Task 1 The convolution of two finite length signals can be written as a matrix vector product. Look at the documentation for the MATLAB convmtx command and the following MATLAB code that shows the convolution of two signals by (1) a matrix vector product and (2) the conv command as follows: >> x= [1 42 5]; h= [1 3-1 2]; >> convmtx(h',4)*x' >> conv(h,x)' Describe the form of the convolution matrix and why it works. Task 2 The N-point moving average filter has the impulse response: h(n) = { // 0nN-1 otherwise 0 1/N Use the MATLAB conv command to compute, y(n) = h(n) * h(n) for N = 5; 10; 20, and in each case make a stem plot of h(n) and y(n). Task 3 The signals f(n) and g(n) are shown below: -2 fin) 0 n g(n) n a) Using MATLAB, compute the convolution x(n) = f(n)* g(n) and plot it. b) What is the length of the output sequence?