Define the time variable t in Matlab as ‘t=linspace(-pi*6,pi*6,6000)’, and generate three sine waves according to the equation

1: Fourier Series and Fourier Transform:
⦁ Define the time variable t in Matlab as ‘t=linspace(-pi*6,pi*6,6000)’, and generate three sine waves according to the equation
where the parameter a is an arbitrary number of your choice. Plot the three sine waves against time superimposed in one figure, assigning each curve a different colour of your choice. What are the periods of the three sine waves respectively? Comment on the effect of the parameter n on the frequency of the sine wave.
⦁ Discuss the use of Fourier Series and Fourier Transform representations.
⦁ Use the following Matlab code to plot f(t).

t= linspace(-pi*6,pi*6,6000);
f=ones(size(t));
f(find(mod(t,2*pi)>pi))=0;
figure;plot(t,f,’r’);

The time series f(t) is a sequence of square waves. Find the 3rd and the 25th order Fourier Series approximation of f(t) using the equation given in slide 9 of the lecture note. The Matlab code is provided in the same slide, with slight modification needed to change the number of iterations in each case. Plot each approximation superimposed with the original signal. Discuss the effect of the order of the Fourier Series on the accuracy of the approximation for f(t).

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