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Nonlinear-Phase FIR Filter Design

Above, we considered only linear-phase (symmetric) FIR filters. The same methods also work for antisymmetric FIR filters having a purely imaginary frequency response, when zero-centered, such as differentiators and Hilbert transformers [224].

We now look at extension to nonlinear-phase FIR filters, managed by treating the real and imaginary parts separately in the frequency domain [218]. In the nonlinear-phase case, the frequency response is complex in general. Therefore, in the formulation Eq.(4.35) both $ {\underline{d}}$ and $ \mathbf {A}$ are complex, but we still desire the FIR filter coefficients $ {\underline{h}}$ to be real. If we try to use ' $ \backslash$ ' or pinv in matlab, we will generally get a complex result for $ {\underline{\hat{h}}}$ .

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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