dsp.FilterCascade

Create cascade of filter System objects

Description

The dsp.FilterCascade object creates a multistage System object™ that enables cascading of filter System objects and scalar gains. This object operates similar to the cascade function. However, the cascade function does not support delay as a filter stage.

You can pass the dsp.FilterCascade System object as a stage to another dsp.FilterCascade System object. You can also pass dsp.FilterCascade System object as an input to the cascade function.

When you call the object, the size, data type, and complexity of the input signal must be supported by all of the stages in the filter cascade. This object supports variable-size signals if the filter stages within the object support variable-size signals.

To filter a signal with a cascade of filters:

Create the dsp.FilterCascade 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?

Alternatively, you can generate a MATLAB^® function from the filter cascade object, and call that function to filter a signal. The generated function supports C/C++ code generation. For more details, see the generateFilteringCode function.

Creation

Syntax

FC = dsp.FilterCascade

FC = dsp.FilterCascade(filt1,filt2,...,filtn)

Description

FC = dsp.FilterCascade returns a System object, FC that has a single stage, a dsp.FIRFilter System object with default properties.

FC = dsp.FilterCascade(filt1,filt2,...,filtn) returns a multistage System object, FC, with the first stage set to filt1, the second stage set to filt2, and so on. Each stage can be a filter System object or a scalar gain value.

For example, create a filter cascade that includes a lowpass filter, a highpass filter, and a gain stage.

lpFilt = dsp.LowpassFilter(StopbandFrequency=15000,...
                           PassbandFrequency=12000);
hpFilt = dsp.HighpassFilter(StopbandFrequency=5000,...
                            PassbandFrequency=8000);
gain = 2;
bpFilt = dsp.FilterCascade(lpFilt,hpFilt,2);

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 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.

`Stagei` — Filter stage
`dsp.FIRFilter` System object with default properties (default) | filter System object | scalar gain value

Filter stage, specified as a filter System object or a scalar gain value. To see which System objects you can add to a filter cascade, use:

dsp.FilterCascade.helpSupportedSystemObjects

You can modify an existing stage by modifying the associated property. For example:

FC = dsp.FilterCascade(dsp.FIRFilter,5)

FC = 

  dsp.FilterCascade with properties:

    Stage1: [1×1 dsp.FIRFilter]
    Stage2: 5

K>> FC.Stage2 = dsp.FIRDecimator

FC = 

  dsp.FilterCascade with properties:

    Stage1: [1×1 dsp.FIRFilter]
    Stage2: [1×1 dsp.FIRDecimator]

To change the number of stages in a cascade, use the addStage and removeStage functions.

Usage

Syntax

y = FC(x)

Description

y = FC(x) filters input signal x by using the filter cascade defined in FC and returns filtered output y. The size, data type, and complexity of the input signal must be supported by all of the stages in the filter cascade. This object supports variable-size signals if the filter stages within the object support variable-size signals.

example

Input Arguments

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`x` — Data input
vector | matrix

Data input, specified as a vector or a matrix. When the input is a matrix, each column of the matrix represents an independent data channel.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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`y` — Filtered output data
vector | matrix

Filtered output data, 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: double | single
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)

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Specific to `dsp.FilterCascade`

`addStage`	Add filter stage to cascade
`generateFilteringCode`	Generate MATLAB code for a filter cascade
`getNumStages`	Get number of stages in filter cascade
`releaseStages`	Release locked state of all stages in cascade
`removeStage`	Remove stage from filter cascade
`outputDelay`	Determine output delay of single-rate or multirate filter
`freqzmr`	Compute DTFT approximation of impulse response of multirate or single-rate filter

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

Examples

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Filter Signal Using Cascaded Lowpass and Highpass Filters

Open Live Script

Design a bandpass filter by cascading:

A highpass filter with a stopband frequency of 5000 Hz and a passband frequency of 8000 Hz
A lowpass filter with a passband frequency of 12,000 Hz and a stopband frequency of 15,000 Hz

Visualize the frequency response.

lpFilt = dsp.LowpassFilter(StopbandFrequency=15000,...
    PassbandFrequency=12000);
hpFilt = dsp.HighpassFilter(StopbandFrequency=5000,...
    PassbandFrequency=8000);

bpFilt = dsp.FilterCascade(lpFilt,hpFilt);

filterAnalyzer(bpFilt,FilterNames="BandpassFilter");

Pass a noisy sine wave as the input to the bandpass filter. The input is a sum of three sine waves with frequencies at 3 kHz, 10 kHz, and 15 kHz. The sampling frequency is 48 kHz. View the input and the filtered output on a spectrum analyzer.

The tones at 3 kHz and 15 kHz are attenuated, and the tone at 10 kHz is preserved by the bandpass filter.

Sine1 = dsp.SineWave(Frequency=3e3,...
    SampleRate=48e3,...
    SamplesPerFrame=6000);
Sine2 = dsp.SineWave(Frequency=10e3,...
    SampleRate=48e3,...
    SamplesPerFrame=6000);
Sine3 = dsp.SineWave(Frequency=15e3,...
    SampleRate=48e3,...
    SamplesPerFrame=6000);

SpecAna = spectrumAnalyzer(...
    PlotAsTwoSidedSpectrum=false,...
    SampleRate=Sine1.SampleRate, ...
    ShowLegend=true, ...
    YLimits=[-160,60]);

SpecAna.ChannelNames = {'Original noisy signal','Filtered signal'};

for i = 1:1000
    x = Sine1()+Sine2()+Sine3()+0.1.*randn(Sine1.SamplesPerFrame,1);
    y = bpFilt(x);
    SpecAna(x,y);

end
release(SpecAna)

Design Compensation Decimator for CIC Decimator

Open Live Script

Create a CIC decimator. Cascade the decimator with a gain.

cicdecim = dsp.CICDecimator(...
    DecimationFactor=6,...
    NumSections=6);
decimcasc = dsp.FilterCascade(cicdecim,...
    1/gain(cicdecim));

Design a compensation decimator and cascade it with the filter cascade, decimcasc. This operation nests a dsp.FilterCascade object as a stage in another filter cascade. The CIC compensation decimator has an inherent gain, gain(cicdecim). The factor of 1/gain(cicdecim) from the decimation filter cascade, decimcasc, compensates for the compensation filter gain.

% Sample rate of input of compensation decimator
fs = 16e3;   
% Passband frequency
fPass = 4e3;   
% Stopband frequency
fStop = 4.5e3; 
ciccomp = dsp.CICCompensationDecimator(cicdecim,...
    DecimationFactor=2, ...
    PassbandFrequency=fPass, ...
    StopbandFrequency=fStop, ...
    SampleRate=fs);
filtchain = dsp.FilterCascade(decimcasc,ciccomp);

Visualize the frequency response of the cascade of cascades.

f = fvtool(decimcasc,ciccomp,...
    filtchain,Fs=[fs*6,fs,fs*6],...
    Arithmetic="fixed");
legend(f,'CIC Decimator',...
    'CIC Compensation Decimator',...
    'Overall Response');

Generate Code to Filter Using Cascade

Open Live Script

Design a two-stage decimator with a 100-Hz transition width, a 2-kHz sampling frequency, and 60-dB attenuation in the stopband. The decimator needs to downsample by a factor of 4.

filtCasc = designRateConverter(DecimationFactor=4,...
    InputSampleRate=2000,Bandwidth=200,StopbandAttenuation=60,...
    Verbose=true)

designRateConverter(InterpolationFactor=1, DecimationFactor=4, InputSampleRate=2000, Bandwidth=200, StopbandAttenuation=60, MaxStages=Inf, CostMethod="estimate", Tolerance=0, ToleranceUnits="absolute")

Conversion ratio: 1:4
Input sample rate: 2000
Output sample rate: 500

filtCasc = 
  dsp.FilterCascade with properties:

         Stage1: [1x1 dsp.FIRDecimator]
         Stage2: [1x1 dsp.FIRDecimator]
    CloneStages: true

Verify your design.

 info(filtCasc)

ans = 
    'Discrete-Time Filter Cascade
     ----------------------------
     Number of stages: 2
     Stage cloning: enabled
     
     Stage1: dsp.FIRDecimator
     -------
     Discrete-Time FIR Multirate Filter (real)               
     -----------------------------------------               
     Filter Structure   : Direct-Form FIR Polyphase Decimator
     Decimation Factor  : 2                                  
     Polyphase Length   : 10                                 
     Filter Length      : 19                                 
     Stable             : Yes                                
     Linear Phase       : Yes (Type 1)                       
                                                             
     Arithmetic         : double                             
     
     
     Stage2: dsp.FIRDecimator
     -------
     Discrete-Time FIR Multirate Filter (real)               
     -----------------------------------------               
     Filter Structure   : Direct-Form FIR Polyphase Decimator
     Decimation Factor  : 2                                  
     Polyphase Length   : 18                                 
     Filter Length      : 35                                 
     Stable             : Yes                                
     Linear Phase       : Yes (Type 1)                       
                                                             
     Arithmetic         : double                             
     
     '

 freqz(filtCasc)

$Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.$

Generate code to filter data using this design. You cannot generate C/C++ code from the dsp.FilterCascade object directly, but you can generate C/C++ code from the generated function. The function defines the filter stages and calls them in sequence. The function is saved in a file called myDecimator.m in the current directory.

 generateFilteringCode(filtCasc,'myDecimator');

The myDecimator function creates a filter cascade and calls each stage object in turn.

 type myDecimator

function y = myDecimator(x)
%MYDECIMATOR Construct a filter cascade and process its stages

% MATLAB Code
% Generated by MATLAB(R) 24.2 and DSP System Toolbox 24.2.
% Generated on: 05-Sep-2024 23:47:01

% To generate C/C++ code from this function use the codegen command.
% Type 'help codegen' for more information.
%#codegen

%% Construction
persistent firdn1 firdn2
if isempty(firdn1)
    firdn1 = dsp.FIRDecimator(  ...
        Numerator=[0.0021878514650437845 0 -0.010189095418136306 0 0.031140395225498115 0 -0.082785931644222821 0 0.30979571849010851 0.5 0.30979571849010851 0 -0.082785931644222821 0 0.031140395225498115 0 -0.010189095418136306 0 0.0021878514650437845]);
    firdn2 = dsp.FIRDecimator(  ...
        Numerator=[0.0011555011750488237 0 -0.0027482166351233102 0 0.0057681982289523072 0 -0.010736374060960912 0 0.018592020073668478 0 -0.031093723586671229 0 0.052603914610235683 0 -0.099130756073130377 0 0.31592697826202448 0.5 0.31592697826202448 0 -0.099130756073130377 0 0.052603914610235683 0 -0.031093723586671229 0 0.018592020073668478 0 -0.010736374060960912 0 0.0057681982289523072 0 -0.0027482166351233102 0 0.0011555011750488237]);
end

%% Process
y1 = firdn1(x);
y = firdn2(y1);

Extended Capabilities

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

Usage notes and limitations:

You cannot generate code directly from dsp.FilterCascade. If the filters in each stage support code generation, you can generate C/C++ code from the function returned by generateFilteringCode.
See System Objects in MATLAB Code Generation (MATLAB Coder).

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

This object supports HDL code generation with the Filter Design HDL Coder™ product. For workflows and limitations, see Generate HDL Code for Filter System Objects (Filter Design HDL Coder).

Version History

Introduced in R2014b

dsp.FilterCascade

Description

Creation

Syntax

Description

Properties

Stagei — Filter stage dsp.FIRFilter System object with default properties (default) | filter System object | scalar gain value

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

Output Arguments

y — Filtered output data vector | matrix

Object Functions

Specific to dsp.FilterCascade

Common to All System Objects

Examples

Filter Signal Using Cascaded Lowpass and Highpass Filters

Design Compensation Decimator for CIC Decimator

Generate Code to Filter Using Cascade

Extended Capabilities

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

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

Version History

See Also

Functions

Objects

`Stagei` — Filter stage
`dsp.FIRFilter` System object with default properties (default) | filter System object | scalar gain value

`x` — Data input
vector | matrix

`y` — Filtered output data
vector | matrix

Specific to `dsp.FilterCascade`

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

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