dsp.SOSFilter

Second-order section biquadratic IIR filter structures

Description

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

To implement an IIR filter structure using SOS:

1. Create the dsp.SOSFilter object and set its properties.

2. Call the object with arguments, as if it were a function.

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

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.

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

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) | N-by-3 matrix

Numerator coefficients of the filter, specified as an N-by-3 matrix, where N is the number of biquadratic sections.

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'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

Denominator — Denominator coefficients of filter

[1 -0.9428 0.3333] (default) | N-by-3 matrix

Denominator coefficients of the filter, specified as an N-by-3 matrix, where N is the number of biquadratic sections.

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'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

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 N + 1, where N is the number of biqaudratic 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 N + 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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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.

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 scale values to give the best possible precision.

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.

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'.

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

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

N-by-3 matrix

Numerator coefficients, specified as an N-by-3 matrix, where N is the number of biquadratic sections.

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

N-by-3 matrix

Denominator coefficients of the filter, specified as an N-by-3 matrix, where N is the number of biquadratic sections.

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-(N +1) vector

Scale values of the biquadratic filter, specified as a 1-by-(N+1) vector, where N 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

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.

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

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)

Specific to dsp.SOSFilter

freqz	Frequency response of discrete-time filter System object
fvtool	Visualize frequency response of DSP filters
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

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

Remove High-Frequency Noise Using Biquad SOS Filter

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 = s(:,1:3);
den = s(:,4:6);
    
sosFilter = dsp.SOSFilter(num,den,...
    'HasScaleValues',true,...
    '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]

  Show all properties

Visualize the frequency response of the designed SOS filter.

fvtool(sosFilter,'Fs',8000)

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

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 with properties:

               FFTLength: 2048
              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

  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

More About

Fixed Point

These diagrams show the data types used in the dsp.SOSFilter object when the input is fixed-point. For each filter structure the object supports, the data types shown in the diagrams can be set through the respective fixed-point properties of the object.

Direct Form I

This diagram shows the data types for one section of the filter for 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

This diagram shows the data types for one section of the filter for 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

This diagram shows the data types for one section of the filter for 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

This diagram shows the data types for one section of the filter for 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 under these conditions:

• Input is a single-channel real-valued signal.

• When you set CoefficientSource to 'Property' or 'Input port'.

• 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 after setting CoefficientSource to 'Input port'.

Version History

Introduced in R2020a

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.