dsphdl.BiquadFilter

R2026b

Biquadratic IIR (SOS) filter

Since R2022a

Description

A biquad filter is a form of infinite-impulse response (IIR) filter that separates the numerator and denominator and implements each part as a series of second-order sections connected by scaling operations. This type of filter can replace a large FIR filter that uses an impractical amount of hardware resources. Designs often use biquad filters as DC blocking filters or to meet a specification originally implemented with an analog filter, such as a pre-emphasis filter.

The dsphdl.BiquadFilter object provides transposed architectures, a pipelined architecture to optimize throughput, or a serial minimum resource architecture that also supports multichannel input.

To filter input data with an HDL-optimized biquad filter:

1. Create the dsphdl.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?

Note

You can also generate HDL code for this hardware-optimized algorithm, without creating a MATLAB^® script, by using the DSP HDL IP Designer app. The app provides the same interface and configuration options as the System object™.

Creation

Syntax

myFilt = dsphdl.BiquadFilter

myFilt = dsphdl.BiquadFilter(PropertyName=Value)

Description

myFilt = dsphdl.BiquadFilter creates an HDL-optimized biquad filter. The default filter uses a direct form II architecture with one section.

myFilt = dsphdl.BiquadFilter(PropertyName=Value) sets properties using one or more name-value arguments. For example,

dsphdl.BiquadFilter(Structure='Direct form II transposed', ...
                             OutputDataType='Custom', ...
                             CustomOutputDataType=numerictype(1,16,14));

creates a biquad filter that uses a direct form II transposed architecture and sets the output of the filter to the specified numeric type.

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 — HDL filter architecture

'Direct form II' (default) | 'Direct form II transposed' | 'Pipelined feedback form' | 'Direct form I fully serial'

Both the 'Direct form II' and 'Direct form II transposed' architectures are pipelined and quantized to fit well into FPGA DSP blocks. The output of these filters matches the output of the DSP System Toolbox™ System objects dsp.SOSFilter and dsp.FourthOrderSectionFilter. These architectures minimize the number of multipliers used by the filter but have a critical path through the feedback loop and sometimes cannot achieve higher clock rates. These architectures do not support vector input.

'Pipelined feedback form' implements a pipelined architecture that uses more multipliers than either direct form II structure, but achieves higher clock rates after synthesis. This architecture supports scalar or column vector (frame-based) input and does not support row vector (multichannel) input. The output of the pipelined filter is slightly different than the DSP System Toolbox functions dsp.SOSFilter and dsp.FourthOrderSectionFilter because of the timing of data samples applied in the pipelined filter stages.

'Direct form I fully serial' implements a fully serial architecture that uses only one multiplier. This architecture supports scalar or row vector (multichannel) input and does not support column vector (frame-based) input. When you select this option, the object stores the numerator, denominator, and scale values in the same ROM. You can control the data type of the ROM by using the CoefficientDataType property. When you select this architecture, the object has an output ready argument that indicates when the object can accept new input data.

Numerator — Coefficients of filter numerator

[1,2,1] (default) | NumSections-by-3 matrix | NumSections-by-3-by NumChannels matrix

Specify the numerator coefficients as a matrix of NumSections-by-3 values, or for a multichannel filter as a NumSections-by-3-by NumChannels matrix. NumSections is the number of second-order filter sections. The object infers the number of filter sections from the size of the numerator and denominator coefficients. The numerator coefficient and denominator coefficient matrices must be the same size. The default filter has one section.

Dependencies

To specify multichannel coefficients, you must set the Structure property to 'Direct form I fully serial'.

Denominator — Coefficients of filter denominator

[1,.1,.2] (default) | NumSections-by-3 matrix

Specify the denominator coefficients as a matrix of NumSections-by-3 values, or for a multichannel filter as a NumSections-by-3-by NumChannels matrix. The object assumes the first denominator coefficient of each section is 1.0.NumSections is the number of second-order filter sections. The object infers the number of sections from the size of the numerator and denominator coefficients. The numerator coefficient and denominator coefficient matrices must be the same size. The default filter has one section.

Dependencies

To specify multichannel coefficients, you must set the Structure property to 'Direct form I fully serial'.

ScaleValues — Gain values applied before and after second-order filter sections

[1] (default) | vector of 1 to NumSections+1 values

Specify the gain values as a vector of up to NumSections+1 values, or for a multichannel filter as a matrix of up to (NumSections+1)-by-NumChannels values. NumSections is the number of second-order filter sections. The object infers the number of sections from the size of the numerator and denominator coefficients. If the vector has only one value, the object applies that gain before the first section. If you specify fewer values than there are filter sections, the object sets the remaining section gain values to one. The diagram shows a three-section filter and the locations of the four scale values before and after the sections.

Applying these gain factors outside the filter sections reduces the multipliers needed to implement the numerator of the filter.

Dependencies

To use this parameter when you set the Structure property to 'Direct form I fully serial', set HasScaleValues to true.

To specify multichannel scale values, you must set the Structure property to 'Direct form I fully serial'.

HasScaleValues — Use scale values other than 1.0

true (default) | false

Since R2026b

When you clear this parameter, the filter assumes the scale values are all equal to 1 and reduces latency by omitting the scaling calculation.

When you set this property to false, the serial filter applies the specified ScaleValues between each filter section. This selection matches the filter implementation and latency before R2026b.

For more information about the latency of the serial filter, see the Algorithms > Serial section on the Biquad Filter block reference page.

Dependencies

This parameter applies only when you set the Structure property to 'Direct form I fully serial'.

Data Types

Rounding — Rounding method for type-casting the output

'Floor' (default) | 'Ceiling' | 'Convergent' | 'Nearest' | 'Round' | 'Zero'

Rounding mode for type-casting the output and accumulator values to the data types specified by the OutputDataType and AccumulatorDataType properties. When the input data type is floating point, the object ignores this parameter. For more details, see Rounding Modes.

OverflowAction — Overflow handling for type-casting the output

'Wrap' (default) | 'Saturate'

Overflow handling for type-casting the output and accumulator values to the data types specified by the OutputDataType and AccumulatorDataType properties. When the input data type is floating point, the object ignores the OverflowAction property. For more details, see Overflow Handling.

NumeratorDataType — Method to determine data type of numerator coefficients

'Same word length as input' (default) | 'Custom'

Data type of numerator coefficients, specified as 'Same word length as input' or 'Custom'.

The object type-casts the numerator coefficients to the specified data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is floating point, the object ignores this property.

The object returns a warning if the data type of the coefficients does not have enough fractional length to represent the coefficients accurately.

If you specify an unsigned data type for this parameter, the filter uses the unsigned values and converts them to a signed data type. The signed data type is required to map the design onto DSP slices on an FPGA.

Dependencies

To enable this property, set the Structure property to 'Direct form II', 'Direct form II transposed', or 'Pipelined feedback form'. When you use the serial architecture, use the CoefficientDataType property.

DenominatorDataType — Method to determine data type of denominator coefficients

'Same word length as input' (default) | 'Custom'

Data type of denominator coefficients, specified as 'Same word length input' or 'Custom'.

The object type-casts the denominator coefficients to the specified data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is floating point, the object ignores this property.

The object returns a warning if the data type of the coefficients does not have enough fractional length to represent the coefficients accurately.

If you specify an unsigned data type for this parameter, the filter uses the unsigned values and converts them to a signed data type. The signed data type is required to map the design onto DSP slices on an FPGA.

Dependencies

To enable this property, set the Structure property to 'Direct form II', 'Direct form II transposed', or 'Pipelined feedback form'. When you use the serial architecture, use the CoefficientDataType property.

ScaleValuesDataType — Method to determine data type of section gains

'Same word length as input' (default) | 'Custom'

Data type of the scale values, specified as 'Same word length as input' or 'Custom'.

The object type-casts the scale values to the specified data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is floating point, the object ignores this property.

Dependencies

To enable this property, set the Structure property to 'Direct form II', 'Direct form II transposed', or 'Pipelined feedback form'. When you use the serial architecture, use the CoefficientDataType property.

CoefficientsDataType — Method to determine data type of coefficient memory when using serial architecture

'Same word length as input' (default) | 'Custom'

Data type of the scale values, specified as 'Same word length as input' or 'Custom'.

The object casts the numerator, denominator, and scale values to this data type and stores them in an eight-element memory of this word length. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is floating point, the object ignores this property.

If you specify an unsigned data type for this parameter, the filter uses the unsigned values and converts them to a signed data type. The signed data type is required to map the design onto DSP slices on an FPGA.

Dependencies

To enable this property, set the Structure property to 'Direct form I fully serial'.

AccumulatorDataType — Method to determine data type of accumulator signals within each section

'Same as first input' (default) | 'Custom'

Data type of accumulator signals within each section (as indicated in the diagrams in the Algorithms section), specified as 'Same as first input', or 'Custom'.

The object type-casts the output of the filter to the specified data type. The quantization uses the settings of the RoundingMethod and OverflowAction properties. When the input data type is floating point, the object ignores this property.

OutputDataType — Method to determine data type of filter output

'Same as first input' (default) | 'Full precision' | 'Custom'

Data type of filter output, specified as 'Same as first input', 'Full precision', or 'Custom'.

The object type-casts the output of the filter to the specified data type. The quantization uses the settings of the RoundingMethod and OverflowAction properties. When the input data type is floating point, the object ignores this property.

CustomNumeratorDataType — Data type of numerator coefficients

numerictype object

Data type of numerator coefficients, specified as a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

The object type-casts the numerator coefficients to the specified data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is floating point, the object ignores this property.

The object returns a warning if the data type of the coefficients does not have enough fractional length to represent the coefficients accurately.

Dependencies

This property applies when you set the NumeratorDataType property to 'Custom'.

CustomDenominatorDataType — Data type of denominator coefficients

numerictype object

Data type of denominator coefficients, specified as a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

Dependencies

This property applies when you set the DenominatorDataType property to 'Custom'.

CustomScaleValuesDataType — Data type of section gains

numerictype object

Data type of the scale values, specified as 'Same word length as first input' or a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

Dependencies

This property applies when you set the ScaleValuesDataType property to 'Custom'.

CustomCoefficientsDataType — Data type of coefficient memory when using serial architecture

numerictype object

Data type of coefficient memory when using serial architecture, specified as a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

The object casts the numerator, denominator, and scale values to this data type and stores them in an eight-element memory of this word length.

Dependencies

This property applies when you set the CoefficientsDataType property to 'Custom'.

CustomAccumulatorDataType — Data type of accumulator signals within each section

numerictype object

Data type of accumulator signals within each section (as indicated in the diagrams in the Algorithms section), specified as a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

Dependencies

This property applies when you set the AccumulatorDataType property to 'Custom'.

CustomOutputDataType — Data type of filter output

numerictype object

Data type of filter output, specified as a numerictype object. To specify a numerictype object, call numerictype(s,w,f), where:

• s is 1 for signed and 0 for unsigned.

• w is the word length in bits.

• f is the number of fractional bits.

Dependencies

This property applies when you set the OutputDataType property to 'Custom'.

Usage

Syntax

[dataOut,validOut] = myFilt(dataIn,validIn)

[dataOut,validOut,ready] = myFilt(dataIn,validIn)

Description

[dataOut,validOut] = myFilt(dataIn,validIn) filters the input data only when validIn is true.

[dataOut,validOut,ready] = myFilt(dataIn,validIn) filters the input data and returns a control signal, ready, that indicates whether the object can accept new input data.

The object returns the ready argument only when you set the Structure property to 'Direct form I fully serial'.

Input Arguments

dataIn — Input data

scalar or vector

Input data, specified as a scalar or vector of real values. When you provide a column vector, N-by-1, the filter interprets it as N data samples over time. When you provide a row vector, 1-by-K, the filter interprets it as K independent channels. When the input has an integer or fixed-point data type, the object uses fixed-point arithmetic for internal calculations.

Column vector, or frame-based, input is supported only when you set the Structure property to 'Pipelined feedback form'. The object accepts vectors of powers of two up to 64 samples, but large vector sizes can make the calculation of internal data types challenging. Vector sizes of up to 16 samples are practical for hardware implementation.

Row vector, or multichannel, input is supported only when you set the Structure property to 'Direct form I fully serial'.

When you set the Structure property to 'Direct form I fully serial', the object returns the ready argument that indicates when the object can accept new input. Your design can react to the ready argument before providing the next input sample, or you can space your input data with enough cycles in between to process each sample. For more information, see Backpressure Signal.

The software supports double and single data types for simulation, but not for HDL code generation.

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

validIn — Indicates valid input data

scalar

Control signal that indicates if the input data is valid. When validIn is 1 (true), the object captures the values from the dataIn argument. When validIn is 0 (false), the object ignores the values from the dataIn argument.

Data Types: logical

Output Arguments

dataOut — Filtered output data

scalar or vector

Filtered output data, returned as a scalar or vector of real values. For vector input, representing either frame-based (column vector) or multichannel (row vector) data, the output dimensions match the input dimensions.

When the input data is floating point, the output data inherits the data type of the input data. When the input data is an integer type or fixed-point type, the OutputDataType property determines the output data type.

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

validOut — Indicates valid output data

scalar

Control signal that indicates if the output data is valid. When validOut is 1 (true), the object returns valid data from the dataOut argument. When validOut is 0 (false), values from the dataOut argument are not valid.

Data Types: logical

ready — Indicates object can accept new input data

scalar

Control signal that indicates whether the object can accept new input data. The object sets this output to 1 (true) when it can accept data, and sets this output to 0 (false) when it is processing and cannot accept more data. For more information, see Backpressure Signal.

Dependencies

To enable this argument, set the Structure property to 'Direct form I fully serial'.

Data Types: logical

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 dsphdl.BiquadFilter

getLatency	Latency of biquad filter
filterAnalyzer	Analyze filters with Filter Analyzer app

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

Algorithms

This System object implements the algorithms described on the Biquad Filter block reference page.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

This System object supports C/C++ code generation for accelerating MATLAB simulations, and for DPI component generation.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

The software supports double and single data types for simulation, but not for HDL code generation.

To generate HDL code from predefined System objects, see Generate HDL Code for IIR Filter.

Version History

Introduced in R2022a

R2026b: Process multichannel data and optimize scale values

The object now supports multichannel input and reduced logic for scale values equal to 1. Both features are available only when you use the Direct form I fully serial filter structure.

For a multichannel filter, supply input data as a 1-by-K row vector, where K is the number of channels. You can use the same coefficients for all channels or specify coefficients as a N-by-3-by-K matrix, where N is the number of sections. The filter coefficients for all channels must represent the same order filter.

When you set the new HasScaleValues property to false, the filter assumes all scale values are 1.0 and reduces latency by omitting scale value multiplication cycles. If you set this property to true, the filter latency is the same as previous releases.

R2024b: Support for Filter Analyzer

You can import this filter System object into the Filter Analyzer app, or use it as input to the filterAnalyzer function.

R2023a: Minimum resource architecture

The object now has the option to set the Structure property to 'Direct form I fully serial' to implement a fully serial architecture that uses only one multiplier. When you select this option, the object stores the numerator, denominator, and scale values in the same ROM, and you can control the data type of the ROM by using the CoefficientsDataType property. When you select this architecture, the object has an output ready argument that indicates when the object is ready for new input.