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Filter Design using Lp Norms

Formulated as an $ \ensuremath{L_p}$ norm minimization, the FIR filter design problem can be stated as follows:

$\displaystyle \min_h \left\Vert W(\omega_k)\left[H(\omega_k) - D(\omega_k)\right]\right\Vert _p$ (5.31)

where An especially valuable property of FIR filter design under $ \ensuremath{L_p}$ norms is that the error norm is typically a convex function of the filter coefficients, rendering it amenable to a wide variety of convex-optimization algorithms [22]. The following sections look at some specific cases.


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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