Answer Happy

Obtain the complex Fourier series coefficients of the periodic sawtooth wave in the figure below. b) Using the coefficients you obtained in part (a), show that the Fourier series expansion of x(t) can be expressed as follows. 2 x(t)=1+ cos(kit + kat k=1 c) Obtain the Fourier series expansion of the output signal y(t) when the sign x(t) is applied to a Linear time- system with unit impulse response h(t) = e-tu(t) invariant x(t) 4 t -4 -2 2 4 2) a) Plotting the approximate Fourier series expansion of the periodic sawtooth wave obtained in part (b) of the first question in MATLAB using a finite number of components. The time vector t= 3:0.01:7; and plot x for the values M=2, M=4, M=8, M=32, and M=64. Use the for loop to calculate x in each case. For example for k=1:M. b) Plot the approximate Fourier series expansion of the output sign y(t) obtained in part (c) of the first question for M=64. Required: Solutions to the 1st question, *.m file you created in the 2nd question and the outputs of the figures