Constrained-least-squares FIR multiband filter design
b
=
fircls(n,f,amp,up,lo)
fircls(n,f,amp,up,lo,'design_flag
')
b
generates
a length =
fircls(n,f,amp,up,lo)n+1
linear phase FIR filter b
.
The frequency-magnitude characteristics of this filter match those
given by vectors f
and amp
:
f
is a vector of transition frequencies
in the range from 0 to 1, where 1 corresponds to the Nyquist frequency.
The first point of f
must be 0
and
the last point 1
. The frequency
points must be in increasing order.
amp
is a vector describing the
piecewise-constant desired amplitude of the frequency response. The
length of amp
is equal to the number of bands in
the response and should be equal to length(f)-1
.
up
and lo
are
vectors with the same length as amp
. They define
the upper and lower bounds for the frequency response in each band.
fircls
always uses an even filter order for
configurations with a passband at the Nyquist frequency (that is,
highpass and bandstop filters). This is because for odd orders, the
frequency response at the Nyquist frequency is necessarily 0.
If you specify an odd-valued n
, fircls
increments
it by 1.
fircls(n,f,amp,up,lo,'
enables
you to monitor the filter design, where design_flag
')'
design_flag
'
can
be
'trace'
, for a textual display
of the design error at each iteration step.
'plots'
, for a collection of plots
showing the filter's full-band magnitude response and a zoomed view
of the magnitude response in each sub-band. All plots are updated
at each iteration step. The O's on the plot are the estimated extremals
of the new iteration and the X's are the estimated extremals of the
previous iteration, where the extremals are the peaks (maximum and
minimum) of the filter ripples. Only ripples that have a corresponding
O and X are made equal.
'both'
, for both the textual display
and plots.
Note
Normally, the lower value in the stopband will be specified
as negative. By setting |
fircls
uses an iterative least-squares algorithm
to obtain an equiripple response. The algorithm is a multiple exchange
algorithm that uses Lagrange multipliers and Kuhn-Tucker conditions
on each iteration.
[1] Selesnick, I. W., M. Lang, and C. S. Burrus. "Constrained Least Square Design of FIR Filters without Specified Transition Bands." Proceedings of the 1995 International Conference on Acoustics, Speech, and Signal Processing. Vol. 2, 1995, pp. 1260–1263.
[2] Selesnick, I. W., M. Lang, and C. S. Burrus. "Constrained Least Square Design of FIR Filters without Specified Transition Bands." IEEE^{®} Transactions on Signal Processing. Vol. 44, Number 8, 1996, pp. 1879–1892.