8.31. Consider the sequence x[n] = 28[n] + 8[n 1] - 8[n-2]. (a) Determine the DTFT...

 

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8.31. Consider the sequence x[n] = 28[n] + 8[n 1] - 8[n-2]. (a) Determine the DTFT X (ej") of x[n] and the DTFT Y(ej") of the sequence y[n] = x[-n]. (b) Using your results from part (a) find an expression for W(ejw) = X(ejw) Y (eja). (c) Using the result of part (b) make a plot of w[n] = x[n] * y[n]. (d) Now plot the sequence yp[n] = x[((-n))4] as a function of n for 0 ≤ n ≤ 3. (e) Now use any convenient method to evaluate the four-point circular convolution of x[n] with yp[n]. Call your answer wp[n] and plot it. (f) If we convolve x[n] with yp[n] = x[((-n))], how should N be chosen to avoid time- domain aliasing? 8.31. Consider the sequence x[n] = 28[n] + 8[n 1] - 8[n-2]. (a) Determine the DTFT X (ej") of x[n] and the DTFT Y(ej") of the sequence y[n] = x[-n]. (b) Using your results from part (a) find an expression for W(ejw) = X(ejw) Y (eja). (c) Using the result of part (b) make a plot of w[n] = x[n] * y[n]. (d) Now plot the sequence yp[n] = x[((-n))4] as a function of n for 0 ≤ n ≤ 3. (e) Now use any convenient method to evaluate the four-point circular convolution of x[n] with yp[n]. Call your answer wp[n] and plot it. (f) If we convolve x[n] with yp[n] = x[((-n))], how should N be chosen to avoid time- domain aliasing?

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