ctf2sysobj

R2026b

Create System object from cascaded transfer functions

Since R2025a

Syntax

ctfFiltObj = ctf2sysobj(Num,Den)

ctfFiltObj = ctf2sysobj(Num,Den,g)

ctfFiltObj = ctf2sysobj(___,Name=Value)

Description

ctfFiltObj = ctf2sysobj(Num,Den) creates a System object™ from a cascaded transfer function (CTF) with numerator coefficients Num and denominator coefficients Den.

ctfFiltObj = ctf2sysobj(Num,Den,g) also uses the scale values g of a digital filter.

ctfFiltObj = ctf2sysobj(___,Name=Value) uses additional options specified in the name-value arguments. Use this syntax with any of the input arguments in previous syntaxes.

Examples

Convert Second-Order FIR Filter in CTF Format to System Object

Since R2026b

Consider a second-order FIR filter with the numerator coefficients [1 2 1]. Convert this filter to a filter System object™ using the ctf2sysobj function.

You can implement the filter as an FIR filter, second-order section (SOS) filter, fourth-order section (FOS) filter, or as an arbitrary-order IIR filter. By default, the ctf2sysobj function creates a dsp.FIRFilter System object.

filtObjFIR = ctf2sysobj([1 2 1],1)

filtObjFIR = 
  dsp.FIRFilter with properties:

            Structure: 'Direct form'
      NumeratorSource: 'Property'
            Numerator: [1 2 1]
    InitialConditions: 0

  Show all properties

To create other filters, specify the filter type in the FilterTypes argument.

Create an SOS filter by setting the FilterTypes argument to "sos".

filtObjSOS = ctf2sysobj([1 2 1],1,FilterTypes="sos")

filtObjSOS = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [1 2 1]
          Denominator: [1 0 0]
       HasScaleValues: false

  Show all properties

Create an IIR filter by setting the FilterTypes argument to "iir".

filtObjIIR = ctf2sysobj([1 2 1],1,FilterTypes="iir")

filtObjIIR = 
  dsp.IIRFilter with properties:

            Structure: 'Direct form II transposed'
            Numerator: [1 2 1]
          Denominator: 1
    InitialConditions: 0

  Show all properties

Convert Mixed-Order CTF to System Object

Since R2026b

Consider a set of CTF coefficients with mixed orders.

• First row is an FIR filter of order 4.

• Second row is a scalar value.

• Third row is a SOS filter.

• Last row is an allpole filter of order 4.

Num = [1 2 1 3 4;
    17 0 0 0 0
    1 2 1 0 0;
    1 0 0 0 0];
Den = [1 0 0 0 0;
    12 0 0 0 0
    1 0 2 0 0;
    1 -3 2 -1 0];

Convert these CTF coefficients to a filter System object using the ctf2sysobj function.

Allow all filter types by setting the FilterTypes argument to "all". The function opts to use a dsp.FIRFilter object for the first row, a scalar for the second row, and the dsp.FourthOrderSectionFilter object for the last two rows. The function cascades these filter objects as individual stages of the dsp.FilterCascade object.

filtObjCasc = ctf2sysobj(Num,Den,FilterTypes="all")

filtObjCasc = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.FIRFilter]
         Stage2: 1.4167
         Stage3: [1×1 dsp.FourthOrderSectionFilter]
    CloneStages: true

Implement this filter as a single fourth-order section filter by setting the FilterTypes argument to "fos".

filtObjFOS = ctf2sysobj(Num,Den,FilterTypes="fos")

filtObjFOS = 
  FourthOrderSectionFilter with properties:

               Numerator: [4×5 double]
             Denominator: [4×5 double]
          RoundingMethod: 'Floor'
          OverflowAction: 'Wrap'
    CoefficientsDataType: [1×1 embedded.numerictype]
     AccumulatorDataType: 'Inherit: Inherit via internal rule'
          OutputDataType: 'Inherit: Same as input'

You can also avoid the fourth-order section filter implementation and specify other types explicitly. The function then creates a dsp.FilterCascade object with the other filter types.

filtObj = ctf2sysobj(Num,Den,FilterTypes=["fir","scalar","allpole","sos"])

filtObj = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.FIRFilter]
         Stage2: 1.4167
         Stage3: [1×1 dsp.SOSFilter]
         Stage4: [1×1 dsp.AllpoleFilter]
    CloneStages: true

To omit the scalar, remove the "scalar" option from the FilterTypes argument list. The function then implements the scalar stage with a dsp.FIRFilter object.

filtObjNoScalar = ctf2sysobj(Num,Den,FilterTypes=["fir","allpole","sos"])

filtObjNoScalar = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.FIRFilter]
         Stage2: [1×1 dsp.FIRFilter]
         Stage3: [1×1 dsp.SOSFilter]
         Stage4: [1×1 dsp.AllpoleFilter]
    CloneStages: true

Convert CTF Coefficients with Non-Unique Implementations to System Object

Since R2026b

When more than one filter implementation is possible for a given set of coefficients, the ctf2sysobj function implements the filter based on the hierarchy discussed in the Filter Implementation Hierarchy section.

Consider a 3-tap FIR filter with the coefficients [1 2 1]. This filter can be implemented as an FIR filter, second-order section filter, fourth-order section filter, or an IIR filter.

Allow all filter types. The function opts for the FIR implementation as its first choice.

filtObj = ctf2sysobj([1 2 1],1,FilterTypes="all")

filtObj = 
  dsp.FIRFilter with properties:

            Structure: 'Direct form'
      NumeratorSource: 'Property'
            Numerator: [1 2 1]
    InitialConditions: 0

  Show all properties

Exclude "fir" from the filter types list. The function chooses the second-order section filter implementation.

filtObjNoFIR = ctf2sysobj([1 2 1],1,FilterTypes=["sos","fos","iir"])

filtObjNoFIR = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [1 2 1]
          Denominator: [1 0 0]
       HasScaleValues: false

  Show all properties

Exclude the "sos" implementation. The function chooses "fos" and implements a dsp.FourthOrderSectionFilter object.

filtObjNoSOS = ctf2sysobj([1 2 1],1,FilterTypes=["fos","iir"])

filtObjNoSOS = 
  FourthOrderSectionFilter with properties:

               Numerator: [1 2 1 0 0]
             Denominator: [1 0 0 0 0]
          RoundingMethod: 'Floor'
          OverflowAction: 'Wrap'
    CoefficientsDataType: [1×1 embedded.numerictype]
     AccumulatorDataType: 'Inherit: Inherit via internal rule'
          OutputDataType: 'Inherit: Same as input'

Exclude "fos". The function implements an IIR filter.

filtObjIIR = ctf2sysobj([1 2 1],1,FilterTypes="iir")

filtObjIIR = 
  dsp.IIRFilter with properties:

            Structure: 'Direct form II transposed'
            Numerator: [1 2 1]
          Denominator: 1
    InitialConditions: 0

  Show all properties

If you specify "allpole" or "scalar" instead of the other filter types, the function errors out because these two options do not work for the CTF coefficients [1 2 1].

Convert IIR Filter in CTF Format to System Object

Design a sixth-order bandpass elliptic filter. Obtain the numerator and denominator coefficients in CTF format. The size of the filter coefficients matrices indicate three fourth-order sections.

[Num,Den] = ellip(6,3,50,[0.3 0.6],"bandpass","ctf")

Num = 3×5

    0.2275   -0.0435   -0.1999   -0.0435    0.2275
    0.2275   -0.1070    0.1733   -0.1070    0.2275
    0.2275   -0.1188    0.2423   -0.1188    0.2275

Den = 3×5

    1.0000   -0.6236    1.6521   -0.5161    0.6936
    1.0000   -0.5779    1.3890   -0.5327    0.8714
    1.0000   -0.5568    1.2684   -0.5468    0.9715

Convert the filter in the CTF format to a System object. The ctf2sysobj function returns a dsp.FourthOrderSectionFilter object.

ctfObj = ctf2sysobj(Num,Den)

ctfObj = 
  FourthOrderSectionFilter with properties:

               Numerator: [3×5 double]
             Denominator: [3×5 double]
          RoundingMethod: 'Floor'
          OverflowAction: 'Wrap'
    CoefficientsDataType: [1×1 embedded.numerictype]
     AccumulatorDataType: 'Inherit: Inherit via internal rule'
          OutputDataType: 'Inherit: Same as input'

Visualize the magnitude response of the System object and of the filter representation in numerator and denominator coefficients. Both filter representations give the same magnitude response. The filter is in normalized frequency units.

fa = filterAnalyzer(ctfObj);
addFilters(fa,Num,Den)

Specify an absolute sample rate for the filter using the SampleRate argument.

ctfObjAbsSampleRate = ctf2sysobj(Num,Den,SampleRate=22050)

ctfObjAbsSampleRate = 
  FourthOrderSectionFilter with properties:

               Numerator: [3×5 double]
             Denominator: [3×5 double]
          RoundingMethod: 'Floor'
          OverflowAction: 'Wrap'
    CoefficientsDataType: [1×1 embedded.numerictype]
     AccumulatorDataType: 'Inherit: Inherit via internal rule'
          OutputDataType: 'Inherit: Same as input'

Visualize the magnitude response of the filter in absolute frequency units.

filterAnalyzer(ctfObjAbsSampleRate)

To change the sample rate after constructing the object, use the setInputSampleRate function.

setInputSampleRate(ctfObjAbsSampleRate,44100)
filterAnalyzer(ctfObjAbsSampleRate)

Convert Cascade of FIR Filters to System Object

Define a CTF numerator array for a cascade of two FIR filters of order 100. Convert the cascade of filters to a System object.

Num = [designLowpassFIR(FilterOrder=100); ...
       designHighpassFIR(FilterOrder=100)];

Hsys = ctf2sysobj(Num)

Hsys = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.FIRFilter]
         Stage2: [1×1 dsp.FIRFilter]
    CloneStages: true

Cascade of Second-Order Section Filters with Scale Values

Customize the conversion from CTF to System object and add filter cascade stages.

Design an eight-order Butterworth peak IIR filter. The number of columns in the filter coefficients, B and A, indicate that the peak filter is divided in second-order sections. The vector of scale values, g, contains the gain for the four stages and the overall system gain.

[B,A,g] = designNotchPeakIIR(FilterOrder=8, ...
     QualityFactor=5,HasScaleValues=true)

B = 4×3

    1.0000    2.0000    1.0000
    1.0000   -2.0000    1.0000
    1.0000    2.0000    1.0000
    1.0000   -2.0000    1.0000

A = 4×3

    1.0000    0.2738    0.8880
    1.0000   -0.2738    0.8880
    1.0000    0.1067    0.7455
    1.0000   -0.1067    0.7455

g = 5×1

    0.1479
    0.1479
    0.1380
    0.1380
    1.0000

Convert the filter coefficients to a System object.

sosSys = ctf2sysobj(B,A,g)

sosSys = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [4×3 double]
          Denominator: [4×3 double]
       HasScaleValues: true
          ScaleValues: [5×1 double]

  Show all properties

By default, the ctf2sysobj function generates a dsp.SOSFilter System object for IIR filters of the order 2 or less. To generate a dsp.FilterCascade System object, specify the ForceCascade name-value argument as true. You can add filter stages in the next step.

Convert the filter coefficients to a dsp.FilterCascade System object.

ctfSys = ctf2sysobj(B,A,g,ForceCascade=true)

ctfSys = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.SOSFilter]
    CloneStages: true

Add two stages to the dsp.FilterCascade System object. The stages comprise an allpass filter and a polyphase FIR sample-rate conversion filter. Display the System object. The resulting dsp.FilterCascade System object has three stages.

addStage(ctfSys, dsp.AllpassFilter)
addStage(ctfSys, dsp.FIRRateConverter(3,2,triang(9)))
ctfSys

ctfSys = 
  dsp.FilterCascade with properties:

         Stage1: [1×1 dsp.SOSFilter]
         Stage2: [1×1 dsp.AllpassFilter]
         Stage3: [1×1 dsp.FIRRateConverter]
    CloneStages: true

Plot the impulse response discrete-time Fourier transform (DTFT) of the three-stage dsp.FilterCascade System object.

freqzmr(ctfSys)

Input Arguments

Num — CTF numerator coefficients

matrix | row vector | scalar

CTF numerator coefficients, specified as a matrix, vector, or scalar.

Num must be of size L-by-(m + 1), where:

• L represents the number of filter sections.

• m represents the order of the filter numerators.

For more information about the CTF format and coefficient matrices, see Specify Digital Filters in CTF Format.

Data Types: single | double
Complex Number Support: Yes

Den — CTF denominator coefficients

1 (default) | matrix | vector | scalar

CTF denominator coefficients, specified as a matrix, vector, or scalar.

Den must be of size L-by-(n + 1), where:

• L represents the number of filter sections.

• n represents the order of the filter denominators.

For more information about the CTF format and coefficient matrices, see Specify Digital Filters in CTF Format.

Note

If any element of Den(:,1) is not equal to 1, then ctf2sysobj normalizes the filter coefficients by Den(:,1). In this case, Den(:,1) must be nonzero.

Data Types: single | double
Complex Number Support: Yes

g — Scale values

1 (default) | vector | scalar

Scale values, specified as a real-valued scalar or as a real-valued vector with L + 1 elements, where L is the number of filter sections. The scale values represent the distribution of the filter gain across sections of the cascaded filter representation.

Depending on how you specify g, ctf2sysobj applies a gain to the filter sections using the scaleFilterSections function:

• Scalar — ctf2sysobj distributes the gain uniformly across all filter sections.

• Vector — ctf2sysobj applies the first L gain values to the corresponding filter sections and distributes the last gain value uniformly across all filter sections.

Data Types: single | double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: ctfFiltObj = ctf2sysobj([2 4 2;1 0 0],ForceCascade=true) specifies an FIR digital filter with option to wrap each filter stage into System object.

FilterTypes — Type of filter to implement

'all' (default) | "fir" | "iir" | "allpole" | "sos" | "fos" | "scalar" | string array of filter options | cell array of filter options

Since R2026b

Type of filter to implement, specified as one of these:

• 'all' — All available filter types. The function picks a filter type based on the format of the CTF coefficients and the filter implementation hierarchy.

  If the coefficients allow all filter types, the function uses "fir" as the first choice.

• "fir" — FIR filter implemented as a dsp.FIRFilter object.

• "allpole" — Allpole filter implemented as a dsp.AllpoleFilter object. The leading denominator coefficient of the allpole filter must be 1 and the numerator is always 1.

• "sos" — Second-order section filter implemented as a dsp.SOSFilter object.

• "fos" — Fourth-order section filter implemented as a dsp.FourthOrderSectionFilter object.

• "iir" — IIR filter implemented as a dsp.IIRFilter object.

• "scalar" — Scalar gain implemented as one or more stages in the dsp.FilterCascade object.

• Cell array or string array of filter types — You can specify multiple allowable filter types as a string array or a cell array. For example, ["fir","iir","sos"] or {"fir","iir","sos"}. If the CTF coefficients support more than one specified filter type, the function uses the filter implementation hierarchy to determine which filter to implement. For an example, see Convert CTF Coefficients with Non-Unique Implementations to System Object.

Example: ["fir","iir","sos"], {"fir","iir","sos"}

Data Types: char | string

ForceCascade — Option to force single-stage cascades into dsp.FilterCascade System object

false or 0 (default) | true or 1

Option to force single-stage cascades into a dsp.FilterCascade System object, specified as one of these:

• false (0) — ctf2sysobj returns each filter stage as one of these formats:

  • dsp.SOSFilter — Second-order sections (SOS) format.

  • dsp.FourthOrderSectionFilter — Fourth-order sections (FOS) format.

  • dsp.IIRFilter — Infinite impulse response (IIR) filter format.

  • dsp.FIRFilter — Finite impulse response (FIR) filter format.

• true (1) — ctf2sysobj wraps and returns each stage into a dsp.FilterCascade object.

  • Single-stage dsp.FilterCascade object, for filters in SOS and FOS format.

  • Multiple-stage dsp.FilterCascade object, for FIR and IIR filters in CTF format.

Data Types: logical

ParseColumnVectorsAsRows — Option to treat column vectors as rows (single-stage CTF)

true or 1 (default) | false or 0

Option to treat column vectors (Num and Den) as row vectors (single-stage CTF), specified as on these values:

• true (1) — When you specify Num and Den as column vectors, ctf2sysobj assumes that Num and Den list the coefficients of a single-stage filter.

• false (0) — When you specify Num and Den as column vectors, ctf2sysobj assumes that each row of Num and Den relates to a separate filter stage.

  To specify ParseColumnVectorsAsRows as false (0), you must specify Num and Den as vectors with the same number of rows and Den must end with nonzero elements.

Data Types: logical

SampleRate — Input sample rate

scalar | "normalized"

Since R2026a

Input sample rate of the filter object, specified as one of these:

• Positive real scalar — The input sample rate of the filter object is a positive real scalar.

• "normalized" — The input sample rate of the filter object is in normalized frequency units.

Data Types: single | double | char | string

Output Arguments

ctfFiltObj — CTF filter System object

dsp.FilterCascade object | dsp.IIRFilter object | dsp.SOSFilter object | dsp.FourthOrderSectionFilter object | dsp.FIRFilter object

CTF filter System object, returned as one of these System objects:

• dsp.SOSFilter — Second-order sections (SOS)

• dsp.FourthOrderSectionFilter — Fourth-order sections (FOS)

• dsp.IIRFilter — Infinite impulse response (IIR) filter

• dsp.FIRFilter — Finite impulse response (FIR) filter

• dsp.FilterCascade — Cascade of dsp.SOSFilter, dsp.FourthOrderSectionFilter. dsp.IIRFilter and dsp.FIRFilter System objects

The ctf2sysobj identifies filter stages (SOS, FOS, IIR, or FIR) from the coefficients specified in Num and Den.

• While an SOS or FOS filter stage can have multiple sections, each IIR or FIR filter stage has one section.

• The order of each filter stage (stage order) is the maximum between the numerator order and denominator order.

When more than one filter implementation is possible for a given set of CTF coefficients, the ctf2sysobj function uses the filter implementation hierarchy to select the filter type. (since R2026b)

Depending on the number of stages, maximum order of each stage, and the value specified in ForceCascade, ctf2sysobj returns one of the System objects in this table.

Stage Impulse Response Type	Stage Order	ForceCascade=false (Single-stage CTF)	ForceCascade=false (Multiple-stage CTF)	ForceCascade=true (Single-stage and multiple-stage CTF)
IIR	1 or 2	dsp.SOSFilter	Does not apply	Single-stage dsp.FilterCascade
IIR	3 or 4	dsp.FourthOrderSectionFilter	Does not apply	Single-stage dsp.FilterCascade
IIR	Greater than 4	dsp.IIRFilter	dsp.FilterCascade	dsp.FilterCascade
FIR	Any	dsp.FIRFilter	dsp.FilterCascade	dsp.FilterCascade
Combination of the above		Does not apply	dsp.FilterCascade	dsp.FilterCascade

More About

Filter Implementation Hierarchy

Filter implementation is not always unique. For example, any second-order section filter is also a fourth-order section filter, and fourth-order section filter is a special case of an IIR filter. An allpole filter is also a special case of an IIR filter.

When more than one filter implementation is possible for a given set of CTF coefficients, the ctf2sysobj function uses the following filter implementation hierarchy to select the filter type. For example, if you set FilterTypes to ["fir", "sos"], and the CTF coefficients can be implemented using both the filter types, the function chooses "sos" and implements a dsp.SOSFilter object. Similarly, if a set of CTF coefficients can be implemented using both the "allpole" and "sos" filter types, the function chooses "allpole" and creates a dsp.AllpoleFilter object. If you set FilterTypes to "all", and the CTF coefficients satisfy all filter types, the function prefers "fir".

Here is the filter implementation hierarchy.

"scalar" → "fir" → "allpole" → "sos" → "fos" → "iir"

For an example, see Convert CTF Coefficients with Non-Unique Implementations to System Object.

This table lists the default filter implementation for each filter type. For each row of the CTF coefficients that you specify, the ctf2sysobj function identifies the filter type from this table, and then selects the closest implementation from the filter types specified in the FilterTypes argument.

Filter Type	Description	Default Filter Implementation
"scalar"	Scalar gain	Scalar stage of dsp.FilterCascade object
"fir"	FIR filter of any order	dsp.FIRFilter object One or more stages of dsp.FilterCascade object
"allpole"	Allpole filter of any order. The leading denominator coefficient must be 1. The numerator is always 1.	dsp.AllpoleFilter object One or more stages of dsp.FilterCascade object
"sos"	Second-order IIR filter	dsp.SOSFilter object
"fos"	Fourth-order IIR filter	dsp.FourthOrderSectionFilter object
"iir"	Higher order IIR filter	dsp.IIRFilter
"all"	Any of the above	Uses the filter implementation hierarchy

Version History

Introduced in R2025a

R2026b: New FilterTypes argument

You can now specify the type of filter to implement in the ctf2sysobj function using the new FilterTypes argument.