Hello everyone I have a lab for signal and systems course and I need a good expe

Question

Hello everyone I have a lab for signal and systems course and I need a good expert expert who can helps me write some explanation under each figure. Q: Fourier series train & rectangular Q:(2) Find its Fourier series CODES symst T 1 m heaviside (t) -heaviside (t- T/4) +heaviside (t-3 T/4) x 2 m [X, W] fourier series (x,T, 20); subplot (221) ezplot (x, 0 TJ grid subplot (222) stem (W, abs (X)) subplot (223) stem (W, angle (X)) CODES function [X, W] fourtierseries (x, T,N) Syms t scomputation of four ies series for k 1:N X1 (k) int (x exp (-j 2 pi (k 1) *t/T),t, 0, T) /T X (k) subs (X1 (k)); W (k) (k-1) *2 pi*T end figue

Explanation / Answer

The given code is used for finding the fourier series of a given signal. The signal is generated with the help of heaviside function, which is unit step function with time variation option (this is present as input to this function). The fourier series is representing a periodic signal as infinite summation of cosine and sine signals with dc component (may be or may be not) present. The fourier series coefficients can be represented in rectangular form or polar form. The rectangular form in the sum of sine and cosine signals while the polar form representation is sum of different exponentials. The polar form of representation has an advantage of easy computation but it takes large memory compared to the rectangular form.

In the code given, the fourier series co-efficients are calculated with the help exponentials and plotted in 2 of the 3 subplots. The first subplot (i.e. 221 first from the left of the first row) represents the periodic signal vs time. The second subplot (i.e. 222 second from the left of the first row) represents amplitude spectrum vs frequency. And the third subplot (i.e. the bottom plot) represents the phase angle vs frequency.

The following functions are explained below:

syms ---> it is used to create a symbolic variable 't'

heaviside ----> it is used to create a signal of periodicity 1 sec

ezplot ---> it is used to plot the signal created with the help of heaviside function

stem ----> it is used to plot the amplitude and phase calculated with the help of fourierseries function

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