4)In page 28, it was proven that x(t) * y(t) XnYn when both of them have the sam

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4)In page 28, it was proven that x(t) * y(t) XnYn when both of them have the same fundamental period To. Redo the proof for the case of different fundamental periods, and explain the results. Periodic Convolution Let x(t) and y(t) be two periodic signals with same period fundamental period T0. We define the circular convolution of x(t) and y(t) by Where the signal is taken over one period T0. One can show that and therefore z(t) is periodic with period T0. The reader should show that the periodic convolution is commutative and associative. We can write z(t) in a Fourier-series representation with coefficients Where Xn and Yn are the Fourier series coefficients of x(t) and y(t), respectively.

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