フーリエ変換

フーリエ変換 F(u) のグラフ（テキスト中の例, p.64）

\(\(\( (*\ 
      F \((u)\) の定義\ *) \)\(
\)\(f[u_] := 
        1\/\@\(2  π\)\ \(I \((E\^\(\(-I\)\ u\) - 1)\)\)\/u;\)\)\)

Plot[Re[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

Plot[Im[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

\(\(\( (*\ \(|\)\(F \((u)\)\)\(|\)\(のグラフ\)\ *) \)\(
\)\(Plot[Abs[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

\(\(\( (*\ θのグラフ\ *) \)\(
\)\(Plot[Arg[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, Axes -> Automatic, 
      ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

フーリエ変換 F(u) のグラフ（例題1, p.71）

f[
          u_] := (Sqrt[(2/π)]) Sin[u]/u;

Plot[Re[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

Plot[Im[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

\(\(\( (*\ \(|\)\(F \((u)\)\)\(|\)\(のグラフ\)\ *) \)\(
\)\(Plot[Abs[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

\(\(\( (*\ θのグラフ\ *) \)\(
\)\(Plot[Arg[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, Axes -> Automatic, 
      ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

フーリエ変換 F(u) のグラフ（例題2, p.72）

\(\(\( (*\ 
      F \((u)\) の定義\ *) \)\(
\)\(f[
          u_] := \(-I\) \@\(2\/π\)\ \(1 - Cos[u]\)\/u;\)\)\)

Plot[Re[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

Plot[Im[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

\(\(\( (*\ \(|\)\(F \((u)\)\)\(|\)\(のグラフ\)\ *) \)\(
\)\(Plot[Abs[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

\(\(\( (*\ θのグラフ\ *) \)\(
\)\(Plot[Arg[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, Axes -> Automatic, 
      ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

フーリエ変換 F(u) のグラフ（例題3, p.73）

\(\(\( (*\ 
      F \((u)\) の定義\ *) \)\(
\)\(f[
          u_] := \(1\/\@\(2  π\)\) \(I \((E\^\(\(-I\)\ 3  u\) - E\^\(\(-I\)\ 2  u\))\)\)\/u;\)\)\)

Plot[Re[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

Plot[Im[f[x]], {x, -4 Pi, 4 Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{-4 Pi, 4  Pi}, Automatic}, 
      Ticks -> {{-3 Pi, -2 Pi,  -Pi, 0, Pi, 2  Pi, 
            3 Pi}, Automatic}]

\(\(\( (*\ \(|\)\(F \((u)\)\)\(|\)\(のグラフ\)\ *) \)\(
\)\(Plot[Abs[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, 
      Axes -> Automatic, ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)

\(\(\( (*\ θのグラフ\ *) \)\(
\)\(Plot[Arg[f[x]], {x, \(-4\)\ Pi, 4\ Pi}, Axes -> Automatic, 
      ImageSize -> {440, Automatic}, 
      PlotRange -> {{\(-4\)\ Pi, 4  Pi}, Automatic}, 
      Ticks -> {{\(-3\)\ Pi, \(-2\)\ Pi, \ \(-Pi\), 0, Pi, 2  Pi, 
            3\ Pi}, Automatic}]\)\)\)