Consider a system implemented by the follow­ing Matlab program:% xx.mat is a binary file c...

Consider a system implemented by the follow­ing Matlab program:

% xx.mat is a binary file containing the % vector of input samples called "xx" load xx

yyl = conv(ones(1,4),xx);

yy2 = conv([1, -1, -1, 1],xx);

ww = yyl + yy2;

yy = conv(ones(1,3),ww);

The overall system from input xx to output yy is an LTI system composed of three LTI systems.

(a) Draw a block diagram of the system that is implemented by the program given above. Be sure to indicate the impulse responses and difference equations of each of the component systems.

(b) The overall system is an LTI system. What is its impulse response, and what is the difference equation that is satisfied by the input x[n] and the output y[n]?

of H  gives the result

The magnitude and angle form of the frequency response is the most convenient form, since multiplication is most conveniently accomplished in polar form. The angle of the frequency response simply adds to the phase of the input, thereby producing additional phase shift in the complex exponential signal. Since the magnitude of the frequency response multiplies the magnitude of the complex exponential signal, this part of the frequency response controls the size of the output. Thus,  is also referred to as the gain of the system.