Sunday, July 1, 2018

Can two nonzero signals x[n] and y[n] give a zero convolution



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[nk]=0 for all n.



Answer



Yes, for example let


x[k]=1


for all k and


y[k]={1k=01k=10otherwise


It is easy to see that in case of a convolution, the result will be zero for all values of n.


No comments:

Post a Comment

periodic trends - Comparing radii in lithium, beryllium, magnesium, aluminium and sodium ions

Apparently the of last four, MgX2+ is closest in radius to LiX+. Is this true, and if so, why would a whole larger shell ($\ce{...