Obtain the direct form I, direct form II, cascade, and parallel structure for the following systems.

(a) y(n) = 3/4y(n – 1) – 1/8y(n – 2) + x(n) + 1/3x(n – 1)

(b) y(n) = -0.1y(n – 1) + 0.72y(n – 2) + 0.7x(n) – 0.252x(n – 2)

(c) y(n) = -0.1y(n – 1) + 0.2y(n – 2) + 3x(n) + 3.6x(n – 1) + 0.6x(n – 2)

(d) H(z) = 2(1 – z^–1)(1 + √2z^–1 + z^-2) / (1 + 0.5z ^–1)(1 – 0.9z^-1 + 0.81z^-2)

(e) y(n) = ½y(n – 1) + ¼y(n – 2) + x(n) + x(n – 1)

(f) y(n) = y(n – 1) – ½y(n – 2) + x(n) – x(n – 1) + x(n – 2)

Which of the systems above are stable? 

Transcribed Image Text:

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