Given the Fourier series representation for a periodic signal x(t), we can compute derivatives of it just like with any other signal.

(a) Consider the periodic train of pulses shown in Figure 4.22, compute its derivative y(t) = dx(t)/dt and carefully plot it. Find the Fourier series of y(t).

(b) Use the Fourier series representation of x(t) and find its derivative to obtain the Fourier series of y(t). How does it compare to the Fourier series obtained above.

Figure 4.22:

Transcribed Image Text:

x(t) 2 -1.25 -0.75 -0.25 0.25 1.25 0.75 - To = 1