FIR Transfer Function

Chapter Contents:

Search Introduction to Digital Filters

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

The transfer function of an FIR filter is given by the z transform of its impulse response. This is true for any LTI filter, as discussed in Chapter 6. For FIR filters in particular, we have, from Eq. $\,$ (5.6),

$\displaystyle H(z) \isdef \sum_{n=-\infty}^{\infty} h_n z^{-n} = \sum_{n=0}^M b_n z^{-n} \protect$

(6.8)

Thus, the transfer function of every length

FIR filter is an

th-order polynomial in $z^{-1}$ .

Previous: Causal FIR Filters
Next: FIR Order

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

Sign in