Consider the pulses x 1 n u n u n 20 and x 2 n u n u n 10 , and their product x n x 1 n x 2 n (a) Plot the three pulses Could you say that x n is a down sampled version of x 1 n what would be the down sampling rate Find X 1 (e j ) (b) Find directly the DTFT of x n and compare it to X 1 (e j M ), wh...

a xn x 2 n x 1 2n so xn is x 1 n downsampled with a rate of M 2 b The DTFTs of xn and x ...

Consider the pulses x 1 [n] = u[n] u[n 20] and x 2 [n] =

Question:

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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