{"id":100,"date":"2026-02-15T22:10:28","date_gmt":"2026-02-15T13:10:28","guid":{"rendered":"https:\/\/blog.gamtecs.org\/?p=100"},"modified":"2026-02-23T16:42:38","modified_gmt":"2026-02-23T07:42:38","slug":"%e3%83%95%e3%83%bc%e3%83%aa%e3%82%a8%e5%a4%89%e6%8f%9b%e3%82%92%e6%b4%bb%e7%94%a8%e3%81%97%e3%81%a6%e3%83%95%e3%82%a3%e3%83%ab%e3%82%bf%e3%82%92%e8%a8%ad%e8%a8%88%e3%81%97%e3%81%a6%e3%81%bf%e3%82%88-2","status":"publish","type":"post","link":"https:\/\/blog.gamtecs.org\/?p=100","title":{"rendered":"\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3092\u6d3b\u7528\u3057\u3066\u30d5\u30a3\u30eb\u30bf\u3092\u8a2d\u8a08\u3057\u3066\u307f\u3088\u3046 #2"},"content":{"rendered":"\n

\u524d\u56de\u306f\u3053\u3061\u3089<\/a><\/p>\n\n\n\n

\u524d\u56de\u89e3\u8aac\u3057\u305f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306b\u3064\u3044\u3066\uff0c\u5b9f\u6570\u3092\u7528\u3044\u308b\u3053\u3068\u304b\u3089\uff0c\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3068\u547c\u79f0\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n

\u5b9f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306b\u5bfe\u3057\u3066\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u306b\u4f9d\u3063\u3066\u8907\u7d20\u6570\u3092\u5c0e\u5165\u3057\u305f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3092\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n\n\n\n

\u4eca\u56de\u306f\uff0c\u4e3b\u306b\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306b\u3064\u3044\u3066\u89e3\u8aac\u3057\uff0c\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3078\u306e\u5c0e\u5165\u3068\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n\n\n\n

1. \u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f<\/h2>\n\n\n\n

\u9ad8\u6821\u6570\u5b66\u3067\u7528\u3044\u305f\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u3092\u601d\u3044\u51fa\u3057\u307e\u3057\u3087\u3046\uff0e\u865a\u6570\u5358\u4f4d\u3092j<\/mi>j<\/annotation><\/semantics><\/math>\u3068\u3059\u308c\u3070\uff0c\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n\n\n\n
e<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>=<\/mo>cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>+<\/mo>j<\/mi><\/mspace>sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi><\/mrow>e^{j\\theta} = \\cos\\theta + j\\sin\\theta<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u308c\u3092cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi><\/mrow>\\cos\\theta<\/annotation><\/semantics><\/math>\u304a\u3088\u3073sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi><\/mrow>\\sin\\theta<\/annotation><\/semantics><\/math>\u306b\u3064\u3044\u3066\u89e3\u3051\u3070\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n
cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>=<\/mo>e<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>+<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>\u03b8<\/mi><\/mrow><\/msup><\/mrow>2<\/mn><\/mfrac>,<\/mo><\/mspace>sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>=<\/mo>e<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>\u2212<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>\u03b8<\/mi><\/mrow><\/msup><\/mrow>2<\/mn>j<\/mi><\/mrow><\/mfrac><\/mrow>\\cos\\theta = \\frac{e^{j\\theta} + e^{-j\\theta}}{2}, \\quad \\sin\\theta = \\frac{e^{j\\theta} – e^{-j\\theta}}{2j}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

2. \u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u304b\u3089\u306e\u9077\u79fb<\/h2>\n\n\n\n

\u3055\u3066\uff0c\u524d\u56de\u89e3\u8aac\u3057\u305f\u901a\u308a\uff0c\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306f\u4ee5\u4e0b\u3067\u793a\u3055\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n

x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>[<\/mo>a<\/mi>n<\/mi><\/msub>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>+<\/mo>b<\/mi>n<\/mi><\/msub>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>]<\/mo><\/mrow><\/mrow>x(t)=\\frac{a_0}{2}+\\sum_{n=1}^{\\infty}\\left[a_n\\cos(n\\omega_0 t)+b_n\\sin(n\\omega_0 t)\\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u3053\u3067\u03b8<\/mi>=<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow>\\theta=n\\omega_0t<\/annotation><\/semantics><\/math>\u3068\u3057\u3066\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u4e09\u89d2\u95a2\u6570\u3092\u4ee3\u5165\u3057\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>[<\/mo>a<\/mi>n<\/mi><\/msub>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>+<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>2<\/mn><\/mfrac>+<\/mo>b<\/mi>n<\/mi><\/msub>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>\u2212<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>2<\/mn>j<\/mi><\/mrow><\/mfrac>]<\/mo><\/mrow><\/mstyle>\\displaystyle x(t) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\left[ a_n \\frac{e^{jn\\omega_0 t} + e^{-jn\\omega_0 t}}{2} + b_n \\frac{e^{jn\\omega_0 t} – e^{-jn\\omega_0 t}}{2j} \\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n\n\n

\u3053\u308c\u3092e<\/mi>\u00b1<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>e^{\\pm jn\\omega_0 t}<\/annotation><\/semantics><\/math>\u3067\u6574\u7406\u3059\u308c\u3070\uff0c<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>[<\/mo>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>+<\/mo>a<\/mi>n<\/mi><\/msub>+<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>]<\/mo><\/mrow><\/mrow>x(t) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\left[ \\frac{a_n – jb_n}{2} e^{jn\\omega_0 t} + \\frac{a_n + jb_n}{2} e^{-jn\\omega_0 t} \\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff081<\/mn>j<\/mi><\/mfrac>=<\/mo>\u2212<\/mo>j<\/mi><\/mrow>\\frac{1}{j} = -j<\/annotation><\/semantics><\/math>\u3092\u7528\u3044\u305f\uff09\uff0e<\/p>\n\n\n\n

\u3053\u3053\u3067\uff0ce<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math>\u304a\u3088\u3073e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>e^{-jn\\omega_0 t}<\/annotation><\/semantics><\/math>\u306b\u639b\u304b\u308b\u4fc2\u6570\u3092\u305d\u308c\u305e\u308cA, B\u3068\u3057\u3066\u898b\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>[<\/mo>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>\u23df<\/mo><\/munder>(<\/mo>A<\/mi>)<\/mo><\/mrow><\/munder><\/mrow>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>+<\/mo>a<\/mi>n<\/mi><\/msub>+<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>\u23df<\/mo><\/munder>(<\/mo>B<\/mi>)<\/mo><\/mrow><\/munder><\/mrow>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>]<\/mo><\/mrow><\/mrow>x(t) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\left[ \\underbrace{\\frac{a_n – jb_n}{2}}_{(A)} e^{jn\\omega_0 t} + \\underbrace{\\frac{a_n + jb_n}{2}}_{(B)} e^{-jn\\omega_0 t} \\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u2211<\/mo>\\sum<\/annotation><\/semantics><\/math>\u3092A, B\u306b\u305d\u308c\u305e\u308c\u5206\u914d\u3057\u3066\u307f\u308b\u3068\uff0c<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>a<\/mi>n<\/mi><\/msub>+<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>x(t) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\frac{a_n – jb_n}{2} e^{jn\\omega_0 t} + \\sum_{n=1}^{\\infty} \\frac{a_n + jb_n}{2} e^{-jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e\u3053\u3053\u3067\uff0cB\u306b\u639b\u3051\u3089\u308c\u308b\u2211<\/mo>\\sum<\/annotation><\/semantics><\/math>\u306b\u3064\u3044\u3066\uff0cB\u306b\u304a\u3051\u308be<\/mi>e<\/annotation><\/semantics><\/math>\u306f\u8ca0\u306e\u7d2f\u4e57\u3067\u3042\u308b\u304b\u3089\uff0c\u8ca0\u5024\u306e\u7bc4\u56f2\u306b\u304a\u3051\u308b\u6f14\u7b97\u3068\u7f6e\u304d\u307e\u3057\u3087\u3046\uff0e\u305d\u3046\u3059\u308c\u3070e<\/mi>e<\/annotation><\/semantics><\/math>\u306e\u7d2f\u4e57\u306b\u304a\u3051\u308b\u7b26\u53f7\u304c\u63c3\u3046\u306e\u3067\uff0c\u6271\u3044\u3084\u3059\u305d\u3046\u3067\u3059\uff0e<\/p>\n\n\n\n
\u2211<\/mo>n<\/mi>=<\/mo>\u2212<\/mo>\u221e<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/munderover><\/mrow>a<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub>+<\/mo>j<\/mi>b<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>\\sum_{n=-\\infin}^{-1} \\frac{a_{-n} + jb_{-n}}{2} e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3088\u3063\u3066\uff0c<\/p>\n\n\n\n

x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>\u2212<\/mo>\u221e<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/munderover><\/mrow>a<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub>+<\/mo>j<\/mi>b<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>x(t) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\frac{a_n – jb_n}{2} e^{jn\\omega_0 t} +\\sum_{n=-\\infin}^{-1} \\frac{a_{-n} +jb_{-n}}{2} e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e\u3059\u306a\u308f\u3061\uff0c\u5909\u6570\u304c\uff1a<\/p>\n\n\n\n

\u30fb\u8ca0\u3067\u3042\u308c\u3070\uff0c<\/p>\n\n\n\n

\u2211<\/mo>n<\/mi>=<\/mo>\u2212<\/mo>\u221e<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/munderover><\/mrow>a<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub>+<\/mo>j<\/mi>b<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>\\sum_{n=-\\infty}^{-1} \\frac{a_{-n} + jb_{-n}}{2} e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u30fb\uff10\u3067\u3042\u308c\u3070<\/p>\n\n\n\n

a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>e<\/mi>j<\/mi>0<\/mn>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>\\frac{a_0}{2} e^{j0\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u30fb\u6b63\u3067\u3042\u308c\u3070<\/p>\n\n\n\n

\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>\\sum_{n=1}^{\\infty} \\frac{a_n – jb_n}{2} e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u306e\u9805\u304c\u7528\u3044\u3089\u308c\u308b\u308f\u3051\u3067\u3059\uff0e\u5909\u6570\u304c\u2212<\/mo>\u221e<\/mi><\/mrow>-\\infin<\/annotation><\/semantics><\/math>~\u221e<\/mi>\\infin<\/annotation><\/semantics><\/math>\u307e\u3067\u9023\u7d9a\u7684\u3067\u3042\u308b\u3053\u3068\uff0c\u5168\u3066\u306e\u9805\u304ce<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math>\u306e\u4fc2\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u8e0f\u307e\u3048\u3066\uff0c\u3053\u308c\u3089\u3092\u3042\u308b1\u3064\u306e\u5909\u6570\u3068\u3057\u3066\u307e\u3068\u3081\u3066\u3057\u307e\u3048\u3070\uff0c\u3088\u308a\u6271\u3044\u3084\u3059\u3044\u5f62\u306b\u306a\u308a\u305d\u3046\u3067\u3059\uff0e<\/p>\n\n\n\n

\u3053\u306e”\u3042\u308b1\u3064\u306e\u5909\u6570”\u3092c<\/mi>n<\/mi><\/msub>c_n<\/annotation><\/semantics><\/math>\u3068\u3057\u3066\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>c_n<\/annotation><\/semantics><\/math>\u306b\u3064\u3044\u3066\u5b9a\u7fa9\u3059\u308c\u3070\uff0c\u4e0a\u8a18\u3088\u308a<\/p>\n\n\n\n
c<\/mi>n<\/mi><\/msub>=<\/mo>{<\/mo>a<\/mi>n<\/mi><\/msub>\u2212<\/mo>j<\/mi>b<\/mi>n<\/mi><\/msub><\/mrow>2<\/mn><\/mfrac><\/mstyle><\/mtd>(<\/mo>n<\/mi>><\/mo>0<\/mn>)<\/mo><\/mrow><\/mtd><\/mtr>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac><\/mstyle><\/mtd>(<\/mo>n<\/mi>=<\/mo>0<\/mn>)<\/mo><\/mrow><\/mtd><\/mtr>a<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub>+<\/mo>j<\/mi>b<\/mi>\u2212<\/mo>n<\/mi><\/mrow><\/msub><\/mrow>2<\/mn><\/mfrac><\/mstyle><\/mtd>(<\/mo>n<\/mi><<\/mo>0<\/mn>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>c_n = \\begin{cases} \\displaystyle \\frac{a_n – jb_n}{2} & (n > 0 ) \\\\[10pt] \\displaystyle \\frac{a_0}{2} & (n = 0) \\\\[10pt] \\displaystyle \\frac{a_{-n} + jb_{-n}}{2} & (n < 0 ) \\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\uff0c\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u5f0f\u306f<\/p>\n\n\n\n

x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>\u2212<\/mo>\u221e<\/mi><\/mrow>\u221e<\/mi><\/munderover><\/mrow>c<\/mi>n<\/mi><\/msub>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>x(t) = \\sum_{n=-\\infty}^{\\infty} c_n e^{jn\\omega_0 t}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u304b\u3089\uff0c<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>T<\/mi><\/mfrac>\u222b<\/mo>0<\/mn>T<\/mi><\/msubsup>x<\/mi>(<\/mo>t<\/mi>)<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>d<\/mi>t<\/mi><\/mrow>c_n = \\frac{1}{T} \\int_{0}^{T} x(t) e^{-jn\\omega_0 t} dt<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u3044\u3046\u5f62\u3067\u307e\u3068\u3081\u3089\u308c\u307e\u3059\uff0e\u7c21\u5358\u3067\u3059\u306d\uff0c\u7b26\u53f7\u3092\u63c3\u3048\u305f\u308a\uff0c\u4fc2\u6570\u3067\u307e\u3068\u3081\u305f\u7532\u6590\u304c\u5728\u308a\u307e\u3057\u305f\uff0e<\/p>\n\n\n\n

3.\u3053\u3053\u307e\u3067\u306e\u307e\u3068\u3081\uff1a\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3092\u5b9f\u8df5<\/h2>\n\n\n\n

\u4efb\u610f\u306e\u4fe1\u53f7\u306f\uff0c\u5168\u3066\u6b63\u5f26\u6ce2\u306e\u8db3\u3057\u5408\u308f\u305b\u3067\u8868\u3055\u308c\u307e\u3059\uff0e\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u304a\u3088\u3073\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306f\uff0c\u305d\u306e\u4fe1\u53f7\u304b\u3089\uff0c\u3069\u306e\u5468\u6ce2\u6570\u306e\u6b63\u5f26\u6ce2\uff08\u5468\u6ce2\u6570\u6210\u5206\uff09\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u306e\u304b\u3092\u53d6\u308a\u51fa\u3059\u305f\u3081\u306e\u6f14\u7b97\u3067\u3042\u308a\uff0c\u7279\u306b\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306f\u5468\u671f\u4fe1\u53f7\u306b\u304a\u3051\u308b\u5468\u6ce2\u6570\u6210\u5206\u3092\u53d6\u308a\u51fa\u3057\u307e\u3059\uff0e\u3053\u306e\u64cd\u4f5c\u306b\u3088\u3063\u3066\u53d6\u308a\u51fa\u3055\u308c\u305f\u5468\u6ce2\u6570\u6210\u5206\u3092\u53ef\u8996\u5316\u3057\u305f\u3082\u306e\u3092\uff0c\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb\u3068\u8a00\u3044\u307e\u3059(fig.1)\uff0e<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

fig.1 \u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306e\u30a4\u30e1\u30fc\u30b8\u56f3 (AllElectroHub<\/a>)<\/p>\n\n\n\n

\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306f\u5468\u671f\u4fe1\u53f7\u304c\u5bfe\u8c61\u3067\u3059\uff0e\u5468\u671f\u4fe1\u53f7\u3068\u306f\uff0c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u3053\u3093\u306a\u6ce2\u5f62\u3060\u3063\u305f\u308a\uff0c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u3053\u3093\u306a\u6ce2\u5f62\u3060\u3063\u305f\u308a\uff0c<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u3053\u3093\u306a\u6ce2\u5f62\u3092\u793a\u3059\u4fe1\u53f7\u3092\u6307\u3057\u307e\u3059\uff0e\u3088\u3046\u306f\u4e00\u5b9a\u5468\u671f\u3067\u540c\u3058\u6ce2\u5f62\u3092\u7e70\u308a\u8fd4\u3059\u4fe1\u53f7\u3092\u5468\u671f\u4fe1\u53f7\u3068\u8a00\u3044\u307e\u3059\uff08\u3053\u308c\u3089\u306e\u3088\u3046\u306b\uff0c\u7dba\u9e97\u306a\u5f62\u306e\u3082\u306e\u3070\u304b\u308a\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\uff09\uff0e<\/p>\n\n\n\n

\u4eca\u307e\u3067\u5b66\u7fd2\u3057\u305f\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\uff0c\u304a\u3088\u3073\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306b\u3088\u3063\u3066\uff0c\u4eca\u56de\u306f\u77e9\u5f62\u6ce2\uff08\u4e00\u756a\u4e0b\u306e\u56db\u89d2\u5f62\u306e\u6ce2\uff0c\u304f\u3051\u3044\u306f\uff09\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\uff0e\u96fb\u5b50\u56de\u8def\u306b\u304a\u3044\u3066\u7528\u3044\u3089\u308c\u308b\u5834\u9762\u304c\u591a\u3044\u3067\u3059\u304b\u3089\u306d\uff0e<\/p>\n\n\n\n

3.1. \u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3067\u6c42\u3081\u308b<\/h2>\n\n\n\n

\u5468\u671fT<\/mi>T<\/annotation><\/semantics><\/math>\u306e\uff0c\u3042\u308b\u77e9\u5f62\u6ce2\u306e\u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u3092\u8003\u3048\u307e\u3059(fig.2)\uff0e<\/p>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

fig.2 \u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u306e\u6982\u5f62<\/p>\n\n\n\n

\u3053\u306e\u4fe1\u53f7\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u306d\uff0e<\/p>\n\n\n\n

x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>{<\/mo>1<\/mn><\/mtd>(<\/mo>0<\/mn>\u2264<\/mo>t<\/mi><<\/mo>T<\/mi>2<\/mn><\/mfrac>)<\/mo><\/mrow><\/mtd><\/mtr>\u2212<\/mo>1<\/mn><\/mrow><\/mtd>(<\/mo>T<\/mi>2<\/mn><\/mfrac>\u2264<\/mo>t<\/mi><<\/mo>T<\/mi>)<\/mo><\/mrow><\/mtd><\/mtr>0<\/mn><\/mtd>(<\/mo>otherwise<\/mtext>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>x(t) = \n\\begin{cases}\n1 & (0 \\le t < \\frac{T}{2}) \\\\[10pt]\n-1 & (\\frac{T}{2} \\le t < T) \\\\[10pt]\n0 & (\\text{otherwise})\n\\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u307e\u305f\u4f55\u5ea6\u3082\u8cbc\u308a\u307e\u3059\u304c\uff0c\u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u306e\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u307e\u3059\uff0e<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>a<\/mi>0<\/mn><\/msub>2<\/mn><\/mfrac>+<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>[<\/mo>a<\/mi>n<\/mi><\/msub>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>+<\/mo>b<\/mi>n<\/mi><\/msub>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>]<\/mo><\/mrow><\/mrow>x(t)=\\frac{a_0}{2}+\\sum_{n=1}^{\\infty}\\left[a_n\\cos(n\\omega_0 t)+b_n\\sin(n\\omega_0 t)\\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u3053\u306b\u542b\u307e\u308c\u308b\u4fc2\u6570a<\/mi>0<\/mn><\/msub>,<\/mo>a<\/mi>n<\/mi><\/msub>,<\/mo>b<\/mi>n<\/mi><\/msub><\/mrow>a_0, a_n, b_n<\/annotation><\/semantics><\/math>\u3092\u6c42\u3081\u308c\u3070\uff0c\u5468\u6ce2\u6570\u6210\u5206\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u306d\uff0e<\/p>\n\n\n\n

\u524d\u56de\u6c42\u3081\u305f\u901a\u308a\uff0ca<\/mi>0<\/mn><\/msub>a_0<\/annotation><\/semantics><\/math>\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u307e\u3059\uff1a<\/p>\n\n\n\n
a<\/mi>0<\/mn><\/msub>=<\/mo>1<\/mn>T<\/mi><\/mfrac>\u222b<\/mo>0<\/mn>T<\/mi><\/msubsup>x<\/mi>(<\/mo>t<\/mi>)<\/mo>d<\/mi>t<\/mi><\/mrow>a_0 = \\frac{1}{T} \\int_{0}^{T} x(t) dt<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u660e\u3089\u304b\u306b\u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u306e\u5e73\u5747\u5024\uff08\u76f4\u6d41\u6210\u5206\uff09\u3092\u793a\u3057\u307e\u3059\uff0e\u5b9a\u7fa9\u3088\u308a\uff0c\u8a08\u7b97\u3059\u308b\u307e\u3067\u3082\u306a\u304f\u5e73\u5747\u306f0\u3068\u306a\u308a\u307e\u3059\u304b\u3089\uff0c<\/p>\n\n\n\n
a<\/mi>0<\/mn><\/msub>=<\/mo>0<\/mn><\/mrow>a_0=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u307e\u305f\u540c\u69d8\u306b\uff0ca<\/mi>n<\/mi><\/msub>a_n<\/annotation><\/semantics><\/math>\u306f<\/p>\n\n\n\n
a<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>T<\/mi><\/mfrac>\u222b<\/mo>0<\/mn>T<\/mi><\/msubsup>x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mspace>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi><\/mrow>a_n = \\frac{2}{T} \\int_{0}^{T} x(t) \\cos(n\\omega_0 t) dt<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3067\u3059\uff0e\u5b9a\u7fa9\u3088\u308a\uff0c\u7a4d\u5206\u533a\u9593\u306f2\u3064\u306b\u5206\u5272\u3059\u3079\u304d\u3067\u3059\uff1a<\/p>\n\n\n\n

a<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>T<\/mi><\/mfrac>(<\/mo>\u222b<\/mo>0<\/mn>T<\/mi>2<\/mn><\/mfrac><\/msubsup>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi>\u2212<\/mo>\u222b<\/mo>T<\/mi>2<\/mn><\/mfrac>T<\/mi><\/msubsup>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi>)<\/mo><\/mrow><\/mrow>a_n = \\frac{2}{T} \\left( \\int_{0}^{\\frac{T}{2}} \\cos(n\\omega_0 t) dt – \\int_{\\frac{T}{2}}^{T} \\cos(n\\omega_0 t) dt \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u5f8c\u534a\u306e\u7a4d\u5206\u533a\u9593\u306f\u8ca0\u5024\u306a\u306e\u3067\uff0c\u5dee\u5206\u3092\u53d6\u308b\u3088\u3046\u306a\u5f62\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u307e\u305acos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\\cos<\/annotation><\/semantics><\/math>\u3092\u7a4d\u5206\u3059\u308c\u3070sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\\sin<\/annotation><\/semantics><\/math>\u306b\u306a\u308a\u307e\u3059\u306d\uff0e\u307e\u305f<\/p>\n\n\n\n
\u03c9<\/mi>0<\/mn><\/msub>=<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>T<\/mi><\/mfrac><\/mrow>\\omega_0 = \\frac{2\\pi}{T}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3067\u3042\u3063\u3066\uff0c\u5909\u5f62\u3059\u308c\u3070<\/p>\n\n\n\n

\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>=<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>\\omega_0 T = 2\\pi<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\u306d\uff0e<\/p>\n\n\n\n

\u3053\u3053\u3067\uff0c\u5404\u533a\u9593\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u307f\u308b\u3068\uff1a<\/p>\n\n\n\n

\u30fbt<\/mi>=<\/mo>0<\/mn><\/mrow>t=0<\/annotation><\/semantics><\/math>\u306e\u3068\u304d<\/p>\n\n\n\n
sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>0<\/mn>)<\/mo>=<\/mo>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>0<\/mn>)<\/mo><\/mrow>\\sin(n\u03c9_00)=\\sin(0)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u30fbt<\/mi>=<\/mo>T<\/mi>2<\/mn><\/mfrac><\/mrow>t=\\frac{T}{2}<\/annotation><\/semantics><\/math>\u306e\u3068\u304d<\/p>\n\n\n\n
sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>2<\/mn><\/mfrac>)<\/mo>=<\/mo>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi><\/mrow>2<\/mn><\/mfrac>)<\/mo><\/mrow>\\sin(n\\omega_0\\frac{T}{2})=\\sin(n\\omega_0\\frac{\\omega_0T}{2})<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u3053\u3067\uff0c\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>=<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>\\omega_0 T = 2\\pi<\/annotation><\/semantics><\/math>\u3088\u308a<\/p>\n\n\n\n
sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi><\/mrow>2<\/mn><\/mfrac>)<\/mo>=<\/mo>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c0<\/mi>)<\/mo>=<\/mo>0<\/mn><\/mrow>\\sin(n\\omega_0\\frac{\\omega_0T}{2})=\\sin(n\\pi)=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u30fbt<\/mi>=<\/mo>T<\/mi><\/mrow>t=T<\/annotation><\/semantics><\/math>\u306e\u3068\u304d<\/p>\n\n\n\n
sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>)<\/mo>=<\/mo>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>2<\/mn>n<\/mi>\u03c0<\/mi>)<\/mo>=<\/mo>0<\/mn><\/mrow>\\sin(n\\omega_0T) = \\sin(2n\\pi)=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u4ee5\u4e0a\u3088\u308a\uff0c\u5168\u3066\u306e\u533a\u9593\u30670\u3068\u306a\u308b\u3053\u3068\u304b\u3089\uff0c\u4fc2\u6570a<\/mi>n<\/mi><\/msub>a_n<\/annotation><\/semantics><\/math>\u306e\u6210\u5206\u3082\u5168\u30660\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\uff0e\u3059\u306a\u308f\u3061cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\\cos<\/annotation><\/semantics><\/math>\u306e\uff0c\u5076\u95a2\u6570\u306e\u6210\u5206\u304c0\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u4fe1\u53f7\u306e\u6ce2\u5f62\u304b\u3089\uff0c\u660e\u3089\u304b\u306b\u5947\u95a2\u6570\u3067\u3059\u304b\u3089\uff0c\u59a5\u5f53\u306a\u7d50\u679c\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u6700\u5f8c\u306b\uff0c\u4fc2\u6570b<\/mi>n<\/mi><\/msub>b_n<\/annotation><\/semantics><\/math>\u306b\u3064\u3044\u3066\u6c42\u3081\u307e\u3057\u3087\u3046\uff0e\u4eca\u307e\u3067\u306e\u7d50\u679c\u304b\u3089\uff0c\u304a\u305d\u3089\u304f\u975e\u30bc\u30ed\u306e\u5024\u304c\u51fa\u3066\u6765\u308b\u306f\u305a\u3067\u3059\uff0e<\/p>\n\n\n\n

b<\/mi>n<\/mi><\/msub>b_n<\/annotation><\/semantics><\/math>\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u306d\uff1a<\/p>\n\n\n\n
b<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>T<\/mi><\/mfrac>\u222b<\/mo>0<\/mn>T<\/mi><\/msubsup>x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mspace>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi><\/mrow>b_n = \\frac{2}{T} \\int_{0}^{T} x(t) \\sin(n\\omega_0 t) dt<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

a<\/mi>n<\/mi><\/msub>a_n<\/annotation><\/semantics><\/math>\u306e\u969b\u3068\u540c\u69d8\uff0c2\u3064\u306e\u7a4d\u5206\u3067\u8003\u3048\u307e\u3059\uff1a<\/p>\n\n\n\n
b<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>T<\/mi><\/mfrac>(<\/mo>\u222b<\/mo>0<\/mn>T<\/mi>2<\/mn><\/mfrac><\/msubsup>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi>\u2212<\/mo>\u222b<\/mo>T<\/mi>2<\/mn><\/mfrac>T<\/mi><\/msubsup>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo>d<\/mi>t<\/mi>)<\/mo><\/mrow><\/mrow>b_n = \\frac{2}{T} \\left( \\int_{0}^{\\frac{T}{2}} \\sin(n\\omega_0 t) dt – \\int_{\\frac{T}{2}}^{T} \\sin(n\\omega_0 t) dt \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u666e\u901a\u306b\u7a4d\u5206\u3092\u3057\u3066\u3044\u304f\u3068\uff0c<\/p>\n\n\n\n

=<\/mo>2<\/mn>T<\/mi><\/mfrac>(<\/mo>[<\/mo>\u2212<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo><\/mrow>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>]<\/mo><\/mrow>0<\/mn>T<\/mi>2<\/mn><\/mfrac><\/msubsup>\u2212<\/mo>[<\/mo>\u2212<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo><\/mrow>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>]<\/mo><\/mrow>T<\/mi>2<\/mn><\/mfrac>T<\/mi><\/msubsup>)<\/mo><\/mrow><\/mrow>= \\frac{2}{T} \\left( \\left[ \\frac{-\\cos(n\\omega_0 t)}{n\\omega_0} \\right]_{0}^{\\frac{T}{2}} – \\left[ \\frac{-\\cos(n\\omega_0 t)}{n\\omega_0} \\right]_{\\frac{T}{2}}^{T} \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u03c9<\/mi>0<\/mn><\/msub>=<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>T<\/mi><\/mfrac><\/mrow>\\omega_0 = \\frac{2\\pi}{T}<\/annotation><\/semantics><\/math>\u3068\u3059\u308b\u3068\uff0c<\/p>\n\n\n\n
=<\/mo>1<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>[<\/mo>\u2212<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c0<\/mi>)<\/mo>+<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>0<\/mn>)<\/mo>]<\/mo>\u2212<\/mo>[<\/mo>\u2212<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>2<\/mn>n<\/mi>\u03c0<\/mi>)<\/mo>+<\/mo>cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c0<\/mi>)<\/mo>]<\/mo>)<\/mo><\/mrow><\/mrow>= \\frac{1}{n\\pi} \\left( [-\\cos(n\\pi) + \\cos(0)] – [-\\cos(2n\\pi) + \\cos(n\\pi)] \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u3053\u3067\uff0c<\/p>\n\n\n\n

cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>0<\/mn>)<\/mo>=<\/mo>1<\/mn><\/mrow>\\cos(0)=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>2<\/mn>n<\/mi>\u03c0<\/mi>)<\/mo>=<\/mo>1<\/mn><\/mrow>\\cos(2n\\pi)=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
cos<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c0<\/mi>)<\/mo>=<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup><\/mrow>\\cos(n\\pi)=(-1)^n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308b\u304b\u3089\uff0c<\/p>\n\n\n\n

=<\/mo>1<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>(<\/mo>\u2212<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>+<\/mo>1<\/mn>)<\/mo>\u2212<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>+<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>)<\/mo>)<\/mo><\/mrow><\/mrow>= \\frac{1}{n\\pi} \\left( ( -(-1)^n + 1 ) – ( -1 + (-1)^n ) \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u6574\u7406\u3057\u3066\uff0c<\/p>\n\n\n\n

b<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>1<\/mn>\u2212<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>)<\/mo><\/mrow>b_n = \\frac{2}{n\\pi} (1 – (-1)^n)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u3053\u3053\u3067\uff0cn<\/mi>n<\/annotation><\/semantics><\/math>\u304c\u5076\u6570\u3067\u3042\u308b\u306a\u3089\uff0c\u8a08\u7b97\u305b\u305a\u3068\u3082b<\/mi>n<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>b_n=0<\/annotation><\/semantics><\/math>\u3067\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059(1<\/mn>\u2212<\/mo>1<\/mn>=<\/mo>0<\/mn><\/mrow>1-1=0<\/annotation><\/semantics><\/math>)\uff0e<\/p>\n\n\n\n

\u307e\u305fn<\/mi>n<\/annotation><\/semantics><\/math>\u304c\u5947\u6570\u3067\u3042\u308b\u306a\u3089\uff0c<\/p>\n\n\n\n
b<\/mi>n<\/mi><\/msub>=<\/mo>2<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>1<\/mn>\u2212<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>)<\/mo>=<\/mo>4<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac><\/mrow>b_n=\\frac{2}{n\\pi}(1-(-1))=\\frac{4}{n\\pi}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u4ee5\u4e0a\u306e\u7d50\u679c\u3092\u307e\u3068\u3081\u308b\u3068\uff0c<\/p>\n\n\n\n

a<\/mi>0<\/mn><\/msub>=<\/mo>0<\/mn><\/mrow>a_0=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
a<\/mi>n<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>a_n=0<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
b<\/mi>n<\/mi><\/msub>=<\/mo>{<\/mo>4<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac><\/mstyle><\/mtd>(<\/mo>n<\/mi> is odd<\/mtext>)<\/mo><\/mrow><\/mtd><\/mtr>0<\/mn><\/mtd>(<\/mo>n<\/mi> is even<\/mtext>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>b_n = \n\\begin{cases}\n\\displaystyle \\frac{4}{n\\pi} & (n \\text{ is odd}) \\\\[10pt]\n0 & (n \\text{ is even})\n\\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\uff0c\u5947\u6570\u500d\u306esin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\\sin<\/annotation><\/semantics><\/math>\u6ce2\u6210\u5206\u304c\u7121\u9650\u500b\u73fe\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u3059\u306a\u308f\u3061\uff0c\u6700\u7d42\u7684\u306b\u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u3092\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3057\u305f\u7d50\u679c\uff0c<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>1<\/mn>,<\/mo>3<\/mn>,<\/mo>5…<\/mn><\/mrow>\u221e<\/mi><\/munderover><\/mrow>4<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>sin<\/mi>\u2061<\/mo><\/mrow>(<\/mo>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi>)<\/mo><\/mrow>x(t) = \\sum_{n=1, 3, 5…}^{\\infty} \\frac{4}{n\\pi} \\sin(n\\omega_0 t)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u8868\u3055\u308c\u307e\u3059\uff0e<\/p>\n\n\n\n

\u3053\u306e\u7d50\u679c\u3092\uff0c\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb\u3068\u3044\u3046\u5f62\u3067\u53ef\u8996\u5316\u3057\u3066\u307f\u307e\u3057\u3087\u3046(fig.3)<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

fig.3 \u77e9\u5f62\u6ce2\u306e\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb<\/p>\n\n\n\n

\u4e0a\u8a18\u306e\u8a08\u7b97\u901a\u308a\uff0c\u5947\u6570\u500d\u306e\u9ad8\u8abf\u6ce2\u306b\u306e\u307f\uff0c\u6210\u5206\u304c\u73fe\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\uff0e\u7b2c\u4e00\u9ad8\u8abf\u6ce2\u304c\u6700\u5927\u3068\u306a\u308a\uff0c\u305d\u3053\u304b\u3089\u6307\u6570\u95a2\u6570\u7684\u306b\u632f\u5e45\u304c\u6e1b\u8870\u3057\u3066\u3044\u304f\u3053\u3068\u3082\u8aad\u307f\u53d6\u308c\u307e\u3059\uff0e<\/p>\n\n\n\n

\u307e\u305f\uff0c\u3053\u306e\u6210\u5206\u306e\u6b63\u5f26\u6ce2\u3092\u9806\u306b\u8db3\u3057\u5408\u308f\u305b\u3066\u3044\u304f\u3068\uff0c\u3060\u3093\u3060\u3093\u3068\u77e9\u5f62\u6ce2\u306e\u5f62\u304c\u73fe\u308c\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059(fig.4)\uff0e\u306a\u304a\uff0c\u7d1a\u6570\u5c55\u958b\u306a\u306e\u3067\uff0c\u6709\u9650\u56de\u8db3\u3057\u5408\u308f\u305b\u3066\u3082\uff0c\u77e9\u5f62\u6ce2\u304c\u73fe\u308c\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\uff0e<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

fig.4 \u6ce2\u306e\u8db3\u3057\u5408\u308f\u305b<\/p>\n\n\n\n

\u4ee5\u4e0a\u304b\u3089\uff0c\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3092\u7528\u3044\u3066\uff0c\u9069\u5207\u306b\u77e9\u5f62\u6ce2\u306e\u5468\u6ce2\u6570\u6210\u5206\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\uff0e<\/p>\n\n\n\n

\u306a\u304a\uff0cfig.4\u306b\u304a\u3051\u308bn=1~15\u3042\u305f\u308a\u3067\u7279\u306b\u9855\u8457\u306b\u306a\u308b\uff0c\u30c4\u30ce\u306e\u3088\u3046\u306a\u4e21\u30b5\u30a4\u30c9\u306e\u51fa\u3063\u5f35\u308a\u306f\uff0c\u30ae\u30d6\u30b9\u73fe\u8c61\u306b\u3088\u308b\u3082\u306e\u3067\u3042\u308a\uff0c\u7121\u9650\u56de\u8db3\u3057\u5408\u308f\u305b\u3066\u3082\uff0c\u5fc5\u305a\u5143\u306e\u6ce2\u5f62\u306e9%\u306e\u98db\u3073\u51fa\u3057\u304c\u767a\u751f\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n

3.2. \u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3067\u6c42\u3081\u308b<\/h2>\n\n\n\n

3.1.\u306b\u304a\u3044\u3066\u7528\u3044\u305f\u4fe1\u53f7x<\/mi>(<\/mo>t<\/mi>)<\/mo><\/mrow>x(t)<\/annotation><\/semantics><\/math>\u3092\u7528\u3044\u307e\u3059\uff1a<\/p>\n\n\n\n
x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>{<\/mo>1<\/mn><\/mtd>(<\/mo>0<\/mn>\u2264<\/mo>t<\/mi><<\/mo>T<\/mi>2<\/mn><\/mfrac>)<\/mo><\/mrow><\/mtd><\/mtr>\u2212<\/mo>1<\/mn><\/mrow><\/mtd>(<\/mo>T<\/mi>2<\/mn><\/mfrac>\u2264<\/mo>t<\/mi><<\/mo>T<\/mi>)<\/mo><\/mrow><\/mtd><\/mtr>0<\/mn><\/mtd>(<\/mo>otherwise<\/mtext>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>x(t) = \n\\begin{cases}\n1 & (0 \\le t < \\frac{T}{2}) \\\\[10pt]\n-1 & (\\frac{T}{2} \\le t < T) \\\\[10pt]\n0 & (\\text{otherwise})\n\\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u307e\u3057\u305f\uff1a<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>T<\/mi><\/mfrac>\u222b<\/mo>0<\/mn>T<\/mi><\/msubsup>x<\/mi>(<\/mo>t<\/mi>)<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>d<\/mi>t<\/mi><\/mrow>c_n = \\frac{1}{T} \\int_{0}^{T} x(t) e^{-jn\\omega_0 t} dt<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u7a4d\u5206\u533a\u9593\u3092\u5206\u5272\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>T<\/mi><\/mfrac>[<\/mo>\u222b<\/mo>0<\/mn>T<\/mi>2<\/mn><\/mfrac><\/msubsup>(<\/mo>1<\/mn>)<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>d<\/mi>t<\/mi>+<\/mo>\u222b<\/mo>T<\/mi>2<\/mn><\/mfrac>T<\/mi><\/msubsup>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>d<\/mi>t<\/mi>]<\/mo><\/mrow><\/mrow>c_n = \\frac{1}{T} \\left[ \\int_{0}^{\\frac{T}{2}} (1) e^{-jn\\omega_0 t} dt + \\int_{\\frac{T}{2}}^{T} (-1) e^{-jn\\omega_0 t} dt \\right]<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3053\u3053\u3067\u222b<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>d<\/mi>t<\/mi>=<\/mo>1<\/mn>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup><\/mrow>\\int e^{-jn\\omega_0t} dt = \\frac{1}{-jn\\omega_0} e^{-jn\\omega_0t} <\/annotation><\/semantics><\/math>\u3092\u7528\u3044\u308b\u3068\uff0c<\/p>\n\n\n\n
c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>T<\/mi><\/mfrac>(<\/mo>[<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>]<\/mo><\/mrow>0<\/mn>T<\/mi>2<\/mn><\/mfrac><\/msubsup>\u2212<\/mo>[<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub><\/mrow><\/mfrac>]<\/mo><\/mrow>T<\/mi>2<\/mn><\/mfrac>T<\/mi><\/msubsup>)<\/mo><\/mrow><\/mrow>c_n = \\frac{1}{T} \\left( \\left[ \\frac{e^{-jn\\omega_0 t}}{-jn\\omega_0} \\right]_{0}^{\\frac{T}{2}} – \\left[ \\frac{e^{-jn\\omega_0 t}}{-jn\\omega_0} \\right]_{\\frac{T}{2}}^{T} \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u307e\u305f\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>=<\/mo>2<\/mn>\u03c0<\/mi><\/mrow>\\omega_0 T = 2\\pi<\/annotation><\/semantics><\/math>\u3067\u3042\u308b\u304b\u3089\uff0c\u5b9a\u6570\u3092\u62ec\u308a\u51fa\u3057\u3066<\/p>\n\n\n\n
c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>\u2212<\/mo>j<\/mi>2<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>[<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>2<\/mn><\/mfrac><\/mrow><\/msup>\u2212<\/mo>e<\/mi>0<\/mn><\/msup>]<\/mo><\/mrow>\u2212<\/mo>[<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi><\/mrow><\/msup>\u2212<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>2<\/mn><\/mfrac><\/mrow><\/msup>]<\/mo><\/mrow>)<\/mo><\/mrow><\/mrow>c_n = \\frac{1}{-j2n\\pi} \\left( \\left[ e^{-jn\\omega_0 \\frac{T}{2}} – e^0 \\right] – \\left[ e^{-jn\\omega_0 T} – e^{-jn\\omega_0 \\frac{T}{2}} \\right] \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u307e\u305f\uff0c<\/p>\n\n\n\n

e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi>2<\/mn><\/mfrac><\/mrow><\/msup>=<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c0<\/mi><\/mrow><\/msup>=<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup><\/mrow>e^{-jn\\omega_0\\frac{T}{2}}=e^{-jn\\pi}=(-1)^n<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>T<\/mi><\/mrow><\/msup>=<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>n<\/mi>2<\/mn>\u03c0<\/mi><\/mrow><\/msup>=<\/mo>1<\/mn><\/mrow>e^{-jn\\omega_0T}=e^{-jn2\\pi}=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
e<\/mi>0<\/mn><\/msup>=<\/mo>1<\/mn><\/mrow>e^0=1<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3088\u308a\uff0c<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>1<\/mn>\u2212<\/mo>j<\/mi>2<\/mn>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>[<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>\u2212<\/mo>1<\/mn>]<\/mo>\u2212<\/mo>[<\/mo>1<\/mn>\u2212<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>]<\/mo>)<\/mo><\/mrow><\/mrow>c_n = \\frac{1}{-j2n\\pi} \\left( [(-1)^n – 1] – [1 – (-1)^n] \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u6574\u7406\u3057\u3066\uff0c<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>j<\/mi>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>)<\/mo>n<\/mi><\/msup>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow><\/mrow>c_n = \\frac{j}{n\\pi} \\left( (-1)^n – 1 \\right)<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0e\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306e\u969b\u3068\u540c\u69d8\uff0cn<\/mi>n<\/annotation><\/semantics><\/math>\u304c\u5076\u6570\u3067\u3042\u308c\u3070\uff0cc<\/mi>n<\/mi><\/msub>=<\/mo>0<\/mn><\/mrow>c_n=0<\/annotation><\/semantics><\/math>\u3068\u306a\u308a\u307e\u3059\uff0e<\/p>\n\n\n\n

\u307e\u305f\u5947\u6570\u3067\u3042\u308c\u3070\uff0c<\/p>\n\n\n\n

c<\/mi>n<\/mi><\/msub>=<\/mo>j<\/mi>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>(<\/mo>\u2212<\/mo>1<\/mn>\u2212<\/mo>1<\/mn>)<\/mo>=<\/mo>\u2212<\/mo>2<\/mn>j<\/mi><\/mrow>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac><\/mrow>c_n = \\frac{j}{n\\pi} (-1 – 1) = \\frac{-2j}{n\\pi}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308b\u304b\u3089\uff0c\u6700\u7d42\u7684\u306b<\/p>\n\n\n\n

x<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>\u2211<\/mo>n<\/mi>=<\/mo>\u2212<\/mo>\u221e<\/mi><\/mrow>\u221e<\/mi><\/munderover><\/mrow>(<\/mo>\u2212<\/mo>2<\/mn>j<\/mi><\/mrow>n<\/mi>\u03c0<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow>e<\/mi>j<\/mi>n<\/mi>\u03c9<\/mi>0<\/mn><\/msub>t<\/mi><\/mrow><\/msup>,<\/mo>(<\/mo>n<\/mi> is odd<\/mtext>)<\/mo><\/mrow>x(t) = \\sum_{n=-\\infty}^{\\infty} \\left( \\frac{-2j}{n\\pi} \\right) e^{jn\\omega_0 t} , (n \\text{ is odd})<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\uff0efig.3\u3068\u540c\u69d8\u306e\u30b9\u30da\u30af\u30c8\u30eb\u3092\u793a\u3057\u305d\u3046\u3067\u3059\u306d\uff0e\u5ff5\u306e\u305f\u3081\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3057\u3087\u3046(fig.5)\uff0e<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

fig.5 \u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306e\u5468\u6ce2\u6570\u30b9\u30da\u30af\u30c8\u30eb<\/p>\n\n\n\n

\u78ba\u304b\u306b\u5947\u6570\u6b21\u306e\u9ad8\u8abf\u6ce2\u306b\u306e\u307f\u30b9\u30da\u30af\u30c8\u30eb\u304c\u73fe\u308c\u3066\u3044\u307e\u3059\uff0e\u304c\uff0c\u8ca0\u5024\u306b\u3082\u30b9\u30da\u30af\u30c8\u30eb\u304c\u8868\u308c\u3066\u3044\u308b\u4e8b\u304c\u5206\u304b\u308a\u307e\u3059\uff0e\u2211<\/mo>\\sum<\/annotation><\/semantics><\/math>\u306e\u7bc4\u56f2\u304c\u2212<\/mo>\u221e<\/mi><\/mrow>-\\infin <\/annotation><\/semantics><\/math>~\u221e<\/mi>\\infin<\/annotation><\/semantics><\/math>\u3067\u3042\u308b\u304b\u3089\uff0e\u3068\u8a00\u3048\u3070\u305d\u3046\u306a\u3093\u3067\u3059\u304c\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u3088\u308a\uff0c\u4e09\u89d2\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u793a\u3055\u308c\u307e\u3057\u305f\u3088\u306d\uff0e<\/p>\n\n\n\n
cos<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>=<\/mo>e<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>+<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>\u03b8<\/mi><\/mrow><\/msup><\/mrow>2<\/mn><\/mfrac>,<\/mo><\/mspace>sin<\/mi>\u2061<\/mo><\/mspace><\/mrow>\u03b8<\/mi>=<\/mo>e<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>\u2212<\/mo>e<\/mi>\u2212<\/mo>j<\/mi>\u03b8<\/mi><\/mrow><\/msup><\/mrow>2<\/mn>j<\/mi><\/mrow><\/mfrac><\/mrow>\\cos\\theta = \\frac{e^{j\\theta} + e^{-j\\theta}}{2}, \\quad \\sin\\theta = \\frac{e^{j\\theta} – e^{-j\\theta}}{2j}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

\u305d\u308c\u305e\u308c\u306be<\/mi>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>e^{j\\theta}<\/annotation><\/semantics><\/math>\u304a\u3088\u3073e<\/mi>\u2212<\/mo>j<\/mi>\u03b8<\/mi><\/mrow><\/msup>e^{-j\\theta}<\/annotation><\/semantics><\/math>\u306e\u9805\u304c\u542b\u307e\u308c\u3066\u304a\u308a\uff0c\u3088\u3046\u306f\u53cd\u6642\u8a08\u5468\u308a\u3068\u6642\u8a08\u56de\u308a\u306e\u4e21\u65b9\u306e\u6210\u5206\u304c\u542b\u307e\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059(fig.7)\uff0e<\/p>\n\n\n
\n
\"\"<\/figure>\n<\/div>\n\n\n

fig.7 \u8907\u7d20\u5e73\u9762\u306b\u304a\u3051\u308b\u56de\u8ee2\u306b\u3088\u308a\u6b63\u5f26\u6ce2\u304c\u4f5c\u3089\u308c\u308b\uff0e\uff08Wirelesspi.com<\/a>)<\/p>\n\n\n\n

\u4eee\u306b\u53cd\u6642\u8a08\u56de\u308a\uff08\u6b63\u5024\uff09\u306e\u6210\u5206\u306e\u307f\u3067\u3042\u3063\u305f\u5834\u5408\uff0c\u5024\u306f\u5e38\u306b\u865a\u6570\u3068\u306a\u308a\u307e\u3059\uff0e\u305d\u308c\u3067\u306f\u73fe\u5b9f\u4e16\u754c\u306b\u4f5c\u7528\u3057\u307e\u305b\u3093\u304b\u3089\uff0c\u9006\u56de\u8ee2\u306e\u8ca0\u5024\u3092\u7528\u610f\u3059\u308b\u3053\u3068\u3067\uff0c\u865a\u6570\u6210\u5206\u3092\u6253\u3061\u6d88\u3057\u5408\u3044\uff0c\u5b9f\u6570\u306e\u307f\u3092\u6b8b\u3057\u307e\u3059\uff0e<\/p>\n\n\n\n

\u305d\u308c\u306b\u3088\u308a\uff0c\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3067\u306f\uff0c\u6b63\u8ca0\u4e21\u5074\u306b\u30b9\u30da\u30af\u30c8\u30eb\u304c\u73fe\u308c\u307e\u3059\uff0e<\/p>\n\n\n\n

\u3000<\/p>\n\n\n\n

\u4eca\u56de\u306f\u3053\u3053\u307e\u3067\u3068\u306a\u308a\u307e\u3059\uff0e\u6b21\u56de\u306f\uff0c\u3044\u3088\u3044\u3088\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u3068DSP\uff08:Digital Signal Processing\uff0c\u30c7\u30a3\u30b8\u30bf\u30eb\u4fe1\u53f7\u51e6\u7406\uff09\u306b\u3064\u3044\u3066\u89e6\u308c\u3066\u884c\u3053\u3046\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n","protected":false},"excerpt":{"rendered":"

\u524d\u56de\u306f\u3053\u3061\u3089 \u524d\u56de\u89e3\u8aac\u3057\u305f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u306b\u3064\u3044\u3066\uff0c\u5b9f\u6570\u3092\u7528\u3044\u308b\u3053\u3068\u304b\u3089\uff0c\u5b9f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3068\u547c\u79f0\u3057\u307e\u3059\uff0e \u5b9f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\u306b\u5bfe\u3057\u3066\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f\u306b\u4f9d\u3063\u3066\u8907\u7d20\u6570\u3092\u5c0e\u5165\u3057\u305f\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3092\u8907\u7d20\u30d5\u30fc\u30ea\u30a8\u5c55\u958b\u3068\u547c\u3073\u307e\u3059\uff0e \u4eca\u56de\u306f\uff0c\u4e3b\u306b\u8907 […]<\/p>\n","protected":false},"author":1,"featured_media":14,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-100","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-4"],"_links":{"self":[{"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/posts\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=100"}],"version-history":[{"count":13,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions"}],"predecessor-version":[{"id":149,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/posts\/100\/revisions\/149"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=\/wp\/v2\/media\/14"}],"wp:attachment":[{"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.gamtecs.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}