波のフーリエ変換(1)

フーリエ変換 (Subscript[X, (Subscript[T, 0])]) (f) のグラフ（cos波形の波）

\(\(\( (*\ \(X\_\(T\_0\)\) \((f)\) の定義\ *) \)\(
\)\(\(la = 1;\)

    \(lx[f_] := 
        la\/\(2  π\)\ \(I\ f \((1 - E\^\(\(-I\)\ 2\ π\ f\))\)\)\/\(1 - f\^2\);\)\)\)\)

\(\(\( (*\ 
      Re\ \(X\_\(T\_0\)\) \((f)\) のグラフ\ *) \)\(
\)\(Plot[Re[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, {\(-la\)/2*1.2, la/2*1.2}}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {{\(-1\)/2, "-A/2"}, {1/2, "A/2"}}}]\)\)\)

\(\(\( (*\ 
      Im\ \(X\_\(T\_0\)\) \((f)\) のグラフ\ *) \)\(
\)\(Plot[Im[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, {\(-la\)/2*1.2, la/2*1.2}}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {{\(-1\)/2, "-A/2"}, {1/2, "A/2"}}}]\)\)\)

Plot[Abs[lx[f]], {f, -4.5, 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4.5, 4.5}, {-la/2*0.2, la/2*1.2}}, 
      Ticks -> {{-4, -3, -2, -1, 0, 1, 2, 3, 
            4}, {{-1/2, "-A/2"}, {1/2, "A/2"}}}]

\(\(\( (*\ 偏角ϕのグラフ\ *) \)\(
\)\(Plot[Arg[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, Automatic}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {\(-π\), π}}]\)\)\)

フーリエ変換 (Subscript[X, (Subscript[T, 0])]) (f) のグラフ（sin波形の波）

\(\(\( (*\ \(X\_\(T\_0\)\) \((f)\) の定義\ *) \)\(
\)\(\(lb = 1;\)

    \(lx[f_] := 
        lb\/\(2  π\)\ \(1 - E\^\(\(-I\)\ 2\ π\ f\)\)\/\(1 - f\^2\);\)\)\)\)

\(\(\( (*\ 
      Re\ \(X\_\(T\_0\)\) \((f)\) のグラフ\ *) \)\(
\)\(Plot[Re[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, {\(-lb\)/2*1.2, lb/2*1.2}}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {{\(-1\)/2, "-B/2"}, {1/2, "B/2"}}}]\)\)\)

\(\(\( (*\ 
      Im\ \(X\_\(T\_0\)\) \((f)\) のグラフ\ *) \)\(
\)\(Plot[Im[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, {\(-lb\)/2*1.2, lb/2*1.2}}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {{\(-1\)/2, "-B/2"}, {1/2, "B/2"}}}]\)\)\)

Plot[Abs[lx[f]], {f, -4.5, 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4.5, 4.5}, {-lb/2*0.2, lb/2*1.2}}, 
      Ticks -> {{-4, -3, -2, -1, 0, 1, 2, 3, 
            4}, {{-1/2, "-B/2"}, {1/2, "B/2"}}}]

\(\(\( (*\ 偏角ϕのグラフ\ *) \)\(
\)\(Plot[Arg[lx[f]], {f, \(-4.5\), 4.5}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4.5\), 4.5}, Automatic}, 
      Ticks -> {{\(-4\), \(-3\), \(-2\), \(-1\), 0, 1, 2, 3, 
            4}, {\(-π\), π}}]\)\)\)