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See Periodic Convolution_Old Kiwi

Because DT signals repeat, a simple convolution can produce inaccurate results. Therefore, something must be done to correct. The most common operation is to pad the two signals with zeros so that the length of each signal is the length of the longer plus the length of the shorter.

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett