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designBandpassIIR

Design and implement bandpass IIR filter

Since R2023b

Description

example

[B,A] = designBandpassIIR designs a bandpass IIR filter with the filter order of 10, lower 3-dB cutoff frequency of 0.25, and higher 3-dB cutoff frequency of 0.75. 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 fourth-order section matrices of the size P-by-5, 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.FourthOrderSectionFilter object.

example

[B,A] = designBandpassIIR(Name=Value) specifies options using one or more name-value arguments.

For example, [B,A] = designBandpassIIR(FilterOrder=30,HalfPowerFrequency1=0.3,HalfPowerFrequency2=0.8,DesignMethod="cheby1",CascadeSectionsForm="sos") designs a bandpass IIR filter with the filter order of 30, lower 3-dB cutoff frequency of 0.3, and higher 3-dB cutoff frequency of 0.8 by using the Chebyshev Type I window design method.

B and A are the second-order section matrices of the size P-by-3, where P is the number of filter sections.

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] = designBandpassIIR(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 = designBandpassIIR(Name=Value) designs a bandpass IIR filter and implements a dsp.SOSFilter object or a dsp.FourthOrderSectionFilter object.

This syntax applies when you set the SystemObject argument to true.

Examples

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Create a dsp.FourthOrderSectionFilter object.

fosFilt = dsp.FourthOrderSectionFilter
fosFilt = 
  FourthOrderSectionFilter with properties:

      Numerator: [1 0.1000 0.2000 0.3000 0.4000]
    Denominator: [1 0.1000 0.2000 0.3000 0.4000]

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.FourthOrderSectionFilter object. Use the designBandpassIIR function to design the filter coefficients. By default, this function returns a P-by-5 matrix of numerator coefficients and a P-by-5 matrix of denominator coefficients. Assign these coefficients to the dsp.FourthOrderSectionFilter object.

Vary the higher 3-dB cutoff frequency of the filter during simulation. The designBandpassIIR function recomputes the coefficients based on the updated filter specifications. Redesign the fourth-order section filter using these updated coefficients. Visualize the spectra of the input and filtered signals using the spectrum analyzer.

F3dB2 = 0.6;
for idx = 1:500
    [b,a] = designBandpassIIR(FilterOrder=30,CascadeSectionsForm="fos",...
        HalfPowerFrequency1=0.25,...
        HalfPowerFrequency2=F3dB2,DesignMethod="cheby1");
    fosFilt.Numerator = b;
    fosFilt.Denominator = a;
    x = randn(1024,1);
    y = fosFilt(x);
    spectrumScope(x,y);
    filterViz(b,a);
    F3dB2 = F3dB2 + 0.0005;
end

Create a dsp.SOSFilter object, and set the CoefficientSource property to 'Input port' so that you can vary the coefficients of the SOS filter 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 designBandpassIIR function to design the filter coefficients. When you set CascadeSectionsForm to "sos", 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 lower 3-dB cutoff frequency of the filter during simulation. The designBandpassIIR function recomputes the coefficients based on the updated filter specifications. Redesign the SOS filter using these updated coefficients. Visualize the spectra of the input and filtered signals using the spectrum analyzer.

F3dB1 = 0.25;
for idx = 1:500
    [b,a] = designBandpassIIR(FilterOrder=30,CascadeSectionsForm="sos",...
        HalfPowerFrequency1=F3dB1,...
        HalfPowerFrequency2=0.75,DesignMethod="butter");
    x = randn(1024,1);
    y = sosFilt(x,b,a);
    spectrumScope(x,y);
    filterViz(b,a);
    F3dB1 = F3dB1 + 0.0005;
end

Design and implement a bandpass IIR filter object using the designBandpassIIR function. The function returns a dsp.FourthOrderSectionFilter object when you set the SystemObject argument to true.

fosFilt = designBandpassIIR(FilterOrder=30,DesignMethod="cheby2",...
    SystemObject=true);

Create a dsp.DynamicFilterVisualizer object to visualize the magnitude response of the filter.

filterViz = dsp.DynamicFilterVisualizer(NormalizedFrequency=true,YLimits=[-80 20]);
filterViz(fosFilt)

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.FourthOrderSectionFilter object. Visualize the spectra of the input and filtered signals using the spectrum analyzer.

for idx = 1:500
    x = randn(1024,1);
    y = fosFilt(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: designBandpassIIR(FilterOrder=30,HalfPowerFrequency1=0.3,HalfPowerFrequency2=0.7,SystemObject=true)

Order of the bandpass IIR filter, N, specified as an even nonnegative integer.

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

Lower 3-dB cutoff frequency of the bandpass IIR filter, F3dB1, specified as a normalized scalar in the range (0,1].

The value of HalfPowerFrequency1 must be less than the value of HalfPowerFrequency2.

Data Types: single | double

Higher 3-dB cutoff frequency of the bandpass IIR filter, F3dB2, specified as a normalized scalar in the range (0,1].

The value of HalfPowerFrequency1 must be less than the value of HalfPowerFrequency2.

Data Types: single | double

Window design method, specified as one of these options:

  • "default" –– The function designs the bandpass 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 bandpass 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 bandpass IIR filter using the Chebyshev Type I design method. You can use this method when you specify one of these design specification combinations:

    • FilterOrder (N), HalfPowerFrequency1 (F3dB1), and PassBandRipple (APASS)

    • FilterOrder (N), HalfPowerFrequency2 (F3dB2), and PassBandRipple (APASS)

    • FilterOrder (N), HalfPowerFrequency1 (F3dB1), HalfPowerFrequency2 (F3dB2), and PassBandRipple (APASS)

  • "cheby2" –– The function designs the bandpass IIR filter using the Chebyshev Type II design method. You can use this method when you specify one of these design specification combinations:

    • FilterOrder (N), HalfPowerFrequency1 (F3dB1), and StopbandAttenuation (ASTOP)

    • FilterOrder (N), HalfPowerFrequency2 (F3dB2), and StopbandAttenuation (ASTOP)

    • FilterOrder (N), HalfPowerFrequency1 (F3dB1), HalfPowerFrequency2 (F3dB2), and StopbandAttenuation (ASTOP)

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

Form of filter cascade sections, specified as one of these:

  • "fos" –– The function designs the filter using the fourth-order section form and outputs the filter coefficients as P-by-5 matrices.

  • "sos" –– The function designs the filter using the second-order section form and outputs the filter coefficients as P-by-3 matrices.

Data Types: char | string

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

To set the HasScaleValues argument, set CascadeSectionsForm to "sos".

Data Types: logical

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

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 bandpass IIR filter in one of these forms:

  • Second-order section form –– B is a P-by-3 matrix, where P is the number of filter sections and equals ceil(FilterOrder/2).

  • Fourth-order section form –– B is a P-by-5 matrix and P equalsceil(FilterOrder/4).

Data Types: single | double

Denominator coefficients of the bandpass IIR filter in one of these forms:

  • Second-order section form –– A is a P-by-3 matrix, where P is the number of filter sections and equals ceil(FilterOrder/2).

  • Fourth-order section form –– A is a P-by-5 matrix and P equalsceil(FilterOrder/4).

The leading denominator coefficient is always 1.

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.

Dependencies

To enable this output argument, set CascadeSectionsForm to "sos".

Data Types: single | double

Bandpass IIR filter object, returned as a:

.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2023b