# dsp.SOSFilter

## 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

### Description

returns a biquadratic
IIR filter System object, `sos`

= dsp.SOSFilter`sos`

, which independently filters each channel (column)
of the input over time using a specified biquadratic structure.

returns a biquadratic filter object with the `sos`

= dsp.SOSFilter(`num`

,`den`

)`Numerator`

property set
to `num`

and the `Denominator`

property set to
`den`

.

returns a biquadratic filter object with each property set to the specified value. Enclose
each property name in single quotes.`sos`

= dsp.SOSFilter(`Name,Value`

)

**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) | *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'`

.

**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) | *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'`

.

**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 *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`

.

**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.

`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

### Description

### 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

*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

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 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

`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)

### 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 |

## 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,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)

**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 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

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

`sv = `*8×1*
0.1220
0.1220
0.1166
0.1166
0.1133
0.1133
0.1122
1.0000

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

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

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

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*

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

### 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 [*g*_{1},
*g*_{2}, …,
*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 [*g*_{1},
*g*_{2}, …,
*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 [*g*_{1},
*g*_{2}, …,
*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`

.

*P* sections when you
specify scale values [*g*_{1},
*g*_{2}, …,
*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
*b _{0}*,

*b*,

_{1}*b*,

_{2}*a*, and

_{1}*a*operate in full precision.

_{2}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
*b _{0}*,

*b*,

_{1}*b*,

_{2}*a*, and

_{1}*a*operate in full precision.

_{2}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
*b _{0}*,

*b*,

_{1}*b*,

_{2}*a*, and

_{1}*a*operate in full precision.

_{2}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
*b _{0}*,

*b*,

_{1}*b*,

_{2}*a*, and

_{1}*a*operate in full precision. When you set

_{2}`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**

### 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.

## See Also

### Functions

`freqz`

|`filterAnalyzer`

|`impz`

|`info`

|`coeffs`

|`cost`

|`scale`

|`scaleopts`

|`scalecheck`

|`cumsec`

|`tf`

|`scaleFilterSections`

|`outputDelay`

|`designLowpassIIR`

|`designHighpassIIR`

|`designBandpassIIR`

|`designBandstopIIR`

|`designNotchPeakIIR`

### Objects

### Blocks

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