Implementing IIR/FIR Filters

Reference 5). Basically, a guess is made for the initial
N/2 + 1 extremal frequencies. (Usually, this
guess consists of N/2 + 1 equally spaced frequencies
in the Nyquist range.) Using this guess, is
solved for the coefficients and δ. Using these coefficients,
A(θ) is calculated for all frequencies and
the extrema, and frequencies at which the extrema
are attained are determined. If the extrema are all
equal and equal to or less than that specified in the
initial filter specification, the problem is solved.
However, if this is not the case, the frequencies at
which the extrema were attained are used as the
next guess. Note that the final extremal frequencies
do not have to be equally spaced. Clearly, the equiripple
design approach is calculation intensive.
What is the benefit of equiripple designs over window
designs? In general, equiripple designs require
fewer taps for straightforward requirements. When
the specification requires a sharp cutoff and/or a
large stopband attenuation or a narrow bandpass,
the equiripple approach may fail to converge. In
general, when N is decreased, an equiripple design
tends to maintain its transition band while sacrificing
stopband attenuation; window designs tend to
do the opposite. Of the window alternatives, the
Kaiser window is preferred for designing filters because
the passband ripple and stopband
attenuation can be varied relatively independent of
the transition width (see Reference 1). For spectral
analysis, the Blackman-Harris window is preferred
(see Reference 10).
7-28 MOTOROLA