Question

SIGNALS AND SYSTEMS:

PLEASE UPLOAD MATLAB CODING FOR QUESTIONS.

1. In class we found that the Fourier series of a unit amplitude square wave of period 2 seconds was given by (a) Show that this series can be rewritten as 0o 2 (b) Produce plots of x (t) for n-1 to N for N-1,3,9,19,and 199, that is, truncate the infinite sum to these values of N and plot the result. Remember that only odd terms are included in the sum MATLAB is recommended for the plots but not required. 2. The square wave in problem 1 is put through a system defined by 2 dt (a) Find the Fourier series representation of y (t) (b) Plot y (t) for the values of N given in part b of problem 1

Answer 1

Here are the Matlab codes for different value of n

Command Window Figure 1 t 0:0.001:10 File Edit View Insert Tools Desktop Window Help >>wave-zeros (size (t, 1),1): >>n-3 >>for i-1:2:n wave-wave +2 * 3 in (2 *i *pi *t ) / ( İ *pi ) ; end >>plot (t,wave) 0.8 0.6 0.2 0.2 0.6 10

Command Window qure t-0:0.001:10: File Edit View Insert Tools Desktop Window Help >> wave-zeros (size (t, 1),1): >>for i-1:2:n wave-wave+2 sin (2*i*pi t end 0.6 ) / ( İ"p1) ; >plot (t,wave) fx. >> 0.2 0.2 10

Command Window Figure 1 >t-O:0.001:10 File Edit View Insert Tools Desktop Window Help >>wave-zeros (size (t, 1),1): >>for i-1:2:n wave-wave +2 * 3 in (2 *i"p1 *t ) / ( İ *pi ) ; end >>plot (t,wave) 0.6 0.2 0.2 0.6 4 10

Command Window Figure 1 t-0:0.001:10: File Edit View Insert Tools Desktop Window Help >> wave-zeros (size (t, 1),1): for i-1:2:n wave-wave+2 sin (2*i*pi t end >plot (t,wave) 0.6 ) / ( İ"p1) ; -0.2 4

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