Consider the system given in Problem 9.40. Determine the parallel-form structure and wri...

Consider the system given in Problem 9.40. Determine the parallel-form structure and write a program for its implementation.

where are defined in Table 10.8. Substitution into H(z) yields

Note that the resulting filter has zeros at z = ±1 and a pair of poles that depend on the choice of

For example, suppose that and Since we find that K=1, and Then

This filter has poles at z = ±j0.713 and hence resonates at ω = π/2.

Reference of Problem 9.40:

Consider the system specified by the system function

(a)Choose so that the gain of each second-order section at ω = 0 is equal to 1.

(b)Sketch the direct form 1, direct form 2, and cascade realizations of the system.

(c) Write a program that implements the direct form 1 and direct form 2, and compute the first 100 samples of the impulse response and the step response of the system.

(d) Plot the results in part (c) to illustrate the proper functioning of the programs.