Given a linear time-invariant system, prove the properties below: (a) A constant group delay is a necessary
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Given a linear time-invariant system, prove the properties below:
(a) A constant group delay is a necessary but not sufficient condition for the delay introduced by the system to a sinusoid to be independent of its frequency.
(b) Let \(y_{1}(n)\) and \(y_{2}(n)\) be the outputs of the system to two sinusoids \(x_{1}(n)\) and \(x_{2}(n)\) respectively. A constant group delay \(\tau\) implies that if \(x_{1}\left(n_{0}\right)=x_{2}\left(n_{0}\right)\), then \(y_{1}\left(n_{0}-\tau\right)=y_{2}\left(n_{0}-\tau\right)\).
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Related Book For
Digital Signal Processing System Analysis And Design
ISBN: 9780521887755
2nd Edition
Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto
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