a) Consider te following periodic signalxt), which is a triangular waveform. Usi
ID: 3349058 • Letter: A
Question
a) Consider te following periodic signalxt), which is a triangular waveform. Using the techniques discussed in class, determine the Fourier coefficients: ,an and hn b) Using the Fourier coefficients that you determined from a), plot ) in MATALB that considers 8. [Note: you should the first 40 terms in the Fourier series if T= 4 seconds. Plot x(t) for-8 not simply enter term by term in MATLAB to complete the plot r x(f) -21 2T c) Based on the Fourier coefficients that you determined from a), if T = 4 seconds, plot both the magnitude spectrum and phase spectrum of ) as a function of n for -10n10 in MATLAB Remember the magnitude spectrum is the magnitude of the exponential Fourier series coefficients i.e. De) and the phase spectrum is the phase of the exponential Fourier series coefficients. Use MATLAB built-in unction stem(to plot all the points in both plots. Use subplot) to plot the magnitude spectrum in the upper plot and the phase spectrum in the lower plot. Label both plots d) "O) is now an input signal for an LTC system with impulse response h(r), and the Fourier transform of it) in this system is: H (--. Determine the output response signal y(1). Plot both xit) and the output signal yif) on the same gruph. Plot a few cycles. Note: in this part 5- jo shoulExplanation / Answer
clear , close all;
Fs=60;
t=0:1/Fs:20-1/Fs;
y=square(t,50);
y(y>0)=2;
y(y<0)=-12;
figure, plot(t,y);
axis ([0 20 -20 10])
% Fourier Series
a0=0;
Fy=zeros(size(t));
N=10;
for n=1:2:N
Fy=Fy+(4/n*pi)*sin(2*pi*n*t/(2*pi));
end
hold on,
plot(t,Fy,'r')
legend(' Square ','Fourier Approx');
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