Parks-McClellan optimal FIR filter order estimation
[n,fo,ao,w] = firpmord(f,a,dev)
[n,fo,ao,w] = firpmord(f,a,dev,fs)
c = firpmord(f,a,dev,fs,'cell')
[n,fo,ao,w] = firpmord(f,a,dev)
finds
the approximate order, normalized frequency band edges, frequency
band amplitudes, and weights that meet input specifications f
, a
,
and dev
.
f
is a vector of frequency band
edges (between 0 and F_{s}/2,
where F_{s} is the sampling
frequency), and a
is a vector specifying the desired
amplitude on the bands defined by f
. The length
of f
is two less than twice the length of a
.
The desired function is piecewise constant.
dev
is a vector the same size as a
that
specifies the maximum allowable deviation or ripples between the frequency
response and the desired amplitude of the output filter for each band.
Use firpm
with the resulting
order n
, frequency vector fo
,
amplitude response vector ao
, and weights w
to
design the filter b
which approximately meets the
specifications given by firpmord
input parameters f
, a
,
and dev
.
b = firpm(n,fo,ao,w)
[n,fo,ao,w] = firpmord(f,a,dev,fs)
specifies a sampling frequency fs
. fs
defaults
to 2 Hz, implying a Nyquist frequency of 1 Hz.
You can therefore specify band edges scaled to a particular application's
sampling frequency.
c = firpmord(f,a,dev,fs,'cell')
generates
a cell-array whose elements are the parameters to firpm
.
Note
In some cases, |
firpmord
uses the algorithm suggested in [1]. This method is inaccurate for band
edges close to either 0 or the Nyquist frequency, fs/2
.
[1] Rabiner, Lawrence R., and Otto Herrmann. "The Predictability of Certain Optimum Finite-Impulse-Response Digital Filters." IEEE^{®} Transactions on Circuit Theory. Vol. 20, Number 4, 1973, pp. 401–408.
[2] Rabiner, Lawrence R., and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975, pp. 156–157.