\ubbc0\ub85c \uc6b0\uc120 DFT\ub97c \uc18c\uac1c\ud558\ub294 \uac83\uc774 \uc88b\uaca0\ub2e4.<\/p>\n

\ub9d0\uc740 \uc544\uc8fc \uac70\ucc3d\ud558\uac8c \ud588\uc73c\ub098 \uc2e4\uc81c\ub85c DFT\ub294 \ub300\ub2e8\ud788 \uac04\ub2e8\ud558\uace0, \ub530\ub77c\uc11c \uc774 \uae00\ub3c4 \uc9e7\ub2e4.<\/p>\n

\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 \uc694\uc810\uc740 \uc624\uc9c1 “\uc801\ubd84\uc744 \ud558\uba74 \ub41c\ub2e4”\ub294 \uc810\uc774\ub2e4. \uadf8\ub7f0\ub370 \ub300\ubd80\ubd84, \ubb34\ud55c\ud788 \ub9ce\uc740 \uc218\uc758 \ud568\uc218\ub4e4\uc740 \uc801\ubd84\uc744 \ud560 \uc218 \uc5c6\uac70\ub098 \uc801\ubd84\ud558\uae30 \ud798\ub4e0 \ud568\uc218\ub4e4\uc774\ub2e4. \ud568\uc218 \ud615\ud0dc\uac00 \ub531\ud788 \ud574\uc11d\uc801\uc778 \ud615\ud0dc\ub85c \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\uace0 \ubaa8\ub4e0 \uc810\uc5d0 \uc8fc\uc5b4\uc9c4 \uc22b\uc790\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uacbd\uc6b0\ub3c4 \uc788\ub2e4. \uc774\ub7f0 \uc2dd\uc73c\ub85c, \uc801\ubd84\ud558\uae30 \uad34\ub85c\uc6b8 \ub54c \uc218\ud559\uc790\ub4e4\uc774 \uc0ac\uc6a9\ud558\ub294 \ubc29\ubc95\uc740 \uc6d0\uc810\uc73c\ub85c\uc758 \ud68c\uadc0\ub2e4. \uc801\ubd84\uc740 \uc6d0\ub798 \uc544\uc8fc \ub9ce\uc740 \uac83\ub4e4\uc744 \ub354\ud558\ub2e4\uac00, \ubb34\ud55c\uc744 \ubc1c\uacac\ud558\uac8c \ub418\uc5b4 \ubb34\ud55c\ud788 \ub9ce\uc740 \uac83\uc744 \uc5b4\ub5bb\uac8c \ub354\ud560\uc9c0 \uace0\ubbfc\ud558\ub2e4\uac00 \ub4f1\uc7a5\ud55c \uacc4\uc0b0\ubc95\uc774\ub2e4. \ub530\ub77c\uc11c, \uc801\ubd84\uc740 \uc6d0\ub798 \ub367\uc148\uc774\uace0, \uadf8 \ub367\uc148\uc740 \uc6d0\ub798 \uc5f0\uc18d\uc801\uc778\uac8c \uc544\ub2c8\ub77c \ub744\uc5c4\ub744\uc5c4\ud558\uac8c \ub04a\uc5b4\uc838 \uc788\uc5c8\ub2e4. \uc989, Discretization\uc774\ub2e4.<\/p>\n

\uadf8\ub9ac\ud558\uc5ec,
\n
\n $\\int_0^{2\\pi}dx e^{-ikx}f(x) \\rightarrow \\sum_{n=0}^{N-1} exp(-ikn\\frac{2\\pi}{N})f(n\\frac{2\\pi}{N})\\frac{2\\pi}{N}$
\n
\n \uac00 DFT\uc758 \uc911\uc2ec \uacf5\uc2dd\uc774 \ub41c\ub2e4. \uac01\uac01 \uc801\ubd84\uae30\ud638\ub294 \ud569\uc0b0 \uae30\ud638\ub85c, \uc801\ubd84 \uad6c\uac04\uc740 \uc218\uc5f4 \ubc88\ud638\ub85c, \uc801\ubd84\uc18c dx\ub294 \ud55c \uad6c\uac04\uc758 \uae38\uc774\ub85c \ubc14\uafb8\uba74 \ub41c\ub2e4. \uc774\uc81c, \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740
\n\ud568\uc218\uac12\uc744 \uc5ec\ub7ec\uac1c \ucc3e\uc544\uc11c \ubaa8\ub450 \ub354\ud558\ub294 \ub367\uc148\uc73c\ub85c \ubc14\ub00c\uc5c8\uae30 \ub54c\ubb38\uc5d0 \ucef4\ud4e8\ud130\ub97c \uc774\uc6a9\ud574\uc11c \uacc4\uc0b0\ud560 \uc218\ub3c4 \uc788\ub2e4. (\ubb3c\ub860 \uc0ac\ub78c\uc774 \ud560 \uc218\ub3c4 \uc788\ub2e4)
\n
\n \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740 \uc5b4\ub5a4 \ud568\uc218\ub85c\ubd80\ud130 \ub2e4\ub978 \ud568\uc218\ub97c \uad6c\ud558\ub294 \uac83\uc774\ubbc0\ub85c, \uc704\uc758 \ud568\uc218\ub294 k\uac00 \uacb0\uc815\ub418\uba74 \ud568\uc218\uac12\uc774 \uacb0\uc815\ub418\ub294 \ud568\uc218\uc77c \uac83\uc774\ub2e4.<\/p>\n

\uc0ac\uc2e4 \uc774\uac74 \uacf5\uc2dd\uc774\ub784\uac83\ub3c4 \uc5c6\uc774, \uc5f0\uc18d\uc801\uc778 \uc801\ubd84\uc744 \uad6c\ubd84\uad6c\uc801\ubc95\ucc98\ub7fc \ub2e4\uc2dc \ud45c\ud604\ud55c \uac83\uc5d0 \ubd88\uacfc\ud558\ub2e4.
\n
\n \uc2e4\uc81c\ub85c \uad6c\ubd84\uad6c\uc801\ubc95\uc740 \uad6c\uac04\uc744 \uc798\ub77c\ub0b8 \uac2f\uc218\uc778 N\uc744 \ubb34\ud55c\ub300\ub85c \ubcf4\ub0b4\ub294 \uadf9\ud55c\uc744 \ucde8\ud558\uc9c0\ub9cc \uc190\uc73c\ub85c \uacc4\uc0b0\ud558\uac70\ub098 \ucef4\ud4e8\ud130\uc5d0\uac8c \uc77c\uc744 \uc2dc\ud0ac \ub54c \uc9c4\uc9dc\ub85c N\uc744 \ubb34\ud55c\ub300\ub85c \ubcf4\ub0bc \uc218\ub294 \uc5c6\uc73c\ubbc0\ub85c, \uc6b0\ub9ac\uac00 \uc6d0\ud558\ub294 \uc801\ub2f9\ud55c \uc624\ucc28 \ubc94\uc704\uc640 \uacc4\uc0b0 \uc2dc\uac04\uc744 \uace0\ub824\ud558\uc5ec N\uc744 \uc801\ub2f9\ud788 \ud070 \uc22b\uc790\ub85c \uc815\ud558\uac8c \ub41c\ub2e4.
\n <\/span>
\n
\n \ub9cc\uc57d \uc6d0\ub798 \uc8fc\uc5b4\uc9c4 \ud568\uc218 \uc790\uccb4\uac00 \ub04a\uc5b4\uc838\uc11c \ub4e4\uc5b4\uc628\ub2e4\uba74, \uc989 \uc8fc\uc5b4\uc9c4 \ud568\uc218\uac00 \ubaa8\ub4e0 \uc810\uc5d0\uc11c\uc758 \uac12\uc774 \uc8fc\uc5b4\uc9c4 \uac83\uc774 \uc544\ub2c8\ub77c \uc720\ud55c\ud55c \uc218\uc758 \uc810\uc5d0\uc11c\ub9cc \ud568\uc218\uac12\uc774 \uc8fc\uc5b4\uc838 \uc788\ub2e4\uba74 \uc774 \uacbd\uc6b0\uc5d0\ub294 \uc5f0\uc18d\uc801\uc778 \uc801\ubd84\uc774 \ubd88\uac00\ub2a5\ud558\uace0 \ud56d\uc0c1 \ub367\uc148\uc73c\ub85c \uc815\uc758\ub41c \uc801\ubd84\uc744 \ud574\uc57c \ud55c\ub2e4. \uc774\ub54c\ub294 \ubcc0\ud658\uacfc \uc5ed\ubcc0\ud658 \uc0ac\uc774\uc5d0 \uc624\ucc28\uac00 \uc5c6\uac8c \ub41c\ub2e4. \uac00\ub839, n\uac1c\uc758 \uc810\uc5d0\uc11c \ud568\uc218\uac12\uc774 \uc8fc\uc5b4\uc838 \uc788\ub2e4\uba74, \uc989 $(a_1, f(a_1)), (a_2, f(a_2)), …, (a_n, f(a_n))$ \uc73c\ub85c \ud568\uc218\uac00 \uc8fc\uc5b4\uc838 \uc788\ub294 \uacbd\uc6b0, \uc774\uac83\uc740 \ud558\ub098\uc758 “\ubca1\ud130”\ub77c\uace0 \ubcfc \uc218 \uc788\uace0 \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc740 \uc800 \ubca1\ud130\ub97c \ub2e4\ub978 \ubca1\ud130\ub85c \ubcf4\ub0b4\ub294 1\ucc28 \ubcc0\ud658\uc774 \ub41c\ub2e4. \ubb3c\ub860 \uadf8 \uc5ed\ubcc0\ud658\ub3c4 \uac00\ub2a5\ud558\ub2e4.<\/p>\n

\ud55c\uac00\uc9c0 \uc0dd\uac01\ud574 \ubcf4\uc790. \uc774 \uacc4\uc0b0\uc744 \ub2e4 \ud558\ub824\uba74, \uad6c\uac04\uc744 N\uac1c\ub85c \uc798\ub790\ub2e4\uace0 \ud560 \ub54c \uba87\ubc88\uc758 \uacc4\uc0b0\uc744 \ud574\uc57c \ud560\uae4c? \ud568\uc218\uac12\uc5d0 \ub300\uc785\ud558\ub294\uac74 \ube7c\uace0, \ub367\uc148\uacfc \uacf1\uc148\uc744 \uc218\ud589\ud558\ub824\uba74 N*N\ubc88\uc758 \uacc4\uc0b0\uc744 \ud574\uc57c \ud55c\ub2e4. (\uc2ec\uac01\ud558\uac8c \uace0\ubbfc\ud574 \ubcf4\uc2dc\uae30\ub97c)<\/p>\n

*DFT\uc5d0 \uad00\ud55c \uad1c\ucc2e\uc740 \uc124\uba85\uc740 \uc704\ud0a4\ud53c\ub514\uc544\ub97c \ucc3e\uc544\ubcf4\uba74 \ub41c\ub2e4.
\n
\n
\n http:\/\/en.wikipedia.org\/wiki\/Discrete_Fourier_transform
\n <\/a>
\n
\n *Paul Bourke\uc774\ub77c\ub294 \uc0ac\ub78c\uc774 DFT\uc5d0 \ub300\ud55c \uc54c\uace0\ub9ac\uc998\uacfc \uad6c\ud604\uc5d0 \ub300\ud574 \uc124\uba85\ud55c \uac83\ub3c4 \uc788\ub2e4.
\n
\n
\n http:\/\/local.wasp.uwa.edu.au\/~pbourke\/other\/dft\/
\n <\/a><\/p>\n

\ub2e4\uc74c\ud3b8 \uc2a4\ud3ec\uc77c\ub7ec : FFT\ub294 \uacc4\uc0b0 \uc2dc\uac04\uc744 N*logN\uc73c\ub85c \uc904\uc77c \uc218 \uc788\ub2e4.
\n <\/p>\n

\n
\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

*\uc2e4\uc81c \uacc4\uc0b0\uc5d0\uc11c\ub294 \uc801\ubd84\uc774\ub098 \uc9c0\uc218\ud568\uc218\uc5d0 $2\\pi$\ub9cc\ud07c\uc774 \uacf1\ud574\uc9c0\uac70\ub098 \ub098\ub220\uc9c0\uac70\ub098 \ub4f1\ub4f1\uc758 \uc77c\uc774 \uc77c\uc5b4\ub098\ubbc0\ub85c, \uc815\ud655\ud55c \uacf5\uc2dd\uc740 \ucc45\uc744 \ucc3e\uc544\ubcf4\uace0 \uc0c1\ud669\uc5d0 \uc801\ud569\ud55c \uac83\uc744 \uc0ac\uc6a9\ud560 \uac83\uc744 \uad8c\ud55c\ub2e4. \uc544\ub798\uc758 \uc124\uba85 \ubc0f \uc774 \ube14\ub85c\uadf8\uc5d0\uc11c\uc758 \uc124\uba85\uc740 \ubaa8\ub450 \uc815\uaddc\ud654(Normalization)\uc744 \ud558\uc9c0 \uc54a\uc740 \uac1c\ub150 \uc774\ud574\ub97c \uc704\ud55c \uc124\uba85\uc77c \ubfd0\uc774\ub2e4. *\uc774 \uae00\uc758 \ub313\uae00\uc744 \ucc38\uace0\ud558\uc5ec \ub17c\ub9ac\uc801\/\uc218\ud559\uc801\uc778 \uc624\ub958\uac00 \ub0b4\ud3ec\ub418\uc5b4 \uc788\uc744 \uc218 \uc788\uc74c\uc744 \uacbd\uace0\ud574 \ub450\ub294 \ubc14\uc774\ub2e4. \uc804\uccb4\uc801\uc778 \ub9e5\ub77d\uc758 \uc774\ud574\uc5d0\uc11c\ub294 \ub9de\uc9c0\ub9cc, \uc5ec\uae30 \ub098\uc628 \uacf5\uc2dd\ub4e4\uc744 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-7665","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-1ZD","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/7665","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7665"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/7665\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7665"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}