Order

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

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Order

The order of a filter is defined as the order of its transfer function. Thus, from Eq. (B.2), the order of a causal, length$N+1$ FIR filter is $N$ (provided $h_{N-1}\).

Note from Fig. B.1 that $N$ is the total number of delay elements in the filter. This is the case in general for all filter implementations which are canonical with respect to delay.

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