The diagram in Fig. P-7.6(a) depicts a cascade connection of two LTI systems; i.e., the ou...

The diagram in Fig. P-7.6(a) depicts a cascade connection of two LTI systems; i.e., the output of the first system is the input to the second system, and the overall output is the output of the second system.

In this problem, assume that both systems in Fig. P-7.6 are 4-point running averagers.

Figure 7-6 Zeros on unit circle for second-order nulling filter to remove sinusoidal components at . There are two poles at the origin.

(a) Determine the system function H(z) = H1(z)H2(z) for the overall system.

(b) Plot the poles and zeros of H(z) in the z-plane.

Hint: The poles and zeros of H(z) are the combined poles and zeros of H1(z) and H2(z).

(c) From H(z), obtain an expression for the frequency response H(ejŵ) of the overall cascade system.

(d) Sketch the frequency response (magnitude and phase) functions of the overall cascade system for

(e) Use multiplication of z-transform polynomials to determine the impulse response h[n] of the overall cascade system.