Down sampling and DTFTConsider the pulses x1 n u n u n 20 and x2 n u n u n 10 , and their product x n x1 n x2 n (a) Plot the three pulses Could you say that x n is a down sampled version of x1 n what would be the down sampling rate Find X1(e j) (b) Find directly the DTFT of x n and compare it to X1(e j M), where M is the down sampling rate found above If we down sample x1 n to get x n , would the result be affected by aliasing Use MATLAB to plot the magnitude DTFT of x1 n and x n

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Question: Down-sampling and DTFTConsider the pulses x1[n] = u[n]u[n 20] and x2[n] = u[n] u[n 10], and their product x[n] = x1[n]x2[n]. (a)

Down-sampling and DTFT—Consider the pulses x1[n] = u[n]−u[n − 20] and x2[n] = u[n] − u[n − 10], and their product x[n] = x1[n]x2[n]. (a) Plot the three pulses. Could you say that x[n] is a down-sampled version of x1[n]? what would be the down-sampling rate? Find X1(e jω). (b) Find directly the DTFT of x[n] and compare it to X1(e jω/M), where M is the down-sampling rate found above. If we down-sample x1[n] to get x[n], would the result be affected by aliasing? Use MATLAB to plot the magnitude DTFT of x1[n] and x[n].

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