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# designLowpassIIR

Design and implement lowpass IIR filter

Since R2023b

## Syntax

``[B,A] = designLowpassIIR``
``[B,A] = designLowpassIIR(Name=Value)``
``[B,A,SV] = designLowpassIIR(Name=Value)``
``filtObj = designLowpassIIR(Name=Value)``

## Description

``` `[B,A] = designLowpassIIR` designs a lowpass IIR filter with the filter order of 10 and half-power frequency of 0.25. When you use this syntax, the function designs the IIR filter using the `"default"` window design method and does not compute the scale values.`B` and `A` are the second-order section matrices of the size P-by-3, where P is the number of filter sections.The System object™ argument is `false` by default. To implement the filter, assign the filter coefficients to a `dsp.SOSFilter` object.```

example

````[B,A] = designLowpassIIR(Name=Value)` specifies options using one or more name-value arguments.For example, ```[B,A] = designLowpassIIR(FilterOrder=30,HalfPowerFrequency=0.4,DesignMethod="cheby1")``` designs a lowpass IIR filter with the filter order of 30 and half-power frequency of 0.4 by using the Chebyshev Type I window design method.When you specify only a partial list of filter parameters, the function designs the filter by setting the other design parameters to their default values.The function supports three design methods. Each design method supports a specific set of design combinations. For more information, see `DesignMethod`.```
````[B,A,SV] = designLowpassIIR(Name=Value)` also returns scale values when you specify the `HasScaleValues` argument. `SV` is a vector of 1s when you set the argument to `false` and a vector of scale values when you set it to `true`.```

example

````filtObj = designLowpassIIR(Name=Value)` designs a lowpass IIR filter and implements a `dsp.SOSFilter` System object.This syntax applies when you set the `SystemObject` argument to `true`.```

## Examples

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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 a lowpass IIR filter object using the `designLowpassIIR` function. The function returns a `dsp.SOSFilter` object when you set the `SystemObject` argument to `true`.

```sosFilt = designLowpassIIR(FilterOrder=30,HalfPowerFrequency=0.5,DesignMethod="butter",... SystemObject=true)```
```sosFilt = dsp.SOSFilter with properties: Structure: 'Direct form II transposed' CoefficientSource: 'Property' Numerator: [15x3 double] Denominator: [15x3 double] 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```

## Input Arguments

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### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: `designLowpassIIR(FilterOrder=30,HalfPowerFrequency=0.5,SystemObject=true)`

Order of the lowpass IIR filter, N, specified as a nonnegative integer.

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

3-dB cutoff frequency of the lowpass IIR filter, F3dB, specified as a normalized scalar in the range (`0`,`1`].

Data Types: `single` | `double`

Window design method, specified as one of these options:

• `"default"` –– The function designs the lowpass IIR filter using one of these methods:

• Chebyshev Type I method when you specify the `PassBandRipple` (APASS) argument

• Chebyshev Type II method when you specify the `StopbandAttenuation` (ASTOP) argument

• Butterworth method when you do not specify the `PassBandRipple` (APASS) and the `StopbandAttenuation` (ASTOP) arguments

• `"butter"` –– The function designs the lowpass IIR filter using the Butterworth design method. You can use this method when you specify one of these design specification combinations:

• `"cheby1"` –– The function designs the lowpass IIR filter using the Chebyshev Type I design method. You can use this method when you specify the `FilterOrder` (N), `HalfPowerFrequency` (F3dB), and the `PassBandRipple` (APASS) arguments.

• `"cheby2"` –– The function designs the lowpass IIR filter using the Chebyshev Type II design method. You can use this method when you specify the `FilterOrder` (N), `HalfPowerFrequency` (F3dB), and the `StopbandAttenuation` (ASTOP) arguments.

Data Types: `char` | `string`

Passband ripple of the IIR filter, APASS, specified as a positive scalar.

To specify the `PassbandRipple` argument, set `DesignMethod` to `"default"` or `"cheby1"`.

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

Stopband attenuation of the IIR filter, ASTOP, specified as a positive scalar.

To specify the `StopbandAttenuation` argument, set `DesignMethod` to `"default"` or `"cheby2"`.

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

Option to compute the scale values, `SV`, specified as `true` or `false`.

Data Types: `logical`

Option to create System object, specified as one of these:

• `false` –– The function returns second-order section matrices.

• `true` –– The function returns a `dsp.SOSFilter` object.

Data Types: `logical`

Option to print the entire function call in MATLAB, specified as one of these:

• `false` –– The function does not print the function call.

• `true` –– The function prints the entire function call including the default values of the `Name=Value` arguments that you did not specify when calling the function.

Use this argument to view all the values used by the function to design and implement the filter.

Data Types: `logical`

## Output Arguments

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Numerator coefficients of the lowpass IIR filter in the second-order section form, returned as a P-by-3 matrix, where P is the number of filter sections and equals `ceil`(`FilterOrder`/2).

If you specify single-precision values in any of the input arguments, the function designs single-precision filter coefficients. (since R2024a)

Data Types: `single` | `double`

Denominator coefficients of the lowpass IIR filter in the second-order section form, returned as a P-by-3 matrix, where P is the number of filter sections and equals `ceil`(`FilterOrder`/2).

The leading denominator coefficient is always 1.

If you specify single-precision values in any of the input arguments, the function designs single-precision filter coefficients. (since R2024a)

Data Types: `single` | `double`

Scale values for each section, returned as a (P+1)-by-1 vector, where P is the number of filter sections and equals `ceil`(`FilterOrder`/2).

If you set `HasScaleValues` to `false`, `SV` is a vector of 1s of size (P+1)-by-1.

If you specify single-precision values in any of the input arguments, the function outputs the scale values in single precision. (since R2024a)

Data Types: `single` | `double`

Lowpass IIR filter object, returned as a `dsp.SOSFilter` System object.

The function returns this output when you set the `SystemObject` argument to `true`.

## Version History

Introduced in R2023b

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