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Formulated as an
norm minimization, the FIR filter design problem
can be stated as follows:
|
(5.31) |
where
-
FIR filter coefficients
-
suitable discrete set of frequencies
-
desired (complex) frequency response
-
obtained frequency response (typically fft(h))
-
(optional) error weighting function
An especially valuable property of FIR filter design under
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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