dsp.BiquadFilter - (To be removed) IIR filter using biquadratic structures - MATLAB (original) (raw)

(To be removed) IIR filter using biquadratic structures

The dsp.BiquadFilter object will be removed in a future release. Use the dsp.SOSFilter object instead. For more information on updating your code, see Version History.

Description

The dsp.BiquadFilter object implements a cascade of biquadratic sections, where the coefficients for each section are supplied by a separate row of an_N_-by-6 second-order sections (SOS) matrix. Each row of the SOS matrix contains the numerator and denominator coefficients of the corresponding section of the filter. The resulting filter can be applied to a vector or matrix input, where each column represents a channel of data that is processed independently.

To implement an IIR filter structure using biquadratic or SOS:

1. Create the dsp.BiquadFilter 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

Description

`biquad` = dsp.BiquadFilter returns a biquadratic IIR (SOS) filter System object™, biquad, which independently filters each channel (column) of the input over time using the SOS section [1 0.3 0.4 1 0.1 0.2] with a direct-form II transposed structure.

biquad = dsp.BiquadFilter(sosmatrix,scalevalues) returns a biquadratic filter object, with the SOSMatrix property set to sosmatrix and the ScaleValues property set to scalevalues.

example

biquad = dsp.BiquadFilter(`Name=Value`) sets properties using one or more name-value arguments. For example, to specify the filter structure of the biquadratic filter as "Direct form II", setStructure to "Direct Form II".

example

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 therelease function unlocks them.

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

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

Specify the filter structure as "Direct form I", "Direct form I transposed", "Direct form II", "Direct form II transposed".

Specify the source of the SOS matrix as"Property" or "Input port".

Specify the second-order section (SOS) matrix as an N-by-6 matrix, where N is the number of sections in the filter. Each row of the SOS matrix contains the numerator and denominator coefficients of the corresponding section of the filter. The system function, H(z), of a biquad filter is:

The coefficients are ordered in the rows of the SOS matrix as (b0, b1,b2,1, –a1, –a2). You can use coefficients of real or complex values. This property applies only when you set the SOSMatrixSource property to Property. The leading denominator coefficient of the biquad filter, a0, equals 1 for each filter section, regardless of the specified value.

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

Specify the scale values to apply before and after each section of a biquad filter. ScaleValues must be either a scalar or a vector of length N+1, whereN is the number of sections. If you set this property to a scalar, the scalar value is used as the gain value only before the first filter section. The remaining gain values are set to1. If you set this property to a vector ofN+1values, each value is used for a separate section of the filter.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty.

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

Specify the initial conditions of the filter states when theStructure property is one of | Direct form II | Direct form II transposed |. The number of states or delay elements (zeros and poles) in a direct-form II biquad filter equals twice the number of filter sections. You can specify the initial conditions as a scalar, vector, or matrix.

When you specify a scalar value, the biquad filter initializes all delay elements in the filter to that value. When you specify a vector of length equal to the number of delay elements in the filter, each vector element specifies a unique initial condition for the corresponding delay element.

The biquad filter applies the same vector of initial conditions to each channel of the input signal. When you specify a vector of length equal to the product of the number of input channels and the number of delay elements in the filter, each element specifies a unique initial condition for the corresponding delay element in the corresponding channel. When you specify a matrix with the same number of rows as the number of delay elements in the filter, and one column for each channel of the input signal, each element specifies a unique initial condition for the corresponding delay element in the corresponding channel.

Dependencies

This property applies only when you set theStructure property to one of Direct form II or Direct form II transposed.

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

Specify the initial conditions of the filter states on the side of the filter structure with the zeros. The number of states or delay elements in the numerator of a direct-form I biquad filter equals twice the number of filter sections. You can specify the initial conditions as a scalar, vector, or matrix. When you specify a scalar, the biquad filter initializes all delay elements on the zeros side in the filter to that value. When you specify a vector of length equal to the number of delay elements on the zeros side in the filter, each vector element specifies a unique initial condition for the corresponding delay element on the zeros side.

The biquad filter applies the same vector of initial conditions to each channel of the input signal. When you specify a vector of length equal to the product of the number of input channels and the number of delay elements on the zeros side in the filter, each element specifies a unique initial condition for the corresponding delay element on the zeros side in the corresponding channel. When you specify a matrix with the same number of rows as the number of delay elements on the zeros side in the filter, and one column for each channel of the input signal, each element specifies a unique initial condition for the corresponding delay element on the zeros side in the corresponding channel.

Dependencies

This property applies only when you set theStructure property to one of Direct form I or Direct form I transposed.

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

Specify the initial conditions of the filter states on the side of the filter structure with the poles. The number of denominator states, or delay elements, in a direct-form I (noncanonic) biquad filter equals twice the number of filter sections. You can specify the initial conditions as a scalar, vector, or matrix. When you specify a scalar, the biquad filter initializes all delay elements on the poles side of the filter to that value. When you specify a vector of length equal to the number of delay elements on the poles side in the filter, each vector element specifies a unique initial condition for the corresponding delay element on the poles side.

The object applies the same vector of initial conditions to each channel of the input signal. When you specify a vector of length equal to the product of the number of input channels and the number of delay elements on the poles side in the filter, each element specifies a unique initial condition for the corresponding delay element on the poles side in the corresponding channel. When you specify a matrix with the same number of rows as the number of delay elements on the poles side in the filter, and one column for each channel of the input signal, each element specifies a unique initial condition for the corresponding delay element on the poles side in the corresponding channel.

Dependencies

This property only applies when you set theStructure property to one of Direct form I or Direct form I transposed.

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

When this Boolean property is set to true, the biquad filter removes all unity scale gain computations. This reduces the number of computations and increases the fixed-point accuracy.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty.

Select how to specify scale values. By default, this property istrue, and the scale values are specified via the input port. When this property is false, all scale values are 1.

Dependencies

This property applies only when theSOSMatrixSource property is Input port.

Fixed-Point Properties

Specify the rounding method.

Specify the overflow action as one of Wrap orSaturate.

Specify the multiplicand fixed-point data type as one of Same as output or Custom.

Dependencies

This property applies only when you set theStructure property to Direct form I transposed.

Specify the multiplicand fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness ofAuto.

Dependencies

This property applies only when you set theMultiplicandDataType property toCustom.

Specify the section input fixed-point data type as eitherSame as input orCustom.

Specify the section input fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness ofAuto.

Dependencies

This property applies only when you set theSectionInputDataType property toCustom.

Specify the section output fixed-point data type as eitherSame as section input orCustom.

Specify the section output fixed-point type as a signed, scalednumerictype (Fixed-Point Designer) object with a Signedness ofAuto.

Dependencies

This property applies only when you set theSectionOutputDataType property toCustom.

Specify the numerator coefficients fixed-point data type asSame word length as input orCustom. Setting this property also sets theDenominatorCoefficientsDataType andScaleValuesDataType properties to the same value.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty.

Specify the numerator coefficients fixed-point type as a numerictype (Fixed-Point Designer) object with a Signedness of Auto. The word length of theCustomNumeratorCoefficientsDataType,CustomDenominatorCoefficientsDataType, andCustomScaleValuesDataType properties must be the same.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty and theNumeratorCoefficientsDataType property toCustom.

Specify the denominator coefficients fixed-point data type asSame word length as input orCustom. Setting this property also sets theNumeratorCoefficientsDataType andScaleValuesDataType properties to the same value.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty.

Specify the denominator coefficients fixed-point type as a numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorCoefficientsDataType,CustomDenominatorCoefficientsDataType, andCustomScaleValuesDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty and theDenominatorCoefficientsDataType property toCustom.

Specify the scale values fixed-point data type as Same word length as input or Custom. Setting this property also sets theNumeratorCoefficientsDataType andDenominatorCoefficientsDataType properties to the same value.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty.

Specify the scale values fixed-point type as a numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorCoefficientsDataType,CustomDenominatorCoefficientsDataType, andCustomScaleValuesDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theSOSMatrixSource property toProperty and theScaleValuesDataType property toCustom.

Specify the mode to determine the numerator product fixed-point data type as:

• Same as input (default) — The numerator product word and fraction lengths are same as that of the input.
• Custom — Enables theCustomNumeratorProductDataType property, which you can use to specify the custom numerator product data type. Specify the data type as anumerictype object.
• Full precision — Use full-precision rules to specify the data type. These rules provide the most accurate fixed-point numerics. The rules prevent quantization from occurring within the object. Bits are added, as needed, so that no roundoff or overflow occurs. For more information, see Full Precision for Fixed-Point System Objects.

Setting this property also sets theDenominatorProductDataType property to the same value.

Specify the product fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorProductDataType andCustomDenominatorProductDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theNumeratorProductDataType property toCustom.

Specify the mode to determine the denominator product fixed-point data type as:

• Same as input (default) — The denominator product word and fraction lengths are same as that of the input.
• Custom — Enables theCustomDenominatorProductDataType property, which you can use to specify the custom denominator product data type. Specify the data type as anumerictype object.
• Full precision — Use full-precision rules to specify the data type. These rules provide the most accurate fixed-point numerics. The rules prevent quantization from occurring within the object. Bits are added, as needed, so that no roundoff or overflow occurs. For more information, see Full Precision for Fixed-Point System Objects.

Setting this property also sets theNumeratorProductDataType property to the same value.

Specify the product fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorProductDataType andCustomDenominatorProductDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theDenominatorProductDataType toCustom.

Specify the numerator accumulator fixed-point data type asSame as input, Same as product, or Custom. Setting this property also sets the DenominatorAccumulatorDataType property to the same value.

Specify the numerator accumulator fixed-point type as a scalednumerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorAccumulatorDataType andCustomDenominatorAccumulatorDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theNumeratorAccumulatorDataType property toCustom.

Specify the denominator accumulator fixed-point data type asSame as input, Same as product, or Custom. Setting this property also sets the NumeratorAccumulatorDataType property to the same value.

Specify the denominator accumulator fixed-point type as a scalednumerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorAccumulatorDataType andCustomDenominatorAccumulatorDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theDenominatorAccumulatorDataType property toCustom.

Specify the state fixed-point data type as Same as input, Same as accumulator, orCustom.

Dependencies

This property applies when you set the Structure property toDirect form II or Direct form II transposed.

Specify the state fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness ofAuto.

Dependencies

This property applies only when you set theStateDataType property toCustom.

Specify the numerator state fixed-point data type as Same as input, Same as accumulator, orCustom. Setting this property also sets theDenominatorStateDataType property to the same value.

Dependencies

This property applies only when you set the Structure property toDirect form I transposed.

Specify the numerator state fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorProductDataType andCustomDenominatorProductDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theStateDataType property toCustom.

Specify the denominator state fixed-point data type as Same as input, Same as accumulator, orCustom. Setting this property also sets theNumeratorStateDataType property to the same value.

Dependencies

This property applies only when you set the Structure property toDirect form I transposed.

Specify the denominator state fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto. TheCustomNumeratorStateDataType andCustomDenominatorStateDataType properties must have the same word lengths.

Dependencies

This property applies only when you set theStateDataType property toCustom.

Specify the output fixed-point data type as Same as input, Same as accumulator, orCustom.

Specify the output fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness ofAuto.

Dependencies

This property applies only when you set the OutputDataType property toCustom.

Usage

Syntax

Description

[y](#mw%5Fb73a5617-a49c-413e-ac75-7fa3f921b40a) = biquad([x](#d126e248151)) filters the input signal x , and outputs the filtered values, y. The biquad filter object filters each channel of the input signal over successive calls to the algorithm.

example

[y](#mw%5Fb73a5617-a49c-413e-ac75-7fa3f921b40a) = biquad([x](#d126e248151),[num](#mw%5F0e79e492-6aa4-4a64-8f18-97f5a01aab48),[den](#mw%5F808a79f3-1370-48b0-a20f-dc0049fc8d07)) filters the input using num as the numerator coefficients, and den as the denominator coefficients of the biquad filter. This configuration applies when the SOSMatrixSource property is Input port and theScaleValuesInputPort property isfalse.

[y](#mw%5Fb73a5617-a49c-413e-ac75-7fa3f921b40a) = biquad([x](#d126e248151),[num](#mw%5F0e79e492-6aa4-4a64-8f18-97f5a01aab48),[den](#mw%5F808a79f3-1370-48b0-a20f-dc0049fc8d07),[g](#mw%5F80056c3f-ef5a-4fc9-a5db-6aaf9cb8e893)) specifies the scale values, g, of the biquad filter. This configuration applies when the SOSMatrixSource property is Input Port and theScaleValuesInputPort property istrue.

Input Arguments

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Data input, specified as a vector or a matrix. This object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

The data type of all the inputs must be the same. If the input is fixed-point, it must be signed fixed point with power-of-two slope and zero bias.

The complexity of x, num, and den must be the same.

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

Numerator coefficients, specified as a 3-by-N numeric matrix, where N is the number of biquad filter sections. The complexity of x,num, and den must be the same.

The data type of all the inputs must be the same. Ifnum is fixed point, it must be signed fixed point with power-of-two slope and zero bias.

Dependencies

This input applies only when you set SOSMatrixSource property is Input port.

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

Denominator coefficients, specified as a 2-by-N numeric matrix, where N is the number of biquad filter sections. The object assumes that the first denominator coefficient of each section is 1.

The data type of all the inputs must be the same. Ifden is fixed point, it must be signed fixed point with power-of-two slope and zero bias.

The complexity of x, num, and den must be the same.

Dependencies

This input applies only when you set SOSMatrixSource property is Input port.

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

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

The data type of all the inputs must be the same. Ifg is fixed point, it must be signed fixed point with power-of-two slope and zero bias.

Dependencies

This input applies when the SOSMatrixSource property is Input Port and the ScaleValuesInputPort property is true.

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

Output Arguments

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

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:

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Examples

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Use a fourth order, lowpass biquadratic filter object with a normalized cutoff frequency of 0.4 to filter high frequencies from an input signal. Display the result as a power spectrum using the Spectrum Analyzer.

t = (0:1000)'/8e3; % Input is 0.3 & % 3kHz sinusoids xin = sin(2pi0.3e3t)+sin(2pi3e3t);

src = dsp.SignalSource(xin, 100); sink = dsp.SignalSink; % Set up the filter [z,p,k] = ellip(4,1,60,.4);
[sosMatrix,scaleValues] = zp2sos(z,p,k); biquad = dsp.BiquadFilter(sosMatrix,... scaleValues,Structure="Direct form I");

sa = spectrumAnalyzer(SampleRate=8e3,... Method="welch",... PlotAsTwoSidedSpectrum=false,... OverlapPercent=80,SpectrumUnits="dBW",... YLimits=[-160 -10]);

while ~isDone(src) input = src(); filteredOutput = biquad(input); sink(filteredOutput); sa(filteredOutput) end

filteredResult = sink.Buffer; fvtool(biquad,Fs=8000)

Demonstrate the Linf-norm scaling of a biquadratic SOS filter using the scale function.

Fs = 8000; Fcutoff = 2000; [z,p,k] = butter(10,Fcutoff/(Fs/2)); [sosMatrix,scaleValues] = zp2sos(z,p,k); sosFilt = dsp.SOSFilter(Structure="Direct form I", ... Numerator=sosMatrix(:,1:3),Denominator=sosMatrix(:,4:6), ... HasScaleValues=true,ScaleValues=scaleValues)

sosFilt = dsp.SOSFilter with properties:

        Structure: "Direct form I"
CoefficientSource: "Property"
        Numerator: [5x3 double]
      Denominator: [5x3 double]
   HasScaleValues: true
      ScaleValues: [0.0029 1 1 1 1 1]

Use get to show all properties

scale(sosFilt,"linf",scalevalueconstraint="none",maxscalevalue=2)

More About

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The following diagrams show the data types used in the dsp.BiquadFilter 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

The following diagram shows the data types for one section of the filter for fixed-point signals.

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

When the data is not optimized:

When you specify OptimizeUnityScaleValues totrue, and scale values to 1:

Direct Form I Transposed

The following diagram shows the data types for one section of the filter for fixed-point signals.

The dashed casts are omitted when you specifyOptimizeUnityScaleValues to true, and scale values to 1.

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

When the data is not optimized:

When you specify OptimizeUnityScaleValues totrue, and scale values to 1:

Direct Form II

The following diagram shows the data types for one section of the filter for fixed-point signals.

The dashed casts are omitted when you specifyOptimizeUnityScaleValues to true, and scale values to 1.

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

When the data is not optimized:

When you specify OptimizeUnityScaleValues totrue, and scale values to 1:

Direct Form II Transposed

The following diagram shows the data types for one section of the filter for fixed-point signals.

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

When the data is not optimized:

When you specify OptimizeUnityScaleValues totrue, and scale values to 1:

Algorithms

This object implements the algorithm, inputs, and outputs described on the Biquad Filter block reference page. The object properties correspond to the block parameters, except:

• Coefficient source
• Action when the a0 values of the SOS matrix are not one – the biquad filter object assumes the zero-th-order denominator coefficient equals 1 regardless of the specified value. The biquad filter object does not support the Error or Warn options found in the corresponding block.

Both this object and its corresponding block support variable-size input. When you call the object, it can handle an input argument which is changing in size.

Extended Capabilities

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For workflows and limitations, see HDL Code Generation for System Objects (HDL Coder).

Note

For a hardware-optimized biquad filter algorithm that supports HDL code generation, use the dsphdl.BiquadFilter (DSP HDL Toolbox) System object. This object has hardware-friendly valid and reset control signals, and models exact hardware latency behavior. The DSP HDL Toolbox™ System object does not support programmable coefficients. The object supports HDL code generation with HDL Coder™ tools.

Version History

Introduced in R2012a

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Starting in R2025a, the Filter Design HDL Coder™ product is discontinued. So, this object no longer supports HDL code generation by using the generatehdl function. The object still supports code generation using HDL Coder tools.

The dsp.BiquadFilter object issues a warning and it will be removed in a future release. Use the dsp.SOSFilter object instead.

Update Code

This table shows how to replace the dsp.BiquadFilter object with the dsp.SOSFilter object in a typical workflow.

HDL Code Generation Support

For a replacement IIR filter that supports HDL code generation, use the dsphdl.BiquadFilter (DSP HDL Toolbox) object and generate code using HDL Coder tools.

Instead of specifying the SOS matrix, specify filter coefficients asNumerator and Denominator matrices. The object provides these hardware-optimized architecture options:

• "Direct form II" and"Direct form II transposed" architectures are pipelined and quantized to fit well into FPGA DSP blocks.
• "Pipelined feedback form" implements a pipelined architecture that uses more multipliers than either direct form II structure, but achieves higher clock rates after synthesis.
• "Direct form I fully serial" implements a fully serial architecture that uses only one multiplier.

For an example, see Generate HDL Code for IIR Filter (DSP HDL Toolbox).

The dsp.BiquadFilter object will be removed in a future release. Use the dsp.SOSFilter object instead.