Transfer Function

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Transfer Function

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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 © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Transfer Function

The transfer function associated with any filter is defined as the $z$ transform of its impulse response. For the FIR filter we have

\

Thus, the transfer function of every length $N+1$ causal FIR filter is an $N$th-order polynomial in $z$.

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