Extend the sequences given in Problem by zero padding, and perform circular convolution on the extended sequences so that the result equals that obtained by linear convolution of the original sequences.
Given the two four-point sequences
x[n] = [–1, – 2, 1, 3] and y[n] = [–2, – 1, 0, 2], find the following:
(a) x[n]*y[n], the linear convolution;
(b) the circular convolution;
(c) Rxy[p], the cross-correlation of x[n] and y[n];
(d) Ryx[p], the cross-correlation of y[n] and x[n];
(e) Rxx[p], the autocorrelation of x[n];
(f) Use MATLAB to confirm the results of Parts (a) through (e).
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