Question

Find the trigonometric and exponential FS representations of the following periodic signals: a) 1 -20% 10% 20t -10 b) 1 TAJA. -/4 /4 -2 2R -I Verify that Parseval's Theorem holds for signal both sides of the following equation and verify that you get equality for case (a) above: a. That is, evaluate 4+7 1 To You may use MATLAB, calculator, etc. to approximately evaluate D(the larger 4+7 1 SxOf dt_ To the summation range, the better the approximation). Analytically evaluate Include your ".m" files and MATLAB output.

Answer 1

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Calculation of power for part(a) using MATLAB clc clear all close al1 To 10 pi; wo (2*pi) /To; t linspace -20,20,10000); f = 0*t; Do 0.2 N-input (' Enter the Number of terms you want to approximate \n: '); number of harmonics Time period of the given signal fundamental frequency in rad/sec creating the time vector creates a zero valued function for n-N1:N if (n--0) skip the zeroth term n=n+1 continue; end D_n sin (n*pi/5)) (n*pi); computes the n-th Fourier coefficient of the exponential form f = f + adds the n-th term to |Dn | ^2 (abs (D n) . ^2; end Pavg-f (Do. *Do) Final obtained average power plot (t, Pavg, 'LineWidth', 2); grid on xlabel \bf t'); ylabel\bf Pavg in Watts)'); title (strcat ('\bf Average power of the periodic signal f(t) with N=', int2str (N), harmonics.'));

Average power of the periodic signal f(t) with N-100 harmonics. 1.5 0.5 : 2.514 - 0.199 0 Pavg 0.199 Watt -0.5 20 -15 10 20 10 15 Average power obtained using MATLAB u) 6Aed Watts)