11.3.3 Convolution of functions

Problem: For piecewise constant functions \( f(x) \) and \( g(x) \) of the form \[ \begin{array}{c} f(x)=\left\{\begin{array}{cc} 0, & x<-1 \\ 1, & -1 \leq x<0 \\ -2, & 0 \leq x<2 \\ 0, & x \geq 2 \end{array}\right. \\ g(x)=\left\{\begin{array}{cc} 0, & x<0 \\ 1, & 0 \leq x<1 \\ -2, & 1 \leq x<3 \\ 0, & x \geq 3 \end{array}\right. \end{array} \] find the cross-covariance and cross-correlation functions.