MathStudio MathStudio Express

Fourier Analysis

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

Examples


Square wave

Slider(n, 1, 30, 1, 6) Plot(SquareWave(x), color=orange) Plot(FourierSeries([[-1, -@pi..0], [1, 0..@pi]], x, n), color=red)

Sawtooth wave

Slider(n, 1, 30, 1, 6) Plot(2@pi*SawToothWave(x-@pi)-@pi, color=cyan) Plot(FourierTrigSeries(x, x, n), color=blue)

Triangle wave

Slider(n, 1, 30, 1, 1) Plot(@pi/2*TriangleWave(x-@pi/2)+@pi/2, color=magenta) Plot(FourierSeries([[-x, -@pi..0], [x, 0..@pi]], x, n), color=purple)

Fourier series

FourierTrigSeries(x, x, 5)
FourierExpSeries(x, x, 5)

Fourier cosine transform

FourierCos(sin(x), x, w)

Fourier sine transform

FourierSin(sin(x)^2, x, w)

References

https://en.wikipedia.org/wiki/Fourier_analysis

Related Functions

FourierCos, FourierExpSeries, FourierSin, FourierTrigSeries, FourierSeries
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