Constrained equiripple FIR filter
B = firceqrip(n,Fo,DEV)
B = firceqrip(...,'slope
',r)
B = firceqrip(...,'passedge
')
B = firceqrip(...,'stopedge
')
B = firceqrip(...,'high
')
B = firceqrip(...,'min
')
B = firceqrip(...,'invsinc
',C)
B = firceqrip(...,'invdiric',C)
B = firceqrip(n,Fo,DEV)
designs
an order n
filter (filter length equal n
+
1) lowpass FIR filter with linear phase.
firceqrip
produces the same equiripple
lowpass filters that firpm
produces
using the Parks-McClellan algorithm. The difference is how you specify
the filter characteristics for the function.
The input argument Fo
specifies the frequency
at the upper edge of the passband in normalized frequency (0<Fo
<1).
The two-element vector dev
specifies the peak or
maximum error allowed in the passband and stopbands. Enter [d1
d2]
for dev
where d1
sets
the passband error and d2
sets the stopband error.
B = firceqrip(...,'
uses
the input keyword 'slope
',r)slope
' and input argument r
to
design a filter with a nonequiripple stopband. r
is
specified as a positive constant and determines the slope of the stopband
attenuation in dB/normalized frequency. Greater values of r
result
in increased stopband attenuation in dB/normalized frequency.
B = firceqrip(...,'
designs
a filter where passedge
')Fo
specifies the frequency at which
the passband starts to rolloff.
B = firceqrip(...,'
designs
a filter where stopedge
')Fo
specifies the frequency at which
the stopband begins.
B = firceqrip(...,'
designs
a high pass FIR filter instead of a lowpass filter.high
')
B = firceqrip(...,'
designs
a minimum-phase filter.min
')
B = firceqrip(...,'
designs
a lowpass filter whose magnitude response has the shape of an inverse
sinc function. This may be used to compensate for sinc-like responses
in the frequency domain such as the effect of the zero-order hold
in a D/A converter. The amount of compensation in the passband is
controlled by invsinc
',C)C
, which is specified as a scalar
or two-element vector. The elements of C
are specified
as follows:
If C
is supplied as a real-valued
scalar or the first element of a two-element vector, firceqrip
constructs
a filter with a magnitude response of 1/sinc(C
*pi
*F
)
where F
is the normalized frequency.
If C
is supplied as a two-element
vector, the inverse-sinc shaped magnitude response is raised to the
positive power C(2)
. If we set P=C(2)
, firceqrip
constructs a filter with a magnitude response 1/sinc(C
*pi
*F
)^{P}.
If this FIR filter is used with a cascaded integrator-comb (CIC)
filter, setting C(2)
equal to the number of stages
compensates for the multiplicative effect of the successive sinc-like
responses of the CIC filters.
Note:
Since the value of the inverse sinc function becomes unbounded
at |
B = firceqrip(...,'invdiric',C)
designs
a lowpass filter with a passband that has the shape of an inverse
Dirichlet sinc function. The frequency response of the inverse Dirichlet
sinc function is given by
where C, r,
and p are scalars. The input C
can
be a scalar or vector containing 2 or 3 elements. If C
is
a scalar, p
and r
equal 1. If C
is
a two-element vector, the first element is C
and
the second element is p
, [C p]
.
If C
is a three-element vector, the third element
is r
, [C p r]
.
To introduce a few of the variations on FIR filters that you
design with firceqrip
, these five examples cover
both the default syntax b = firceqrip(n,wo,del)
and
some of the optional input arguments. For each example, the input
arguments n
, wo
, and del
remain
the same.
firceqrip
Design a 30th order FIR filter using firceqrip
.
b = firceqrip(30,0.4,[0.05 0.03]); fvtool(b)
Design a 30th order FIR filter with the stopedge
keyword to define the response at the edge of the filter stopband.
b = firceqrip(30,0.4,[0.05 0.03],'stopedge'); fvtool(b)
Design a 30th order FIR filter with the slope
keyword and r = 20.
b = firceqrip(30,0.4,[0.05 0.03],'slope',20,'stopedge'); fvtool(b)
Design a 30th order FIR filter defining the stopband and specifying that the resulting filter is minimum phase with the min
keyword.
b = firceqrip(30,0.4,[0.05 0.03],'stopedge','min'); fvtool(b)
Comparing this filter to the filter in Figure 1. The cutoff frequency wo = 0.4
now applies to the edge of the stopband rather than the point at which the frequency response magnitude is 0.5.
Viewing the zero-pole plot shown here reveals this is a minimum phase FIR filter - the zeros lie on or inside the unit circle, z = 1
fvtool(b,'polezero')
Design a 30th order FIR filter with the invsinc
keyword to shape the filter passband with an inverse sinc function.
b = firceqrip(30,0.4,[0.05 0.03],'invsinc',[2 1.5]); fvtool(b)
The inverse sinc function being applied is defined as 1/sinc(2*w)^1.5.
Design two order 30 constrained equiripple FIR filters with inverse-Dirichlet-sinc-shaped passbands. The cutoff frequency in both designs is pi/4 radians/sample. Set C=1
in one design C=2
in the second design. The maximum passband and stopband ripple is 0.05. Set p=1
in one design and p=2
in the second design.
Design the filters.
b1 = firceqrip(30,0.25,[0.05 0.05],'invdiric',[1 1]); b2 = firceqrip(30,0.25,[0.05 0.05],'invdiric',[2 2]);
Obtain the filter frequency responses using freqz
. Plot the magnitude responses.
[h1,~] = freqz(b1,1); [h2,w] = freqz(b2,1); plot(w,abs(h1)); hold on; plot(w,abs(h2),'r'); axis([0 pi 0 1.5]); xlabel('Radians/sample'); ylabel('Magnitude'); legend('C=1 p=1','C=2 p=2');
Inspect the stopband ripple in the design with C=1
and p=1
. The constrained design sets the maximum ripple to be 0.05. Zoom in on the stopband from the cutoff frequency of pi/4 radians/sample to 3pi/4 radians/sample.
figure; plot(w,abs(h1)); set(gca,'xlim',[pi/4 3*pi/4]); grid on;
diric
| fdesign.decimator
| fircls
| firgr
| firhalfband
| firls
| firnyquist
| firpm
| ifir
| iirgrpdelay
| iirlpnorm
| iirlpnormc
| sinc