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
and
are complex, but we still desire the FIR filter coefficients
to be real. If we try to use '
' or `pinv` in
matlab, we will generally get a complex result for
.

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