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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
convexoptimization algorithms [22]. The following sections
look at some specific cases.
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