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Linear Phase Signals

In practice, a signal may be said to be linear phase when its phase is of the form

$\displaystyle \Theta(\omega_k)= - \Delta \cdot \omega_k\pm \pi I(\omega_k),
$

where $ \Delta$ is any real constant (usually an integer), and $ I(\omega_k)$ is an indicator function which takes on the values 0 or $ 1$ over the points $ \omega_k$ , $ k=0,1,2,\ldots,N-1$ . An important class of examples is when the signal is regarded as a filter impulse response.7.15 What all such signals have in common is that they are symmetric about the time $ n=\Delta$ in the time domain (as we will show on the next page). Thus, the term ``linear phase signal'' often really means ``a signal whose phase is linear between $ \pm\pi$ discontinuities.''


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-06 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA