ctf

R2026b

Convert digital filter to coefficients in cascaded transfer function format

Since R2026a

Syntax

[B,A] = ctf(filtObj)

[B,A,sv] = ctf(filtObj)

Description

[B,A] = ctf(filtObj) returns the numerator and denominator coefficients in the Cascaded Transfer Functions (CTF) format for the digitalFilter object or filter System object™.

[B,A,sv] = ctf(filtObj) returns the scale values in addition to the numerator and denominator coefficients.

To output scale values, filtObj must be one of the supported filter System objects from DSP System Toolbox™.

Examples

Get Coefficients in CTF Format for digitalFilter Object

Design a lowpass IIR filter with the passband frequency of 0.65π rad/sample and the stopband frequency of 0.80π rad/sample. The passband ripple is 1 dB and the stopband attenuation is 50 dB. Use the designfilt function to create a digitalFilter object with these specifications.

digiFilt = designfilt("lowpassiir", ...
    PassbandFrequency=0.65,StopbandFrequency=0.80, ...
    PassbandRipple=1,StopbandAttenuation=50)

digiFilt = 
 digitalFilter with properties:

   Coefficients:
              Numerator: [6×3 double]
            Denominator: [6×3 double]

   Specifications:
      FrequencyResponse: 'lowpass'
        ImpulseResponse: 'iir'
    NormalizedFrequency: 1
    StopbandAttenuation: 50
         PassbandRipple: 1
      StopbandFrequency: 0.8000
      PassbandFrequency: 0.6500
           DesignMethod: 'butter'

 Use filterAnalyzer to visualize filter
 Use designfilt to edit filter
 Use filter to filter data

Get coefficients in the CTF format for this filter.

[num,den] = ctf(digiFilt)

num = 6×3

    0.6865    1.3729    0.6865
    0.5694    1.1388    0.5694
    0.4953    0.9907    0.4953
    0.4498    0.8996    0.4498
    0.4250    0.8500    0.4250
    0.6459    0.6459         0

den = 6×3

    1.0000    0.9601    0.7857
    1.0000    0.7964    0.4812
    1.0000    0.6928    0.2885
    1.0000    0.6291    0.1701
    1.0000    0.5944    0.1056
    1.0000    0.2917         0

Get Coefficients in CTF Format for dsp.SOSFilter Object

Design a lowpass IIR filter of order 8 using the designLowpassIIR function. Set the SystemObject flag to true to generate a dsp.SOSFilter object. Set HasScaleValues to true.

sosFilt = designLowpassIIR(FilterOrder=8,HasScaleValues=true, ...
    SystemObject=true)

sosFilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [4×3 double]
          Denominator: [4×3 double]
       HasScaleValues: true
          ScaleValues: [0.1287 0.1051 0.0922 0.0865 1]

  Show all properties

Use the ctf function to obtain the filter coefficients in the CTF format. The function also outputs the scale values.

[sosnum,sosden,sv] = ctf(sosFilt)

sosnum = 4×3

     1     2     1
     1     2     1
     1     2     1
     1     2     1

sosden = 4×3

    1.0000   -1.2428    0.7575
    1.0000   -1.0153    0.4359
    1.0000   -0.8906    0.2595
    1.0000   -0.8351    0.1810

sv = 5×1

    0.1287
    0.1051
    0.0922
    0.0865
    1.0000

Get Coefficients in CTF Format for dsp.AllpassFilter Object

Create a dsp.AllpassFilter object and specify the allpass polynomial coefficients.

apFilt = dsp.AllpassFilter(AllpassCoefficients=[0   0.5539   0   0.2503;
                                                0  -0.4364   0   0.2218;
                                                0   0.3781   0  -0.3933])

apFilt = 
  dsp.AllpassFilter with properties:

                    Structure: 'Minimum multiplier'
          AllpassCoefficients: [3×4 double]
    TrailingFirstOrderSection: false

Use the ctf function to obtain coefficients in the CTF format and the scale values.

[apnum,apden,sv] = ctf(apFilt)

apnum = 3×5

    0.2503         0    0.5539         0    1.0000
    0.2218         0   -0.4364         0    1.0000
   -0.3933         0    0.3781         0    1.0000

apden = 3×5

    1.0000         0    0.5539         0    0.2503
    1.0000         0   -0.4364         0    0.2218
    1.0000         0    0.3781         0   -0.3933

sv = 
1

Get Coefficients in CTF format for Single-Rate Filter Cascade

Create a dsp.FilterCascade object with these filter stages:

• dsp.FIRFilter object

• dsp.SOSFilter object

• dsp.FourthOrderSectionFilter object

• dsp.IIRFilter object

• A scalar value of 3

Create a dsp.FIRFilter object using the designLowpassFIR function.

firFilt = designLowpassFIR(FilterOrder=8,SystemObject=true);

Create a dsp.SOSFilter object using the designLowpassIIR function.

sosFilt = designLowpassIIR(FilterOrder=8, ...
    HasScaleValues=true,SystemObject=true);

Create a dsp.FourthOrderSectionFilter object. Specify the filter coefficients.

fosNum =[0.0135    0.0541    0.0812    0.0541    0.0135
         0.0080    0.0319    0.0478    0.0319    0.0080];
fosDen =[1.0000   -2.2581    2.4552   -1.3108    0.3302
         1.0000   -1.7257    1.1842   -0.3779    0.0470];
fosFilt = dsp.FourthOrderSectionFilter(fosNum,fosDen);

Create a dsp.IIRFilter object. Specify the filter coefficients.

sosNum = [0.1287    0.2574    0.1287
          0.1051    0.2103    0.1051
          0.0922    0.1844    0.0922
          0.0865    0.1729    0.0865];
sosDen = [1.0000   -1.2428    0.7575
          1.0000   -1.0153    0.4359
          1.0000   -0.8906    0.2595
          1.0000   -0.8351    0.1810];
iirFilt = dsp.IIRFilter(sos2tf([sosNum,sosDen]));

Cascade these filters into a single dsp.FilterCascade object using the cascade function.

filtCascadeObj = cascade(firFilt,cascade(sosFilt,fosFilt),3,iirFilt)

filtCascadeObj = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.FIRFilter]
         Stage2: [1×1 dsp.FilterCascade]
         Stage3: 3
         Stage4: [1×1 dsp.IIRFilter]
    CloneStages: true

Use the ctf function to obtain the filter coefficients and scale values of the overall filter cascade in the CTF format.

[cascNum,cascDen,cascSV] = ctf(filtCascadeObj)

cascNum = 9×9

    0.0000    0.0191    0.1019    0.2309    0.2963    0.2309    0.1019    0.0191    0.0000
    1.0000    2.0000    1.0000         0         0         0         0         0         0
    1.0000    2.0000    1.0000         0         0         0         0         0         0
    1.0000    2.0000    1.0000         0         0         0         0         0         0
    1.0000    2.0000    1.0000         0         0         0         0         0         0
    0.0135    0.0541    0.0812    0.0541    0.0135         0         0         0         0
    0.0080    0.0319    0.0478    0.0319    0.0080         0         0         0         0
    3.0000         0         0         0         0         0         0         0         0
    0.0001    0.0009    0.0030    0.0060    0.0076    0.0060    0.0030    0.0009    0.0001

cascDen = 9×5

    1.0000         0         0         0         0
    1.0000   -1.2428    0.7575         0         0
    1.0000   -1.0153    0.4359         0         0
    1.0000   -0.8906    0.2595         0         0
    1.0000   -0.8351    0.1810         0         0
    1.0000   -2.2581    2.4552   -1.3108    0.3302
    1.0000   -1.7257    1.1842   -0.3779    0.0470
    1.0000         0         0         0         0
    1.0000    0.1000         0         0         0

cascSV = 10×1

    1.0000
    0.1287
    0.1051
    0.0922
    0.0865
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000

Input Arguments

filtObj — Digital filter

digitalFilter object | filter System object

Digital filter, specified as one of these filter objects:

• digitalFilter — Use designfilt to generate a digital filter based on frequency-response specifications.

• dsp.FIRFilter

• dsp.IIRFilter

• dsp.SOSFilter

• dsp.FourthOrderSectionFilter

• dsp.AllpassFilter

• dsp.FilterCascade

Output Arguments

B,A — Cascaded transfer function (CTF) coefficients

row vector | matrix

Cascaded transfer function (CTF) coefficients, returned as a row vector or matrix. B and A list the numerator and denominator coefficients of the cascaded transfer function, respectively.

The sizes for B and A are L-by-(m+1) and L-by-(n+1), respectively. The function returns the first column of A as 1, thus A(1) = 1 when A is a row vector.

• L represents the number of filter sections.

• m represents the order of the filter numerators.

• n represents the order of the filter denominators.

Each row of the B and A matrices contains the respective polynomial coefficients of each CTF section.

For more information about the cascaded transfer function format and coefficient matrices, see Return Digital Filters in CTF Format.

Data Types: single | double

sv — Scale values

scalar | column vector

Scale values, returned as a scalar or a column vector of length L+1, where L is the number of filter sections. The scale values represent the distribution of the filter gain across the sections of the cascaded filter representation.

To output scale values, the input filtObj argument must be one of the supported filter System objects from DSP System Toolbox.

Data Types: single | double

Version History

Introduced in R2026a