Translations:Frequency response of a digital system/38/en

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We can prove the group-delay theorem as follows: Often it is convenient to change our time scale from a scale in seconds to a scale in which the discrete time-spacing is one unit. Then we can let so . The Nyquist frequency becomes simply , and the Nyquist range becomes . The pure-delay all-pass system, as we have seen, has phase lag where time delay , so it satisfies the theorem. The dispersive all-pass system is made up of q factors of the form . In terms of frequency, this factor becomes