5.38. H(2) is the system function for a stable LTI system and is given by: (1-92-2)(1+1) H(z) = 1 - -1 (a) H(z) can be represented as a cascade of a minimum-phase system Hmin (2) and a unity- gain all-pass system Hap (z). Determine a choice for Hmin (2) and Hap(z) and specify whether or not they are unique up to a scale factor. (b) Is the minimum-phase system, Hmin (2), an FIR system? Explain. (c) Is the minimum-phase system, Hmin (2), a generalized linear-phase system? If not, can H(z) be represented as a cascade of a generalized linear-phase system Hin (2) and an all-pass system Hap2 (2)? If your answer is yes, determine Hin (2) and Hap2(z). If your answer is no, explain why such representation does not exist.

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5.38. H(2) is the system function for a stable LTI system and is given by:
(1-92-2)(1+1)
H(z) =
1 - -1
(a) H(z) can be represented as a cascade of a minimum-phase system Hmin (2) and a unity-
gain all-pass system Hap (z). Determine a choice for Hmin (2) and Hap(z) and specify
whether or not they are unique up to a scale factor.
(b) Is the minimum-phase system, Hmin (2), an FIR system? Explain.
(c) Is the minimum-phase system, Hmin (2), a generalized linear-phase system? If not, can
H(z) be represented as a cascade of a generalized linear-phase system Hin (2) and an
all-pass system Hap2 (2)? If your answer is yes, determine Hin (2) and Hap2(z). If your
answer is no, explain why such representation does not exist.
Transcribed Image Text:5.38. H(2) is the system function for a stable LTI system and is given by: (1-92-2)(1+1) H(z) = 1 - -1 (a) H(z) can be represented as a cascade of a minimum-phase system Hmin (2) and a unity- gain all-pass system Hap (z). Determine a choice for Hmin (2) and Hap(z) and specify whether or not they are unique up to a scale factor. (b) Is the minimum-phase system, Hmin (2), an FIR system? Explain. (c) Is the minimum-phase system, Hmin (2), a generalized linear-phase system? If not, can H(z) be represented as a cascade of a generalized linear-phase system Hin (2) and an all-pass system Hap2 (2)? If your answer is yes, determine Hin (2) and Hap2(z). If your answer is no, explain why such representation does not exist.
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