Constrained-least-squares linear-phase FIR lowpass and highpass filter design
b
=
fircls1(n,wo,dp,ds)
b =
fircls1(n,wo,dp,ds,'high
')
b =
fircls1(n,wo,dp,ds,wt)
b =
fircls1(n,wo,dp,ds,wt,'high
')
b =
fircls1(n,wo,dp,ds,wp,ws,k)
b =
fircls1(n,wo,dp,ds,wp,ws,k,'high
')
b =
fircls1(n,wo,dp,ds,...,'design_flag
')
b
generates
a lowpass FIR filter =
fircls1(n,wo,dp,ds)b
, where n+1
is
the filter length, wo
is the normalized cutoff
frequency in the range between 0 and 1 (where 1 corresponds
to the Nyquist frequency), dp
is the maximum passband
deviation from 1 (passband ripple), and ds
is the
maximum stopband deviation from 0 (stopband ripple).
b
generates
a highpass FIR filter =
fircls1(n,wo,dp,ds,'high
')b
. fircls1
always
uses an even filter order for the highpass configuration. This is
because for odd orders, the frequency response at the Nyquist frequency
is necessarily 0. If you specify an odd-valued n
, fircls1
increments
it by 1.
b
and =
fircls1(n,wo,dp,ds,wt)
b
specifies
a frequency =
fircls1(n,wo,dp,ds,wt,'high
')wt
above which (for wt
> wo
) or below
which (for wt
< wo
)
the filter is guaranteed to meet the given band criterion. This will
help you design a filter that meets a passband or stopband edge requirement.
There are four cases:
Lowpass:
0
< wt
< wo
< 1
: the amplitude of the filter is within dp
of 1 over the frequency range 0
< ω < wt
.
0
< wo
< wt
< 1
: the amplitude of the filter is within ds
of 0 over the frequency range wt
< ω < 1
.
Highpass:
0
< wt
< wo
< 1
: the amplitude of the filter is within ds
of 0 over the frequency range 0
< ω < wt
.
0
< wo
< wt
< 1
: the amplitude of the filter is within dp
of 1 over the frequency range wt
< ω < 1
.
b
generates
a lowpass FIR filter =
fircls1(n,wo,dp,ds,wp,ws,k)b
with a weighted function,
where n+1
is the filter length, wo
is
the normalized cutoff frequency, dp
is the maximum
passband deviation from 1 (passband ripple), and ds
is
the maximum stopband deviation from 0 (stopband ripple). wp
is
the passband edge of the L2 weight function and ws
is
the stopband edge of the L2 weight function, where wp
< wo
< ws
. k
is the ratio
(passband L2 error)/(stopband L2 error)
$$k=\frac{{\displaystyle {\int}_{0}^{{w}_{p}}{\left|A(\omega )-D(\omega )\right|}^{2}d\omega}}{{\displaystyle {\int}_{{w}_{z}}^{\pi}{\left|A(\omega )-D(\omega )\right|}^{2}d\omega}}$$
b
generates
a highpass FIR filter =
fircls1(n,wo,dp,ds,wp,ws,k,'high
')b
with a weighted function,
where ws
< wo
< wp
.
b
enables
you to monitor the filter design, where =
fircls1(n,wo,dp,ds,...,'design_flag
')'
design_flag
'
can
be
'trace'
, for a textual display
of the design table used in the design
'plots'
, for plots of the filter's
magnitude, group delay, and zeros and poles. 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
In the design of very narrow band filters with small |
[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.