dsp.SOSFilter

Implement cascade of second order section filters

Since R2020a

Description

The dsp.SOSFilter System object™ implements an IIR filter structure using second-order sections (SOS).

To implement an IIR filter structure using SOS:

Create the dsp.SOSFilter object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

This object supports C/C++ code generation and SIMD code generation under certain conditions. This object also supports code generation for ARM^® Cortex^®-M and ARM Cortex-A processors. For more information, see Code Generation.

Creation

Syntax

sos = dsp.SOSFilter

sos = dsp.SOSFilter(num,den)

sos = dsp.SOSFilter(Name,Value)

Description

sos = dsp.SOSFilter returns a biquadratic IIR filter System object, sos, which independently filters each channel (column) of the input over time using a specified biquadratic structure.

example

sos = dsp.SOSFilter(num,den) returns a biquadratic filter object with the Numerator property set to num and the Denominator property set to den.

sos = dsp.SOSFilter(Name,Value) returns a biquadratic filter object with each property set to the specified value. Enclose each property name in single quotes.

Example: sos = dsp.SOSFilter('CoefficientSource','Input port')

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`Structure` — Filter structure
`'Direct form II transposed'` (default) | `'Direct form I'` | `'Direct form I transposed'` | `'Direct form II'`

Filter structure, specified as one of 'Direct form I', 'Direct form I transposed', 'Direct form II', or 'Direct form II transposed'.

`CoefficientSource` — Source of filter coefficients
`'Property'` (default) | `'Input port'`

Source of the filter coefficients, specified as one of the following:

'Property' –– The filter coefficients are specified through the Numerator, Denominator, and ScaleValues properties.
'Input port' –– The numerator coefficients, denominator coefficients, and the scale values are specified as inputs to the object while running the algorithm. For more details, see Usage.

`Numerator` — Numerator coefficients of filter
[`0.0975 0.195 0.0975`] (default) | P-by-3 matrix

Numerator coefficients of the filter, specified as an P-by-3 matrix, where P is the number of biquadratic sections. Each row corresponds to the numerator coefficients of the corresponding section of the filter.

The size of this property cannot be modified once you have run the System object algorithm. However, the coefficient values can change as the property is tunable.

Tunable: Yes

Dependencies

To enable this property, set the CoefficientSource property to 'Property'.

`Denominator` — Denominator coefficients of filter
[`1 -0.9428 0.3333`] (default) | P-by-3 matrix

Denominator coefficients of the filter, specified as an P-by-3 matrix, where P is the number of biquadratic sections. Each row corresponds to the denominator coefficients of the corresponding section of the filter.

The leading denominator coefficient is always assumed to be 1. If any other value is specified in the first column, the object ignores this value and treats it as 1.

The size of this property cannot be modified once you step through the algorithm. However, the denominator values can be modified as the property is tunable.

Tunable: Yes

Dependencies

To enable this property, set CoefficientSource property to 'Property'.

`HasScaleValues` — Specify if filter has scale values for each section
`false` (default) | `true`

Specify if the filter has scale values for each section. When set to true, using the ScaleValues property, you can specify the scale values to be applied before and after each section of the biquadratic filter.

`ScaleValues` — Scale values for each biquad second-order section
[`1 1`] (default) | vector

Scale values to apply before and after each section of a biquadratic filter, specified as a vector. The length of the ScaleValues vector must be P + 1, where P is the number of biquadratic sections. If you set this property to a scalar value, the scalar value is used as the gain value only before the first filter section. The remaining gain values are set to 1. If you set this property to a vector of P + 1 values, each value is used for a separate section of the filter.

Tunable: Yes

Dependencies

This property applies only when you set the CoefficientSource property to 'Property' and HasScaleValues property to true.

Fixed-Point Properties

`RoundingMethod` — Rounding method for fixed-point operations
`'Floor'` (default) | `'Ceiling'` | `'Convergent'` | `'Nearest'` | `'Round'` | `'Simplest'` | `'Zero'`

Rounding method for fixed-point operations, specified as one of the following:

'Floor'
'Ceiling'
'Convergent'
'Nearest'
'Round'
'Simplest'
'Zero'

For more details, see Rounding Modes.

`OverflowAction` — Overflow action for fixed-point operations
`Wrap` (default) | `Saturate`

Overflow action for fixed-point operations, specified as one of the following:

'Wrap' –– The object wraps the result of its fixed-point operations.
'Saturate' –– The object saturates the result of its fixed-point operations.

For more details on overflow actions, see Overflow Handling for fixed-point operations.

`SectionInputDataType` — Section input word- and fraction-length designations
`'Same as input'` (default) | `numerictype` object

Section input word- and fraction-length designations, specified as either 'Same as input' or a numerictype (Fixed-Point Designer) object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias.

Dependencies

This property applies only when you set the HasScaleValues property to true.

`SectionOutputDataType` — Section output word- and fraction-length designations
`'Same as section input'` (default) | `numerictype` object

Section output word- and fraction-length designations, specified as either 'Same as section input' or a numerictype (Fixed-Point Designer) object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias.

Dependencies

This property applies only when you set the HasScaleValues property to true.

`NumeratorDataType` — Numerator coefficients word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

Numerator coefficients word- and fraction-length designations, specified as either 'Same word length as input' or as a numerictype object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias. If not specified, the fraction length is determined based on the numerator coefficient values to give the best possible precision.

Dependencies

This property applies only when you set the CoefficientSource property to 'Property'.

`DenominatorDataType` — Denominator coefficients word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

Denominator coefficients word- and fraction-length designations, specified as either 'Same word length as input' or as a numerictype object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias. If not specified, the fraction length is determined based on the denominator coefficient values to give the best possible precision.

Dependencies

This property applies only when you set the CoefficientSource property to 'Property'.

`ScaleValuesDataType` — Scale values word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

Scale values word- and fraction-length designations, specified as either 'Same word length as input' or as a numerictype object.

Dependencies

This property applies only when you set the CoefficientSource property to 'Property' and HasScaleValues property to true.

`MultiplicandDataType` — Multiplicand word- and fraction-length designations
`'Same as output'` (default) | `numerictype` object

Multiplicand word- and fraction-length designations, specified as either 'Same as output' or as a numerictype object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias.

Dependencies

This property applies only when you set the Structure property to 'Direct form I transposed'.

`StateDataType` — State word- and fraction-length designations
`'Full precision'` (default) | `numerictype` object

State word- and fraction-length designations, specified as either 'Full precision' or as a numerictype object.

When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias.

Dependencies

This property applies only when you set the Structure property to 'Direct form II'.

`DenominatorAccumulatorDataType` — Denominator accumulator word- and fraction-length designations
`numerictype(1,64,48)` (default) | `numerictype` object

Denominator accumulator word- and fraction-length designations, specified as a numerictype object.

`OutputDataType` — Output word- and fraction-length designations
`'Full precision'` (default) | `numerictype` object

Output word- and fraction-length designations, specified as either 'Full precision' or as a numerictype object. When specified as a numerictype object, the data type must be signed fixed point with a power-of-two slope and zero bias.

When the input is floating-point, the output data type matches the input data type since floating-point inheritance takes precedence over the fixed-point settings.

Usage

Syntax

y = sos(x)

y = sos(x,num,den)

y = sos(x,num,den,g)

Description

y = sos(x) filters the input signal x and outputs the filtered values y. The sos filter object filters each channel (column) of the input signal independently over successive calls to the algorithm.

This syntax is valid only when the CoefficientSource property is set to 'Property'.

example

y = sos(x,num,den) filters the input using num as the numerator coefficients and den as the denominator coefficients of the sos filter.

This syntax is valid only when the CoefficientSource property is set to 'Input port' and HasScaleValues property is set to false.

y = sos(x,num,den,g) specifies the scale values g of the sos filter.

This syntax is valid only when the CoefficientSource property is set to 'Input port' and HasScaleValues property is set to true.

Input Arguments

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`x` — Data input
vector | matrix

Data input, specified as a vector or a matrix.

This object also accepts variable-size inputs. Once you have run the System object algorithm, you can change the size of each input channel, but you cannot change the number of channels.

If the input is fixed-point, it must be signed fixed point with a power-of-two slope and zero bias. When the fraction length is not specified, the object determines the fraction length based on the input data to give the best possible precision.

The data type of all inputs must be the same.

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

`num` — Numerator coefficients
P-by-3 matrix

Numerator coefficients, specified as an P-by-3 matrix, where P is the number of biquadratic sections. Each row corresponds to the numerator coefficients of the corresponding section of the filter.

Once you step through the algorithm, the size of this input cannot be modified. However, the numerator coefficient values can be modified as the input is tunable.

If num is fixed-point, it must be signed fixed point with a power-of-two slope and zero bias. When the fraction length is not specified, the object determines the fraction length based on the numerator coefficient values to give the best possible precision.

The data type of all inputs must be the same.

The size and complexity of the num and den inputs must be the same.

Tunable: Yes

Dependencies

This input applies only when you set the CoefficientSource property to 'Input port'.

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

`den` — Denominator coefficients
P-by-3 matrix

The leading denominator coefficient is always assumed to be 1. If any other value is specified in the first column, the object ignores this value and treats it as 1.

The size of this input cannot be modified once you step through the algorithm. However, the denominator values can be modified as the input is tunable.

If den is fixed-point, it must be signed fixed point with a power-of-two slope and zero bias. When the fraction length is not specified, the object determines the fraction length based on the denominator coefficient values to give the best possible precision.

The data type of all inputs must be the same.

The size and complexity of the num and den inputs must be the same.

Tunable: Yes

Dependencies

This input applies only when you set the CoefficientSource property to 'Input port'.

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

`g` — Scale values for each biquad second-order section
1-by-(P +1) vector

Scale values of the biquadratic filter, specified as a 1-by-(P+1) vector, where P is the number of biquadratic filter sections.

If g is fixed-point, it must be signed fixed point with a power-of-two slope and zero bias. When the fraction length is not specified, the object determines the fraction length based on the scale values to give the best possible precision.

The data type of all inputs must be the same.

Tunable: Yes

Dependencies

This input applies only when you set the CoefficientSource property to 'Input port' and HasScaleValues property to true.

Data Types: single | double | int8 | int16 | int32 | int64 | fi

Output Arguments

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`y` — Filtered output
vector | matrix

Filtered output, returned as a vector or a matrix. The size and complexity of the output signal matches that of the input signal.

When the input is fixed-point, the data type of the output is determined based on the value of the OutputDataType property. If you set OutputDataType to 'Full precision', the output data type is computed based on the signal flow diagrams shown in the Fixed-Point Conversion section. If you set OutputDataType to a custom numeric type, the output data type is cast to the specified numeric type.

When the input is floating-point, the output data type matches the input data type since floating-point inheritance takes precedence over the fixed-point settings.

Data Types: single | double | int8 | int16 | int32 | int64 | fi
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Specific to `dsp.SOSFilter`

`freqz`	Frequency response of discrete-time filter System object
`filterAnalyzer`	Analyze filters with Filter Analyzer app
`impz`	Impulse response of discrete-time filter System object
`info`	Information about filter System object
`coeffs`	Returns the filter System object coefficients in a structure
`cost`	Estimate cost of implementing filter System object
`scale`	Scale second-order sections
`scaleopts`	Create an options object for second-order section scaling
`scalecheck`	Check scaling of biquadratic filter
`cumsec`	Cumulative second-order section of the biquadratic filter
`tf`	Convert discrete-time filter System object to transfer function
`reorder`	Reorder second-order sections of biquadratic filter System object
`outputDelay`	Determine output delay of single-rate or multirate filter

Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Remove High-Frequency Noise Using Biquad SOS Filter

Open Live Script

Lowpass filter a noisy sinusoidal signal using the dsp.SOSFilter System object. Visualize the original and filtered signals using a spectrum analyzer.

Input Signal

The input signal is a sinusoidal signal with two tones, one at 1 kHz and the other at 3 kHz. The sampling frequency is 8 kHz.

f1 = 1000;
f2 = 3000;
Fs = 8000;
sine = dsp.SineWave(Frequency=[f1,f2],...
    SampleRate=Fs,...
    SamplesPerFrame=1024);

Create Biquad SOS Filter

Design a 10th-order lowpass Butterworth IIR filter with a cutoff frequency of 2 kHz. The numerator and denominator coefficients are extracted from the designed SOS matrix.

Fcutoff = 2000;
[z,p,k] = butter(10,Fcutoff/(Fs/2));
[s, g]  = zp2sos(z,p,k);
[num,den] = sos2ctf(s);
    
sosFilter = dsp.SOSFilter(num,den,...
    ScaleValues=g)

sosFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [5x3 double]
          Denominator: [5x3 double]
       HasScaleValues: true
          ScaleValues: [0.0029 1 1 1 1 1]

  Use get to show all properties

Visualize the frequency response of the designed SOS filter.

freqz(sosFilter,[],8000)

Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Frequency (kHz), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Frequency (kHz), ylabel Magnitude (dB) contains an object of type line.

Streaming

Add zero-mean white Gaussian noise with a standard deviation of 0.1 to the sum of sine waves. Filter the noisy sinusoidal signal with the designed SOS filter.

While running the simulation, the spectrum analyzer shows that the high-frequency tone above 2 kHz in the source signal is attenuated. The resulting signal maintains the peak at 1 kHz because it falls in the passband of the lowpass filter.

SA = spectrumAnalyzer(...
        PlotAsTwoSidedSpectrum=false, ...
        SampleRate=Fs, ...
        ShowLegend=true,...
        YLimits=[-200 100],...
        ChannelNames={'Input signal','Filtered signal'});

    % Stream processing loop
for k = 1:100
    input = sum(sine(),2) + 0.1.*randn(sine.SamplesPerFrame,1);
    filteredOutput = sosFilter(input);
    SA(input,filteredOutput);
end

Design a Time-Varying Lowpass IIR Filter

Open Live Script

Design a lowpass biquadratic SOS filter with time-varying coefficients. Visualize the magnitude response of the filter using a dynamic filter visualizer.

dfv = dsp.DynamicFilterVisualizer('YLimits',[-120 10])

dfv = 
  dsp.DynamicFilterVisualizer handle with properties:

               FFTLength: 2048
     NormalizedFrequency: 0
              SampleRate: 44100
          FrequencyRange: [0 22050]
                  XScale: 'Linear'
        MagnitudeDisplay: 'Magnitude (dB)'
    PlotAsMagnitudePhase: 0
                PlotType: 'Line'
             AxesScaling: 'Manual'

  Show all properties

Create a dsp.SOSFilter object.

sosfilt = dsp.SOSFilter

sosfilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [0.0975 0.1950 0.0975]
          Denominator: [1 -0.9428 0.3333]
       HasScaleValues: false

  Use get to show all properties

Use the maxflat function to design a lowpass maximally flat filter. Set the numerator and denominator order of the filter to 2 since the SOS filter is biquadratic. Vary the cutoff frequency in 0.001 increments and design the filter for each increment. Pass the computed coefficients to the SOS filter. Visualize the time-varying magnitude response of the SOS filter using the dsp.DynamicFilterVisualizer object.

for Wn = 0.1:0.001:0.6
 [b,a] = maxflat(2,2,Wn);
 sosfilt.Numerator = b;
 sosfilt.Denominator = a;
 dfv(sosfilt)
end

Design and Implement Peak Filter

Open Live Script

Design a peak filter of order 14 and a center frequency at 0.2 rad/s using the designNotchPeakIIR function. Output scale values by setting the HasScaleValues property to true.

[b,a,sv] = designNotchPeakIIR(FilterOrder=14, CenterFrequency=0.2,...
    HasScaleValues=true)

b = 7×3

    1.0000    2.0000    1.0000
    1.0000   -2.0000    1.0000
    1.0000    2.0000    1.0000
    1.0000   -2.0000    1.0000
    1.0000    2.0000    1.0000
    1.0000   -2.0000    1.0000
    1.0000         0   -1.0000

a = 7×3

    1.0000   -1.4026    0.9374
    1.0000   -1.7004    0.9549
    1.0000   -1.3637    0.8373
    1.0000   -1.6111    0.8736
    1.0000   -1.3788    0.7823
    1.0000   -1.5195    0.8103
    1.0000   -1.4366    0.7757

Assign the filter design coefficients to a dsp.SOSFilter object.

peakFilter = dsp.SOSFilter(b,a,ScaleValues=sv)

peakFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [7x3 double]
          Denominator: [7x3 double]
       HasScaleValues: true
          ScaleValues: [8x1 double]

  Use get to show all properties

Create a dsp.DynamicFilterVisualizer object to display the magnitude response of the filter.

dfv = dsp.DynamicFilterVisualizer(NormalizedFrequency=true);
dfv(peakFilter)

Create a spectrumAnalyzer object to visualize the input and output spectra.

scope = spectrumAnalyzer(SampleRate=2,PlotAsTwoSidedSpectrum=false,...
    ChannelNames=["Input Signal","Filtered Signal"]);

Stream in random data and filter the signal using the peak filter you have designed.

for i = 1:1000
    x = randn(1024, 1);
    y = peakFilter(x);
    scope(x,y);
end

Design and Implement Notch Filter Object

Open Live Script

Design a notch filter object of order 48 and a bandwidth of 0.15 using the designNotchPeakIIR function.

notchFilter = designNotchPeakIIR(FilterOrder=48,Bandwidth=0.15,...
    Response='notch',SystemObject=true)

notchFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [24x3 double]
          Denominator: [24x3 double]
       HasScaleValues: false

  Use get to show all properties

Create a dsp.DynamicFilterVisualizer object to display the magnitude response of the filter.

dfv = dsp.DynamicFilterVisualizer(NormalizedFrequency=true,YLimits=[-250 50]);
dfv(notchFilter)

Create a spectrumAnalyzer object to visualize the input and output spectra.

scope = spectrumAnalyzer(SampleRate=2,PlotAsTwoSidedSpectrum=false,...
    ChannelNames=["Input Signal","Filtered Signal"]);

Stream in random data and filter the signal using the notch filter.

for i = 1:1000
    x = randn(1024, 1);
    y = notchFilter(x);
    scope(x,y);
end

Design and Implement Lowpass IIR Filter with Tunable 3-dB Cutoff Frequency

Open Live Script

Create a dsp.SOSFilter object, and set the CoefficientSource property to 'Input port' so that you can vary the coefficients of the SOS filter coefficients through the input port during simulation.

sosFilt = dsp.SOSFilter(CoefficientSource="Input port")

sosFilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Input port'
       HasScaleValues: false

  Use get to show all properties

Create a spectrumAnalyzer object to visualize the spectra of the input and output signals.

spectrumScope = spectrumAnalyzer(SampleRate=96000,PlotAsTwoSidedSpectrum=false,...
    ChannelNames=["Input Signal","Filtered Signal"]);

Create a dsp.DynamicFilterVisualizer object to visualize the magnitude response of the varying filter.

filterViz = dsp.DynamicFilterVisualizer(NormalizedFrequency=true);

Stream in random data and filter the signal using the dsp.SOSFilter object. Use the designLowpassIIR function to design the filter coefficients. By default, this function returns a P-by-3 matrix of numerator coefficients and a P-by-3 matrix of denominator coefficients. Assign these coefficients to the dsp.SOSFilter object.

Vary the 3-dB cutoff frequency of the filter during simulation. The designLowpassIIR function redesigns the coefficients based on the updated filter specifications. Pass these updated coefficients to the SOS filter. Visualize the spectra of the input and filtered signals using the spectrum analyzer.

F3dB = 0.5;
for idx = 1:500
    [b,a] = designLowpassIIR(FilterOrder=30,HalfPowerFrequency=F3dB,DesignMethod="butter");
    x = randn(1024,1);
    y = sosFilt(x,b,a);
    spectrumScope(x,y);
    filterViz(b,a);
    F3dB = F3dB + 0.0005;
end

Design and Implement Lowpass IIR Filter Object

Open Live Script

Design and implement a lowpass IIR filter object using the designLowpassIIR function. The function returns a dsp.SOSFilter object when you set the SystemObject argument to true. To design the filter in single-precision, use the Datatype or like argument. Alternatively, you can specify any of the numerical arguments in single-precision.

sosFilt = designLowpassIIR(FilterOrder=30,HalfPowerFrequency=0.5,DesignMethod="butter",...
        Datatype="single",SystemObject=true)

sosFilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [15x3 single]
          Denominator: [15x3 single]
       HasScaleValues: false

  Use get to show all properties

Create a dsp.DynamicFilterVisualizer object to visualize the magnitude response of the filter.

filterViz = dsp.DynamicFilterVisualizer(NormalizedFrequency=true,YLimits=[-80 20]);
filterViz(sosFilt)

Create a spectrumAnalyzer object to visualize the spectra of the input and output signals.

spectrumScope = spectrumAnalyzer(SampleRate=44100,PlotAsTwoSidedSpectrum=false,...
    ChannelNames=["Input Signal","Filtered Signal"]);

Stream in random data and filter the signal using the dsp.SOSFilter object. Visualize the spectra of the input and filtered signals using the spectrum analyzer.

for idx = 1:50
    x = randn(1024,1);
    y = sosFilt(x);
    spectrumScope(x,y);
end

Design Highpass IIR Filter Using `designfilt`

Since R2023b

Open Live Script

Design a highpass IIR filter using the designfilt function.

The filter is a 20th order highpass IIR filter with a sample rate of 44.1 kHz. The stopband frequency of the filter is 3 kHz and the passband frequency is 8 kHz. Use the IIR least p-norm design method and set the L-infinity norm to 120. Set the SystemObject argument to true.

With these specifications, the designfilt function generates a dsp.SOSFilter System object™.

hpIIRFilter = designfilt('highpassiir', ...
    FilterOrder=20,StopbandFrequency=3000, ...
    PassbandFrequency=8000,SampleRate=44100, ...
    Norm=120,SystemObject=true)

hpIIRFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [10x3 double]
          Denominator: [10x3 double]
       HasScaleValues: true
          ScaleValues: [0.5812 1 1 1 1 1 1 1 1 1 14.8291]

  Use get to show all properties

Visualize the frequency response of this filter.

freqz(hpIIRFilter,[],44100)

More About

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Filter Structures

These diagrams show the filter structures supported by the second-order section filter.

Direct Form I

This is the structure of each section in the filter when you set the filter structure to Direct form I.

This is the structure of the filter with P sections when you specify scale values [g₁, g₂, …, g_P+1].

This is the structure of the filter when you do not specify scale values.

Direct Form I Transposed

This is the structure of each section in the filter when you set the filter structure to Direct form I transposed.

This is the structure of the filter with P sections when you specify scale values [g₁, g₂, …, g_P+1].

This is the structure of the filter when you do not specify scale values.

Direct Form II

This is the structure of each section in the filter when you set the filter structure to Direct form II.

This is the structure of the filter with P sections when you specify scale values [g₁, g₂, …, g_P+1].

This is the structure of the filter when you do not specify scale values.

Direct Form II Transposed

This is the structure of each section in the filter when you set the filter structure to Direct form II transposed.

This is the structure of the filter with P sections when you specify scale values [g₁, g₂, …, g_P+1].

This is the structure of the filter when you do not specify scale values.

Filter Structures with Fixed-Point Settings

These diagrams show the data types used in the SOS filter when the input is fixed-point. For each structure the filter supports, the data types shown in the diagrams can be set through the respective fixed-point settings.

Direct Form I

Here is the structure of each section when you set the filter structure to Direct form I. This diagram shows the data types when you input fixed-point signals. The gain operations b₀, b₁, b₂, a₁, and a₂ operate in full precision.

These diagrams show the fixed-point data types between filter sections.

When the data is not optimized:

When you specify scale values to 1:

Direct Form I Transposed

Here is the structure of each section when you set the filter structure to Direct form I transposed. This diagram shows the data types when you input fixed-point signals. The dashed casts are omitted when you set HasScaleValues to false. The gain operations b₀, b₁, b₂, a₁, and a₂ operate in full precision.

These diagrams show the fixed-point data types between filter sections.

When the data is not optimized:

When you specify scale values to 1:

Direct Form II

Here is the structure of each section when you set the filter structure to Direct form II. This diagram shows the data types when you input fixed-point signals. The dashed casts are omitted when you set HasScaleValues to false. The gain operations b₀, b₁, b₂, a₁, and a₂ operate in full precision.

These diagrams show the fixed-point data types between filter sections.

When the data is not optimized:

When you set scale values to 1:

Direct Form II Transposed

Here is the structure of each section when you set the filter structure to Direct form II transposed. This diagram shows the data types when you input fixed-point signals. The gain operations b₀, b₁, b₂, a₁, and a₂ operate in full precision. When you set HasScaleValues to false, the data type at the section output is automatically determined by the object algorithm and is not controlled by the value of the SectionOutputDataType property.

These diagrams show the fixed-point data types between filter sections.

When the data is not optimized:

When you specify scale values to 1:

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

The dsp.SOSFilter System object supports optimized C code generation on ARM Cortex-M processors and SIMD code generation under these conditions:

Input is a single-channel real-valued signal.
Data type of the input is single.
When you set Structure to 'Direct form I' or 'Direct form II transposed'.
When you set HasScaleValues to false.
In the case of code generation for ARM Cortex-M processors, set HasScaleValues to false after setting CoefficientSource to 'Input port'.

The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this object, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from MATLAB Algorithms.

Version History

Introduced in R2020a

expand all

R2023b: The `designfilt` function and the Design Filter Live Editor task support `dsp.SOSFilter` object

The designfilt function generates a dsp.SOSFilter object when you specify 'lowpassiir' and 'highpassiir' filter responses and set the 'SystemObject' flag to 'true'.

hpIIRFilter = designfilt('highpassiir', ...
    'FilterOrder',20,'StopbandFrequency',3000, ...
    'PassbandFrequency',8000,'SampleRate',44100, ...
    'Norm',120,'SystemObject',true)

hpIIRFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II'
    CoefficientSource: 'Property'
            Numerator: [10×3 double]
          Denominator: [10×3 double]
       HasScaleValues: true
          ScaleValues: [0.4745 1 1 1 1 1 1 1 1 1 1.6434]

The Design Filter Live Editor task generates a dsp.SOSFilter object for lowpass IIR and highpass IIR filter responses when you select the Use a System object to implement filter check box in the task UI and run the designfilt code the task generates.

R2022b: Optimized C code generation for `dsp.SOSFilter` object on ARM Cortex-M processors

In R2022b, you can generate optimized C code for the dsp.SOSFilter object on ARM Cortex-M processors under certain conditions. For more details, see Code Generation.

dsp.SOSFilter

Description

Creation

Syntax

Description

Properties

Structure — Filter structure 'Direct form II transposed' (default) | 'Direct form I' | 'Direct form I transposed' | 'Direct form II'

CoefficientSource — Source of filter coefficients 'Property' (default) | 'Input port'

Numerator — Numerator coefficients of filter [0.0975 0.195 0.0975] (default) | P-by-3 matrix

Dependencies

Denominator — Denominator coefficients of filter [1 -0.9428 0.3333] (default) | P-by-3 matrix

Dependencies

HasScaleValues — Specify if filter has scale values for each section false (default) | true

ScaleValues — Scale values for each biquad second-order section [1 1] (default) | vector

Dependencies

Fixed-Point Properties

RoundingMethod — Rounding method for fixed-point operations 'Floor' (default) | 'Ceiling' | 'Convergent' | 'Nearest' | 'Round' | 'Simplest' | 'Zero'

OverflowAction — Overflow action for fixed-point operations Wrap (default) | Saturate

SectionInputDataType — Section input word- and fraction-length designations 'Same as input' (default) | numerictype object

Dependencies

SectionOutputDataType — Section output word- and fraction-length designations 'Same as section input' (default) | numerictype object

Dependencies

NumeratorDataType — Numerator coefficients word- and fraction-length designations 'Same word length as input' (default) | numerictype object

Dependencies

DenominatorDataType — Denominator coefficients word- and fraction-length designations 'Same word length as input' (default) | numerictype object

Dependencies

ScaleValuesDataType — Scale values word- and fraction-length designations 'Same word length as input' (default) | numerictype object

Dependencies

MultiplicandDataType — Multiplicand word- and fraction-length designations 'Same as output' (default) | numerictype object

Dependencies

StateDataType — State word- and fraction-length designations 'Full precision' (default) | numerictype object

Dependencies

DenominatorAccumulatorDataType — Denominator accumulator word- and fraction-length designations numerictype(1,64,48) (default) | numerictype object

OutputDataType — Output word- and fraction-length designations 'Full precision' (default) | numerictype object

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

num — Numerator coefficients P-by-3 matrix

Dependencies

den — Denominator coefficients P-by-3 matrix

Dependencies

g — Scale values for each biquad second-order section 1-by-(P +1) vector

Dependencies

Output Arguments

y — Filtered output vector | matrix

Object Functions

Specific to dsp.SOSFilter

Common to All System Objects

Examples

Remove High-Frequency Noise Using Biquad SOS Filter

Design a Time-Varying Lowpass IIR Filter

Design and Implement Peak Filter

Design and Implement Notch Filter Object

Design and Implement Lowpass IIR Filter with Tunable 3-dB Cutoff Frequency

Design and Implement Lowpass IIR Filter Object

Design Highpass IIR Filter Using designfilt

More About

Filter Structures

Filter Structures with Fixed-Point Settings

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

Version History

R2023b: The designfilt function and the Design Filter Live Editor task support dsp.SOSFilter object

R2022b: Optimized C code generation for dsp.SOSFilter object on ARM Cortex-M processors

See Also

Functions

Objects

Blocks

`Structure` — Filter structure
`'Direct form II transposed'` (default) | `'Direct form I'` | `'Direct form I transposed'` | `'Direct form II'`

`CoefficientSource` — Source of filter coefficients
`'Property'` (default) | `'Input port'`

`Numerator` — Numerator coefficients of filter
[`0.0975 0.195 0.0975`] (default) | P-by-3 matrix

`Denominator` — Denominator coefficients of filter
[`1 -0.9428 0.3333`] (default) | P-by-3 matrix

`HasScaleValues` — Specify if filter has scale values for each section
`false` (default) | `true`

`ScaleValues` — Scale values for each biquad second-order section
[`1 1`] (default) | vector

`RoundingMethod` — Rounding method for fixed-point operations
`'Floor'` (default) | `'Ceiling'` | `'Convergent'` | `'Nearest'` | `'Round'` | `'Simplest'` | `'Zero'`

`OverflowAction` — Overflow action for fixed-point operations
`Wrap` (default) | `Saturate`

`SectionInputDataType` — Section input word- and fraction-length designations
`'Same as input'` (default) | `numerictype` object

`SectionOutputDataType` — Section output word- and fraction-length designations
`'Same as section input'` (default) | `numerictype` object

`NumeratorDataType` — Numerator coefficients word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

`DenominatorDataType` — Denominator coefficients word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

`ScaleValuesDataType` — Scale values word- and fraction-length designations
`'Same word length as input'` (default) | `numerictype` object

`MultiplicandDataType` — Multiplicand word- and fraction-length designations
`'Same as output'` (default) | `numerictype` object

`StateDataType` — State word- and fraction-length designations
`'Full precision'` (default) | `numerictype` object

`DenominatorAccumulatorDataType` — Denominator accumulator word- and fraction-length designations
`numerictype(1,64,48)` (default) | `numerictype` object

`OutputDataType` — Output word- and fraction-length designations
`'Full precision'` (default) | `numerictype` object

`x` — Data input
vector | matrix

`num` — Numerator coefficients
P-by-3 matrix

`den` — Denominator coefficients
P-by-3 matrix

`g` — Scale values for each biquad second-order section
1-by-(P +1) vector

`y` — Filtered output
vector | matrix

Specific to `dsp.SOSFilter`

Design Highpass IIR Filter Using `designfilt`

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

R2023b: The `designfilt` function and the Design Filter Live Editor task support `dsp.SOSFilter` object

R2022b: Optimized C code generation for `dsp.SOSFilter` object on ARM Cortex-M processors