Fourier Series Applet, Frequency Shift

Cuthbert Nyack
In addition to shifting the signal f(t) in time, the spectrum FS(nw) can also also be shifted in frequency.

If the spectrum of f(t) is FS(nw) and the spectrum is shifted by frequency W to become FS(nw - W) then the shifted spectrum is the Fourier Series of the function ejWtf(t).
Since this is a complex function of time with magnitude f(t), it is easier to shift the spectrum to the right and to the left and add the result.

(FS(nw - W) + FS(nw + W))/2 = cos(Wt)f(t).
This is equivalent to multiplying f(t) by cos(Wt)

The applet below shows the result for different f(t).
Fn sets the function of the Applet.
Fn = 1 shows the effect for a square wave.
Fn = 2 to 5 show special cases of Fn = 1.
Fn = 6 shows the effect for a triangle wave.
Fn = 7 to 10 show special cases of Fn = 6.
Fn = 11 shows the effect for a rectangular pulse.
Fn = 12 to 17 show special cases of Fn = 11.
Fn = 18 shows the effect for a triangular pulse.
Fn = 19 to 25 show special cases of Fn = 18.
Fn = 26 shows the effect for a triangular-rectangular pulse.
Fn = 27 to 33 show special cases of Fn = 26.
Fn = 34 shows the effect for a odd triangular pulse.
Fn = 35 to 37 show special cases of Fn = 34.
Fn = 38 shows the effect for a pulse with even and odd parts.
Fn = 39 to 42 show special cases of Fn = 38.