(Solved): Problem 8: The correlation between two signals is a convolution-type operation that arises repeate ...

Problem 8: The correlation between two signals is a convolution-type operation that arises repeatedly in signal processing. Formally, the cross-correlation between signals $$x[n]$$ and $$y[n]$$ is $${?}_{xy}[n]=\underset{k=??}{\overset{?}{?}}x[n+k]y[k]$$ defined by the formula 8.1. Show that the correlation of two signals is nothing more than the convolution of one with a time reversed version of the other. That is, prove $${?}_{xy}[n]=x[n]?y[?n]$$ 8.2. Compute the correlation between the signals $$x[n]={\left(\frac{1}{4}\right)}^{n}u[n+1]\text{ and }y[n]=x[n]$$