Constrained least Pth-norm optimal IIR filter
[num,den] = iirlpnormc(n,d,f,edges,a)
[num,den] = iirlpnormc(n,d,f,edges,a,w)
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius)
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p)
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p,dens)
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p,dens,initnum,initden)
[num,den,err] = iirlpnormc(...)
[num,den,err,sos,g] = iirlpnormc(...)
[num,den] = iirlpnormc(n,d,f,edges,a) returns
a filter having numerator order
n and denominator
d which is the best approximation to the
desired frequency response described by
the least-pth sense. The vector
the band-edge frequencies for multi-band designs. A constrained Newton-type
algorithm is employed.
be chosen so that the zeros and poles are used effectively. See the Hints section. Always check the resulting
[num,den] = iirlpnormc(n,d,f,edges,a,w) uses
the weights in
w to weight the error.
one entry per frequency point (the same length as
iirlpnormc how much emphasis to put
on minimizing the error in the vicinity of each frequency point relative
to the other points.
have the same number of elements, which can exceed the number of elements
edges. This allows for the specification of
filters having any gain contour within each band. The frequencies
edges must also appear in the vector
[num,den] = iirlpnormc(5,5,[0 .15 .4 .5 1],[0 .4 .5 1],... [1 1.6 1 0 0],[1 1 1 10 10])
designs a lowpass filter with a peak of 1.6 within the passband.
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius) returns
a filter having a maximum pole radius of
to 0.999999. Filters that have a reduced pole radius may retain better
transfer function accuracy after you quantize them.
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p) where
a two-element vector [
pmin pmax] allows for the
specification of the minimum and maximum values of
in the least-pth algorithm. Default is [2 128] which essentially yields
the L-infinity, or Chebyshev, norm.
be even. If
no optimization will occur. This can be used to inspect the initial
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p,dens) specifies
the grid density
dens used in the optimization.
The number of grid points is
default is 20.
dens can be specified as a single-element
cell array. The grid is not equally spaced.
[num,den] = iirlpnormc(n,d,f,edges,a,w,radius,p,dens,initnum,initden) allows
for the specification of the initial estimate of the filter numerator
and denominator coefficients in vectors
This may be useful for difficult optimization problems. The pole-zero
editor in Signal Processing Toolbox™ software can be used for generating
[num,den,err] = iirlpnormc(...) returns
the least-Pth approximation error
[num,den,err,sos,g] = iirlpnormc(...) returns
the second-order section representation in the matrix SOS and gain
G. For numerical reasons you may find SOS and G beneficial in some
This is a weighted least-pth optimization.
Check the radii and location of the resulting poles and zeros.
If the zeros are all on the unit circle and the poles are well inside of the unit circle, try increasing the order of the numerator or reducing the error weighting in the stopband.
Similarly, if several poles have a large radius and the zeros are well inside of the unit circle, try increasing the order of the denominator or reducing the error weight in the passband.
If you reduce the pole radius, you might need to increase the order of the denominator.
Poorly conditioned matrix. See the "help" file.
iirlpnormc cannot accurately
compute the optimization because either:
The approximation error is extremely small (try reducing the number of poles or zeros — refer to the hints above).
The filter specifications have huge variation, such as
a=[1 1e9 0 0].
Magnitude Response of Constrained Least Pth-norm Optimal IIR Filter
This example returns a lowpass filter whose pole radius is constrained to 0.8.
[b,a,err,s,g] = iirlpnormc(6,6,[0 .4 .5 1],[0 .4 .5 1],... [1 1 0 0],[1 1 1 1],.8); freqz(b,a);
The magnitude response shows the lowpass nature of the filter. The pole/zero plot following shows that the poles are constrained to 0.8 as specified in the command.
 Antoniou, A., Digital Filters: Analysis, Design, and Applications, Second Edition, McGraw-Hill, Inc. 1993.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
All inputs must be constant. Expressions or variables are allowed if their values do not change.
Does not support syntaxes that have cell array input.
Introduced in R2011a