Can cross-c.(x,y) be positive if signals x and y do not share frequencies?

1. Can convolution of two non zero signals be zero?
2. What is an uncorrelated signal?

Can convolution of two non zero signals be zero?

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

What is an uncorrelated signal?

Two signals which have no covariance are called uncorrelated (the correlation is the covariance normalized to lie between -1 and 1). In general, for two uncorrelated signals, the power of the sum is the sum of the powers: Put in terms of amplitude, this becomes: This is the familiar Pythagorean relation.