iirftransf
IIR frequency transformation of digital filter
Description
[
returns the numerator and the denominator coefficients of the transformed filter. num
,den
] = iirftransf(b
,a
,allpassNum
,allpassDen
)
The iirftransf
function transforms a prototype filter, specified by
the numerator b
and denominator a
, by using an
allpass mapping filter, specified by the numerator allpassNum
and the
denominator allpassDen
. If you do not specify an allpass mapping
filter, then the function returns an original filter.
Examples
Using the iirftransf
function, extend the passband of a lowpass IIR filter by using an allpass mapping filter.
Input Lowpass IIR Filter
Design a prototype real IIR lowpass elliptic filter with a gain of about –3 dB at 0.5π rad/sample.
[b,a] = ellip(3,0.1,30,0.409); freqz(b,a)
Transform Filter Using iirftransf
Extend the passband of the real prototype filter by specifying the allpass mapping filter as a vector of numerator and denominator coefficients, alpnum
and alpden
respectively. Use the allpasslp2lp
function to generate the allpass mapping filter coefficients.
Specify the prototype filter as a vector of numerator and denominator coefficients, b
and a
respectively.
[b,a] = ellip(3,0.1,30,0.409); [alpnum,alpden] = allpasslp2lp(0.5,0.25); [num,den] = iirftransf(b,a,alpnum,alpden);
Compare the magnitude response of the filters.
filterAnalyzer(b,a,num,den,FilterNames=["PrototypeFilterTFForm","TransformedFilterFromTFForm"]);
You can also specify the input lowpass IIR filter as a matrix of coefficients. Pass the second-order section matrices as inputs. The numerator and the denominator coefficients of the transformed filter are given by num2
and den2
, respectively.
[ss,g] = tf2sos(b,a);
[num2,den2] = iirftransf(ss(:,1:3),ss(:,4:6),...
alpnum,alpden);
Compare the magnitude response of the filters.
filterAnalyzer(ss(:,1:3),ss(:,4:6),num2,den2,FilterNames=["PrototypeFilterSOSForm",... "TransformedFilterFromSOSForm"]);
Input Arguments
Numerator coefficients of the prototype lowpass IIR filter, specified as either:
Row vector –– Specifies the values of [b0, b1, …, bn], given this transfer function form:
where n is the order of the filter.
Matrix –– Specifies the numerator coefficients in the form of an P-by-(Q+1) matrix, where P is the number of filter sections and Q is the order of each filter section. If Q = 2, the filter is a second-order section filter. For higher-order sections, make Q > 2.
In the transfer function form, the numerator coefficient matrix bik of the IIR filter can be represented using the following equation:
where,
a –– Denominator coefficients matrix. For more information on how to specify this matrix, see
a
.k –– Row index.
i –– Column index.
When specified in the matrix form, b and a matrices must have the same number of rows (filter sections) Q.
Data Types: single
| double
Complex Number Support: Yes
Denominator coefficients for a prototype lowpass IIR filter, specified as one of these options:
Row vector –– Specifies the values of [a0, a1, …, an], given this transfer function form:
where n is the order of the filter.
Matrix –– Specifies the denominator coefficients in the form of an P-by-(Q+1) matrix, where P is the number of filter sections and Q is the order of each filter section. If Q = 2, the filter is a second-order section filter. For higher-order sections, make Q > 2.
In the transfer function form, the denominator coefficient matrix aik of the IIR filter can be represented using the following equation:
where,
b –– Numerator coefficients matrix. For more information on how to specify this matrix, see
b
.k –– Row index.
i –– Column index.
When specified in the matrix form, a and b matrices must have the same number of rows (filter sections) P.
Data Types: single
| double
Complex Number Support: Yes
Numerator coefficients of the mapping filter, specified as a row vector.
Data Types: single
| double
Complex Number Support: Yes
Denominator coefficients of the mapping filter, specified as a row vector.
Data Types: single
| double
Complex Number Support: Yes
Output Arguments
Numerator coefficients of the transformed filter, returned as one of the following:
Row vector of length n+1, where n is the order of the input filter. The
num
output is a row vector when the input coefficientsb
anda
are row vectors.P-by-(Q+1) matrix, where P is the number of filter sections and Q is the order of each section of the transformed filter. The
num
output is a matrix when the input coefficientsb
anda
are matrices.
Data Types: single
| double
Complex Number Support: Yes
Denominator coefficients of the transformed filter, returned as one of the following:
Row vector of length n+1, where n is the order of the input filter. The
den
output is a row vector when the input coefficientsb
anda
are row vectors.P-by-(Q+1) matrix, where P is the number of filter sections and Q is the order of each section of the transformed filter. The
den
output is a matrix when the input coefficientsb
anda
are matrices.
Data Types: single
| double
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced in R2011a
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