Suppose x[n] and y[n] are two nonzero signals(i.e., x[n]≠0 for at least one value of n and similarly for y[n]).Can the convolution between x[n] and y[n] result in an identically zero signal? In other words, is it possible that k=+∞∑k=−∞x[k]y[n−k]=0 for all n.
Answer
Yes, for example let
x[k]=1
for all k and
y[k]={1k=0−1k=10otherwise
It is easy to see that in case of a convolution, the result will be zero for all values of n.
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