Question

a) Determine the four-point circular convolution of the sequences in time-domain: $x_1(n) = {1, 5, 9, 8}$ $x_2(n) = {5, 5, 4, 7}$ b) Use the four-point DFT and IDFT to determine the sequence $x_3(n) = x_1(n) circledast x_2(n)$ The symbol $circledast$ corresponds to the four-point circular convolution. c) How long should two signals $x_1(n)$ and $x_2(n)$ be so that one period of their circular convolution is not affected by aliasing in time domain? How is this required length of the signals achieved in practice?

          a) Determine the four-point circular convolution of the sequences in time-domain:
$x_1(n) = {1, 5, 9, 8}$
$x_2(n) = {5, 5, 4, 7}$
b) Use the four-point DFT and IDFT to determine the sequence
$x_3(n) = x_1(n) circledast x_2(n)$
The symbol $circledast$ corresponds to the four-point circular convolution.
c) How long should two signals $x_1(n)$ and $x_2(n)$ be so that one period of their circular convolution is not affected by aliasing in time domain? How is this required length of the signals achieved in practice?

a) Determine the four-point circular convolution of the sequences in time-domain:
x1(n) = 1, 5, 9, 8
x2(n) = 5, 5, 4, 7
b) Use the four-point DFT and IDFT to determine the sequence
x3(n) = x1(n) circledast x2(n)
The symbol circledast corresponds to the four-point circular convolution.
c) How long should two signals x1(n) and x2(n) be so that one period of their circular convolution is not affected by aliasing in time domain? How is this required length of the signals achieved in practice?

Added by Antonio M.

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