\u5148\u65e5(\u3068\u3044\u3063\u3066\u30821\u9031\u9593\u304f\u3089\u3044\u524d\u306e\u3053\u3068\u3067\u3059\u304c)\u3001<\/p>\n
\u5b9f\u9a13\u3067\u53d6\u5f97\u3057\u305f\u30c7\u30fc\u30bf\u3092FFT\u3067\u5909\u63db\u3057\u3001\u305d\u306e\u7d50\u679c\u5f97\u3089\u308c\u305f\u5468\u6ce2\u6570\u9818\u57df\u306e\u30c7\u30fc\u30bf\u306e\u5404\u70b9\u306e\u300c\u5468\u6ce2\u6570\u8ef8\u300d\u65b9\u5411\u306e\u9593\u9694\u3063\u3066\u3001\u3069\u3046\u8a08\u7b97\u3059\u308c\u3070\u3088\u3044\u304b\u308f\u304b\u308a\u307e\u3059\u304b?<\/p><\/blockquote>\n
\u3068\u3044\u3046\u8da3\u65e8\u306e\u8cea\u554f\u3092\u53d7\u3051\u305f\u306e\u3067\u3059\u304c\u3001\u5373\u7b54\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\u3001\u6b21\u306e\u65e5\u306b\u56de\u7b54\u3059\u308b\u3088\u3046\u306a\u3053\u3068\u3068\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u3002\u304a\u6065\u305a\u304b\u3057\u3044\u9650\u308a\u3067\u3059\u3002( ;\u00b4\uff65\u03c9\uff65`)<\/p>\n
FFT,DFT,DCT\u306a\u3069\u306e\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u65b9\u9762\u306f\u4eca\u306e\u4ed5\u4e8b\u3067\u306f\u5fc5\u305a\u3057\u3082\u5c02\u9580\u3067\u306f\u306a\u3044\u306e\u3067\u3059\u304c\u3001\u9053\u5177\u3068\u3057\u3066\u4f7f\u3046\u53ef\u80fd\u6027\u304c\u3042\u308b\u3068\u3053\u308d\u3067\u4ed5\u4e8b\u3092\u3057\u3066\u3044\u308b\u3053\u3068\u3068\u3001\u8cea\u554f\u3055\u308c\u3066\u7fcc\u65e5\u306b\u7b54\u3048\u3066\u3082\u5f79\u306b\u7acb\u3064\u30ec\u30d9\u30eb\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001<\/p>\n
\u300c\u5c11\u3057\u52c9\u5f37(\u304a\u3055\u3089\u3044)\u3057\u3066\u304a\u3051\u3070\u3001\u4f55\u304b\u3057\u3089\u306e\u5f79\u306b\u306f\u7acb\u3064\u3093\u3058\u3083\u306d?\u300d<\/p>\n
\u3068\u601d\u3063\u305f\u306e\u3067\u3001\u3061\u3087\u3063\u3068\u52c9\u5f37\u3057\u3066\u307f\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n
\u305d\u3046\u3044\u3046\u3053\u3068\u306a\u306e\u3067\u3001\u9593\u9055\u3044\u3068\u304b\u305d\u3053\u305d\u3053\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u9069\u5f53\u306b\u88dc\u3063\u3066\u8aad\u3093\u3067\u3044\u305f\u3060\u3051\u308b\u3068\u5e78\u3044\u3067\u3059\u3002<\/p>\n
\u6700\u521d\u306e\u8cea\u554f\u306b\u5bfe\u3059\u308b\u56de\u7b54<\/h2>\n
\u307e\u305a\u3001\u6700\u521d\u306e\u8cea\u554f\u306b\u5bfe\u3059\u308b\u56de\u7b54\u304b\u3089\u8003\u3048\u3066\u307f\u307e\u3059\u3002<\/p>\n
FFT\u306e\u5165\u529b\u3068\u3059\u308b\u89b3\u6e2c\u30c7\u30fc\u30bf(\u30c7\u30fc\u30bf\u306f\u3059\u3079\u3066\u5b9f\u6570\u5024\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002)\u3092\u5f97\u308b\u305f\u3081\u306b\u8981\u3057\u305f\u6642\u9593\u3092$T$\u3068\u3057\u307e\u3059\u3002\u307e\u305f\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u306e\u9593\u9694\u3092$N$\u3068\u3059\u308b\u3068\u3001\u3053\u306e\u89b3\u6e2c\u30c7\u30fc\u30bf\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u5468\u6ce2\u6570$f_s$\u306f
\n\\[
\nf_s = \\frac{N}{T}
\n\\]
\n\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\u3053\u306e\u89b3\u6e2c\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066FFT\u3092\u5b9f\u884c\u3057\u305f\u7d50\u679c\u5f97\u3089\u308c\u308b\u30c7\u30fc\u30bf\u306f(\u8907\u7d20\u5171\u5f79\u306b\u306a\u3063\u3066\u3044\u308b\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\u3088\u308a\u5f8c\u306e\u90e8\u5206\u306f\u8ca0\u306e\u5468\u6ce2\u6570\u306e\u30c7\u30fc\u30bf\u3067\u3042\u308a\u3001\u5bfe\u5fdc\u3059\u308b\u6b63\u306e\u5468\u6ce2\u6570\u306e\u30c7\u30fc\u30bf\u304c\u5b58\u5728\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u3053\u3053\u3067\u306f\u9664\u5916\u3057\u3066\u8003\u3048\u308b\u3068)\u3001$\\displaystyle\\frac{N}{2}+1$\u70b9\u306e\u5468\u6ce2\u6570\u9818\u57df\u306e\u30b9\u30da\u30af\u30c8\u30eb\u30c7\u30fc\u30bf\u306b\u306a\u308a\u307e\u3059(“+1″\u306f\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\u6210\u5206\u306b\u76f8\u5f53\u3057\u307e\u3059)\u3002\u307e\u305f\u3001\u30c7\u30fc\u30bf\u306e\u793a\u3059\u30b9\u30da\u30af\u30c8\u30eb\u30c7\u30fc\u30bf\u306f\u5468\u6ce2\u6570$0$(\u76f4\u6d41\u6210\u5206)\u304b\u3089$\\displaystyle\\frac{f_s}{2}$(\u30ca\u30a4\u30ad\u30b9\u30c8\u5468\u6ce2\u6570\u6210\u5206)\u307e\u3067\u306e\u30c7\u30fc\u30bf\u306a\u306e\u3067\u3001\u5468\u6ce2\u6570\u9818\u57df\u306b\u304a\u3051\u308b\u30b9\u30da\u30af\u30c8\u30eb\u30c7\u30fc\u30bf\u306e\u9593\u9694(\u5468\u6ce2\u6570\u5206\u89e3\u80fd)$f_r$\u306f\u3001
\n\\[
\nf_r = \\frac{f_s\/2}{N\/2} = \\frac{f_s}{N} = \\frac{1}{T}
\n\\]
\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\u51b7\u9759\u306b\u8003\u3048\u308c\u3070\u305d\u308c\u307b\u3069\u96e3\u3057\u3044\u8a71\u3067\u306f\u306a\u3044\u3093\u3067\u3059\u304c\u3001\u304d\u308c\u3044\u3055\u3063\u3071\u308a\u5fd8\u308c\u3066\u307e\u3057\u305f\u306d\u3002<\/p>\n
(\u6025\u306b\u8cea\u554f\u304c\u6765\u305f\u304b\u3089\u3068\u3044\u3046\u3053\u3068\u306b\u3057\u3066\u304a\u3053\u3046\u2026)\u3002<\/del><\/div>\n\u3061\u3087\u3063\u3068\u6c17\u306b\u306a\u3063\u305f\u306e\u3067\u3001\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/h2>\n
\u3053\u3053\u3067\u306f\u3001\u5177\u4f53\u7684\u306a\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u8a08\u7b97\u3092\u884c\u308f\u306a\u3044\u307e\u307e\u8a18\u4e8b\u3092\u66f8\u3044\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u3044\u3063\u305f\u3093\u8003\u3048\u305f\u308a\u8abf\u3079\u305f\u308a\u3057\u59cb\u3081\u308b\u3068<\/p>\n
\u300c\u305d\u3046\u3044\u3048\u3070\u3001\u6b63\u5f26\u6ce2\u306eDFT\u3063\u3066\u3069\u3046\u3084\u3063\u3066\u6c42\u3081\u308b\u3093\u3060\u3063\u3051? \u3063\u3066\u304b\u3001\u306a\u3093\u3067$\\delta$\u95a2\u6570\u306b\u306a\u308b\u3093\u3060\u3063\u3051?\u300d<\/p>\n
\u3068\u304b\u3001\u6c17\u306b\u306a\u308a\u59cb\u3081\u305f\u308a\u3057\u3066\u591c\u3082\u7720\u308c\u306a\u304f\u306a\u308b\u3053\u3068\u306f\u4ee5\u524d\u307b\u3069\u306f\u306a\u304f\u306a\u3063\u305f(\u30d9\u30c3\u30c9\u3092\u30b7\u30e2\u30f3\u30ba\u306e\u3084\u3064<\/a>\u306b\u4ea4\u63db\u3057\u305f\u306e\u3067\u3001\u5bdd\u3064\u304d\u304c\u683c\u6bb5\u306b\u826f\u304f\u306a\u308a\u307e\u3057\u305f\u3002(\uff40\u30fb\u03c9\u30fb\u00b4))\u306e\u3067\u3059\u304c\u3001\u305d\u308c\u3067\u3082\u5c0e\u51fa\u65b9\u6cd5\u304f\u3089\u3044\u306f\u601d\u3044\u51fa\u3057\u3066\u304a\u304d\u305f\u304b\u3063\u305f\u306e\u3067\u3001\u4ed6\u306e\u30b5\u30a4\u30c8\u306e\u8a18\u4e8b\u3092\u53c2\u8003\u306b\u3057\u3064\u3064\u3001\u8a08\u7b97\u3057\u3066\u307f\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002<\/p>\n
\u307e\u305a\u3001\u4f59\u5f26\u95a2\u6570\u306eDFT\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/h3>\n
\u307e\u305a\u3001\u5468\u6ce2\u6570$f=\\displaystyle\\frac{f_0}{T}\\left(0 < f_0 \\le \\displaystyle\\frac{N}{2}, f_0 \\in \\mathbb{N} \\right)$\u306e\u4f59\u5f26\u95a2\u6570(\u306e\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u30c7\u30fc\u30bf)
\n\\[
\nx_t = \\cos \\left(\\displaystyle\\frac{2\\pi j f_0 t}{N}\\right)
\n\\]
\n($j$\u306f\u865a\u6570\u5358\u4f4d)\u306b\u5bfe\u3057\u3066DFT\u3092\u5b9f\u884c\u3057\u3066\u307f\u307e\u3059\u3002\u4e0a\u5f0f\u306e\u53f3\u8fba\u306b\u767b\u5834\u3059\u308b\\(f_0\\)\u306f\u5b9f\u969b\u306e\u5468\u6ce2\u6570\u3068\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u306e\u6bd4\u3092\u8868\u3057\u307e\u3059\u3002\u307e\u305f\u3001\\(t\\)\u306f\u89b3\u6e2c\u30c7\u30fc\u30bf\u306e\u89b3\u6e2c\u9593\u9694\u30921\u3068\u3057\u305f\u76f8\u5bfe\u7684\u306a\u7d4c\u904e\u6642\u523b\u3067\u3059\u3002\u524d\u7bc0\u3067\u306e\u8b70\u8ad6\u306e\u901a\u308a\u3001\u89b3\u6e2c\u30c7\u30fc\u30bf\u3092\u5f97\u308b\u305f\u3081\u306b\u8981\u3057\u305f\u6642\u9593\u306f\u5468\u6ce2\u6570\u5206\u89e3\u80fd\u306e\u9006\u6570\u306b\u306a\u3063\u3066\u3044\u308b\u305f\u3081\u306b\u6253\u3061\u6d88\u3057\u5408\u3046\u306e\u3067\u3001\u4e0a\u8a18\u306e\u53f3\u8fba\u306b\u306f\u76f4\u63a5\u73fe\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n(\u2191\u306e\u8b70\u8ad6\u306f\u5fd8\u308c\u304c\u3061\u306b\u306a\u308b\u3068\u3053\u308d\u3067\u3059\u3002)<\/div>\n\u3059\u308b\u3068\u3001\u5909\u63db\u306e\u7d50\u679c\u5f97\u3089\u308c\u308b\u30b9\u30da\u30af\u30c8\u30eb\u30c7\u30fc\u30bf$X_f$\u306f\u4ee5\u4e0b\u306e\u5f0f\u3067\u8868\u3055\u308c\u307e\u3059\u3002
\n\\[
\nX_f = \\sum^{N-1}_{t=0}\\,x_t\\,e^{-\\frac{2\\pi jft}{N}}
\n\\]<\/p>\n$x_t = \\displaystyle\\frac{1}{2}\\left(e^{\\frac{2\\pi j f_0 t}{N}}+e^{-\\frac{2\\pi j f_0 t}{N}}\\right)$\u3068\u5909\u5f62\u3057\u3066\u304b\u3089\u4e0a\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n
\\[
\nX_f = \\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2}\\left\\{e^{\\frac{2\\pi j t}{N}(f_0-f)}+e^{\\frac{2\\pi j t}{N}(-f_0-f)}\\right\\}
\n\\]<\/p>\n\u4e0a\u5f0f\u306e\u53f3\u8fba\u7b2c2\u9805\u306b$e^{-2\\pi j t}$($t$\u304c\u6574\u6570\u306a\u306e\u30671\u306b\u306a\u308a\u307e\u3059\u3002)\u3092\u304b\u3051\u308b\u3068\u3001<\/p>\n
\\begin{eqnarray}
\nX_f &=& \\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2}\\left\\{e^{\\frac{2\\pi j t}{N}(f_0-f)}+e^{-2\\pi j t}\\,e^{\\frac{2\\pi j t}{N}(-f_0-f)}\\right\\} \\nonumber \\\\
\n{} &=& \\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2}\\left\\{e^{\\frac{2\\pi j t}{N}(f_0-f)}+e^{-\\frac{2\\pi j t}{N}(N-f_0-f)}\\right\\} \\nonumber \\\\
\n{} &=& \\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2}e^{\\frac{2\\pi j t}{N}(f_0-f)}+\\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2}e^{-\\frac{2\\pi j t}{N}(N-f_0-f)} \\label{eq:fftfirsteq}
\n\\end{eqnarray}<\/p>\n\u3068\u5f0f\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n
(\\ref{eq:fftfirsteq})\u5f0f\u53f3\u8fba\u306e\u5404\u9805\u306f\u3068\u3082\u306b\u7b49\u6bd4\u7d1a\u6570\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u307e\u305a\u7b2c1\u9805\u306b\u3064\u3044\u3066\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
\u7b2c1\u9805\u306f$f = f_0$\u304b\u5426\u304b\u3067\u5834\u5408\u5206\u3051\u304c\u5fc5\u8981\u3067\u3001$f = f_0$\u306e\u5834\u5408\u306b\u306f\u51aa\u306e\u90e8\u5206\u304c0\u306b\u306a\u308a\u307e\u3059\u306e\u3067\u3001$e^{\\frac{2\\pi j t}{N}(f_0-f)} = 1$\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001$f \\neq f_0$\u306e\u5834\u5408\u306b\u306f\u3001<\/p>\n
\\begin{eqnarray}
\n\\sum^{N-1}_{t=0}\\,e^{\\frac{2\\pi j t}{N}(f_0-f)} &=& \\displaystyle\\frac{1-e^{2\\pi j(f_0-f)}}{1-e^{\\frac{2\\pi j t}{N}(f_0-f)}}
\n\\end{eqnarray}<\/p>\n\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\\(f_0\\)\u53ca\u3073\\(f\\)\u306f\u6574\u6570\u306a\u306e\u3067\u3001\u4e0a\u5f0f\u53f3\u8fba\u306e\u5206\u5b50\u306e\u5024\u306f0\u3068\u306a\u308a\u307e\u3059\u3002\u3088\u3063\u3066\u3001\u4e0a\u5f0f\u5de6\u8fba\u306e\u5024\u30820\u3068\u306a\u308a\u307e\u3059\u306e\u3067\u3001(\\ref{eq:fftfirsteq})\u5f0f\u53f3\u8fba\u306e\u7b2c1\u9805\u306f\u30af\u30ed\u30cd\u30c3\u30ab\u30fc\u306e\u30c7\u30eb\u30bf\\(\\delta_{t,t^{\\prime}}\\)\u3092\u7528\u3044\u3066\u3001<\/p>\n
\\begin{eqnarray}
\n\\sum^{N-1}_{t=0}\\,e^{\\frac{2\\pi j t}{N}(f_0-f)} = N\\delta_{f_0,f} \\label{eq:deltaf0f}
\n\\end{eqnarray}<\/p>\n\u3068\u306a\u308a\u307e\u3059\u3002(\\ref{eq:fftfirsteq})\u5f0f\u53f3\u8fba\u7b2c2\u9805\u306b\u3064\u3044\u3066\u3082\\(N-f_0\\)\u53ca\u3073\\(f\\)\u306b\u3064\u3044\u3066\u540c\u69d8\u306e\u8b70\u8ad6\u304c\u3067\u304d\u307e\u3059\u306e\u3067\u3001<\/p>\n
\\begin{eqnarray}
\n\\sum^{N-1}_{t=0}\\,e^{\\frac{2\\pi j t}{N}(N-f_0-f)} = N\\delta_{N-f_0,f} \\label{eq:deltaNf0f}
\n\\end{eqnarray}<\/p>\n\u3068\u306a\u308a\u307e\u3059\u3002(\\ref{eq:deltaf0f}),(\\ref{eq:deltaNf0f})\u5f0f\u3092(\\ref{eq:fftfirsteq})\u5f0f\u306e\u53f3\u8fba\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n
\\begin{eqnarray}
\nX_f &=& \\displaystyle\\frac{1}{2}(N\\delta_{f_0,f} + N\\delta_{N-f_0,f}) \\\\
\n{} &=& \\displaystyle\\frac{N}{2}(\\delta_{f_0,f} + \\delta_{N-f_0,f})
\n\\end{eqnarray}<\/p>\n\u3068\u306a\u308a\u307e\u3059\u3002\u6b63\u306e\u5468\u6ce2\u6570\u3068\u8ca0\u306e\u5468\u6ce2\u6570\u306e\u6210\u5206\u304c\u51fa\u3066\u304d\u307e\u3059\u304c\u3001\\(N \\to \\infty\\)\u3068\u3059\u308b\u3068\u3001\u30c7\u30eb\u30bf\u95a2\u6570\u3063\u307d\u304f\u306a\u308a\u307e\u3059\u306d\u3002<\/p>\n
\u6b63\u5f26\u95a2\u6570\u306eDFT\u7b49\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/h3>\n
\u6b21\u306b\u3001
\n\\[
\nx_t = \\sin \\left(\\displaystyle\\frac{2\\pi j f_0 t}{N}\\right)
\n\\]<\/p>\n\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4f59\u5f26\u95a2\u6570\u306e\u5834\u5408\u3068\u540c\u69d8\u306b<\/p>\n
\\begin{eqnarray}
\nx_t &=& \\sin \\left(\\displaystyle\\frac{2\\pi j f_0 t}{N}\\right) \\\\
\n{} &=& \\displaystyle\\frac{1}{2j}\\left(e^{\\frac{2\\pi j f_0 t}{N}}-e^{-\\frac{2\\pi j f_0 t}{N}}\\right)
\n\\end{eqnarray}
\n\u3068\u8868\u305b\u308b\u3053\u3068\u3092\u5229\u7528\u3057\u3066\u3001<\/p>\n\\begin{eqnarray}
\nX_f &=& \\sum^{N-1}_{t=0}\\,\\displaystyle\\frac{1}{2j}(\\delta_{f_0,f} – \\delta_{N-f_0,f}) \\\\
\n{} &=& \\displaystyle\\frac{N}{2j}(\\delta_{f_0,f} – \\delta_{N-f_0,f})
\n\\end{eqnarray}<\/p>\n\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u30022\u500b\u306e\u30c7\u30eb\u30bf\u95a2\u6570\u3063\u307d\u3044\u95a2\u6570\u306e\u91cd\u306d\u5408\u308f\u305b\u3067\u8868\u73fe\u3055\u308c\u308b\u306e\u306f\u4f59\u5f26\u95a2\u6570\u306e\u5834\u5408\u3068\u540c\u69d8\u3067\u3059\u304c\u3001\u6b63\u306e\u5468\u6ce2\u6570\u6210\u5206\u306f\u4f59\u5f26\u95a2\u6570\u306e\u6b63\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u8907\u7d20\u5e73\u9762\u4e0a\u3067\\(- \\displaystyle\\frac{\\pi}{2}\\)\u3060\u3051\u3001\u8ca0\u306e\u5468\u6ce2\u6570\u6210\u5206\u306f\u4f59\u5f26\u95a2\u6570\u306e\u8ca0\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u8907\u7d20\u5e73\u9762\u4e0a\u3067\\(\\displaystyle\\frac{\\pi}{2}\\)\u3060\u3051\u56de\u8ee2\u3057\u305f\u3082\u306e\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n
\u3082\u3046\u3061\u3087\u3063\u3068\u4e00\u822c\u306b\u3001\u4f4d\u76f8(\u521d\u671f\u4f4d\u76f8)\\(\\phi\\)\u306e\u6b63\u5f26\u95a2\u6570<\/p>\n
\\[
\nx_t = \\sin \\left(\\displaystyle\\frac{2\\pi j f_0 t}{N}+\\phi\\right)
\n\\]<\/p>\n\u306eDFT\u306f<\/p>\n
\\begin{eqnarray}
\nX_f&=&\\displaystyle\\frac{N}{2j}(\\delta_{f_0,f}e^{j\\phi} – \\delta_{N-f_0,f}e^{-j\\phi})
\n\\end{eqnarray}<\/p>\n\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u307e\u3068\u3081<\/h2>\n
\u3053\u3053\u307e\u3067\u8d85\u7c21\u5358\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3001\u7279\u306bDFT\u3092\u4e2d\u5fc3\u306b\u304a\u3055\u3089\u3044\u3057\u305f\u3053\u3068\u3092\u66f8\u304d\u307e\u3057\u305f\u3002<\/p>\n
\u6700\u8fd1\u306ffftw\u307f\u305f\u3044\u306a\u512a\u79c0\u306a\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u3042\u3063\u305f\u308a\u3059\u308b\u306e\u3067\u3001\u81ea\u5206\u3067FFT\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u3089\u306a\u304f\u3066\u3082\u30c7\u30fc\u30bf\u3092\u98df\u308f\u305b\u308c\u3070\u8a08\u7b97\u7d50\u679c\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3001\u8a08\u7b97\u7d50\u679c\u306e\u898b\u65b9\u3084\u8a08\u7b97\u7d50\u679c\u306b\u5bfe\u3059\u308b\u89e3\u6790\u306e\u65b9\u6cd5\u304f\u3089\u3044\u306f\u982d\u306b\u5165\u3063\u3066\u3044\u306a\u3044\u3068\u3001\u307e\u305f\u6b21\u306b\u6025\u306b\u8cea\u554f\u304c\u6765\u305f\u6642\u306b\u5bfe\u5fdc\u3067\u304d\u306a\u3044\u306e\u3067\u3001\u304a\u3055\u3089\u3044\u306e\u30bf\u30a4\u30df\u30f3\u30b0\u3068\u3057\u3066\u306f\u60aa\u304f\u306f\u306a\u304b\u3063\u305f\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n
\u53c2\u8003\u6587\u732e<\/h2>\n
\u672c\u8a18\u4e8b\u3092\u66f8\u304f\u306b\u3042\u305f\u308a\u3001\u4ee5\u4e0b\u306e\u30b5\u30a4\u30c8\u306e\u8a18\u4e8b\u3092\u53c2\u8003\u306b\u3057\u307e\u3057\u305f\u3002\u7b46\u8005\u306e\u7686\u69d8\u65b9\u306b\u306f\u611f\u8b1d\u7533\u3057\u4e0a\u3052\u307e\u3059\u3002<\/p>\n
\n
- \u5c0f\u91ce\u6e2c\u5668-FFT\u57fa\u672c FAQ -\u300c\u5468\u6ce2\u6570\u6570\u5206\u89e3\u80fd\u306f\u3069\u306e\u3088\u3046\u306b\u6c7a\u3081\u308b\u306e\u304b\uff1f \u300d<\/a><\/li>\n
- \u6b63\u5f26\u6ce2\u306eDFT<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
\u306f\u3058\u3081\u306b \u5148\u65e5(\u3068\u3044\u3063\u3066\u30821\u9031\u9593\u304f\u3089\u3044\u524d\u306e\u3053\u3068\u3067\u3059\u304c)\u3001 \u5b9f\u9a13\u3067\u53d6\u5f97\u3057\u305f\u30c7\u30fc\u30bf\u3092FFT\u3067\u5909\u63db\u3057\u3001\u305d\u306e\u7d50\u679c\u5f97\u3089\u308c\u305f\u5468\u6ce2\u6570\u9818\u57df\u306e\u30c7\u30fc\u30bf\u306e\u5404\u70b9\u306e\u300c\u5468\u6ce2\u6570\u8ef8\u300d\u65b9\u5411\u306e\u9593\u9694\u3063\u3066\u3001\u3069\u3046\u8a08\u7b97\u3059\u308c\u3070\u3088\u3044\u304b\u308f\u304b\u308a\u307e\u3059\u304b? \u3068\u3044\u3046\u8da3\u65e8\u306e\u8cea\u554f\u3092\u53d7\u3051\u305f\u306e\u3067\u3059\u304c\u3001\u5373\u7b54\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\u3001\u6b21\u306e\u65e5\u306b\u56de\u7b54\u3059\u308b\u3088\u3046\u306a\u3053\u3068\u3068\u306a\u3063\u3066\u3057\u307e\u3044\u307e\u3057\u305f\u3002\u304a\u6065\u305a\u304b\u3057\u3044\u9650\u308a\u3067\u3059\u3002( ;\u00b4\uff65\u03c9\uff65`) FFT,DFT,DCT\u306a\u3069\u306e\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u65b9\u9762\u306f\u4eca\u306e\u4ed5\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-1269","post","type-post","status-publish","format-standard","hentry","category-13"],"_links":{"self":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/1269","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1269"}],"version-history":[{"count":95,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/1269\/revisions"}],"predecessor-version":[{"id":9330,"href":"https:\/\/pandanote.info\/index.php?rest_route=\/wp\/v2\/posts\/1269\/revisions\/9330"}],"wp:attachment":[{"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1269"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1269"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pandanote.info\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1269"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}