<<Calculus`FourierTransform` (* Nalozi paket za delo s Fourierovimi vrstami *)

(* Poglejmo, kako se razvije funkcijo Sign (x) v trigonometricno Fourierovo vrsto na intervalu [-π, π] . *)

Plot[Sign[x], {x, -π, π}] (* Skica funkcije *)

[Graphics:HTMLFiles/fourier_4.gif]

⁃Graphics⁃

FourierTrigSeries[Sign[x], x, 1, FourierParameters -> {-1, 1/(2π)}] (* Prvi clen *)

(4 Sin[x])/π

Plot[%, {x, -π, π}]

[Graphics:HTMLFiles/fourier_9.gif]

⁃Graphics⁃

FourierTrigSeries[Sign[x], x, 3, FourierParameters -> {0, 1/(2π)}]//Simplify (* Prvi trije cleni *)

(4 (3 Sin[x] + Sin[3 x]))/(3 π)

Plot[%, {x, -π, π}]

[Graphics:HTMLFiles/fourier_14.gif]

⁃Graphics⁃

FourierTrigSeries[Sign[x], x, 10, FourierParameters -> {0, 1/(2π)}] //Simplify (* Prvih 10 clenov *)

1/(315 π) (4 (315 Sin[x] + 105 Sin[3 x] + 63 Sin[5 x] + 45 Sin[7 x] + 35 Sin[9 x]))

Plot[%, {x, -π, π}]

[Graphics:HTMLFiles/fourier_19.gif]

⁃Graphics⁃

FourierTrigSeries[Sign[x], x, 50, FourierParameters -> {0, 1/(2π)}] //Simplify (* Prvih 50 clenov *)

(4 Sin[x])/π + (4 Sin[3 x])/(3 π) + (4 Sin[5 x])/(5 π) + (4 Sin[7 x])/(7 π ... ])/(43 π) + (4 Sin[45 x])/(45 π) + (4 Sin[47 x])/(47 π) + (4 Sin[49 x])/(49 π)

Plot[%, {x, -π, π}]

[Graphics:HTMLFiles/fourier_24.gif]

⁃Graphics⁃

Created by Mathematica  (January 12, 2005)