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Create a cascade of filter System objects


The dsp.FilterCascade object creates a multistage System object™ that enables cascading of filter System objects, delays, 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 stages within support variable-size signals.

To filter a signal with a cascade of filters:

  1. Create the dsp.FilterCascade 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? (MATLAB).

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. See generateFilteringCode.





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


FC=dsp.FilterCascade(filt1,filt2,...) 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 , a dsp.FilterCascade System object, a dsp.Delay System object, or a scalar gain value.

For example,

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


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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 (MATLAB).

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

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.


For versions earlier than R2016b, use the step function to run the System object algorithm. The arguments to step are the object you created, followed by the arguments shown in this section.

For example, y = step(obj,x) and y = obj(x) perform equivalent operations.





y=FC(x) filters the input signal x using the filter cascade defined in FC, and returns the 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 stages within support variable-size signals.

Input Arguments

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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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Filtered output, 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:


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addStageAdd new filter stage to cascade
generateFilteringCodeGenerate MATLAB code for a filter cascade
getNumStagesGet number of stages in filter cascade
releaseStagesRelease the locked state of all stages in the cascade
removeStageRemove stage from filter cascade
stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object


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Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, myObject(x) becomes step(myObject,x).

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 using fvtool.

lpFilt = dsp.LowpassFilter('StopbandFrequency',15000,...
hpFilt = dsp.HighpassFilter('StopbandFrequency',5000,...

bpFilt = dsp.FilterCascade(lpFilt,hpFilt);

legend('Bandpass Filter');

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.

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 = dsp.SpectrumAnalyzer('PlotAsTwoSidedSpectrum',false, ...
    'SampleRate',Sine1.SampleRate, ...
    'ShowLegend',true, ...

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

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


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

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.

fs = 16e3;     % Sampling frequency of input of compensation decimator
fPass = 4e3;   % Passband frequency
fStop = 4.5e3; % Stopband frequency
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');

The CIC compensation decimator has an inherent gain, gain(cicdecim). By cascading with a factor of 1/gain(cicdecim), the filter cascade compensates for this gain.

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.

decimSpec = fdesign.decimator(4, 'Nyquist', 4, 'Tw,Ast', 100,60,2000);
filtCasc = design(decimSpec, 'multistage', 'SystemObject', true);

Verify your design using fvtool.

ans = 
    'Discrete-Time Filter Cascade
     Number of stages: 2
     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                             


Generate code to filter data using this design. The code is saved in a file called stepDecimator.m in the current directory.

 generateFilteringCode(filtCasc, 'stepDecimator');

The stepDecimator function creates a filter cascade and calls the step method on each stage.

 type stepDecimator
function y = stepDecimator(x)
%STEPDECIMATOR Construct filter cascade and process each stage

% Generated by MATLAB(R) 9.6 and DSP System Toolbox 9.8.
% Generated on: 01-Mar-2019 18:36:50

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

%% Construction
persistent filter1 filter2
if isempty(filter1)
    filter1 = 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]);
    filter2 = 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]);

%% Process
y1 = filter1( x );
y  = filter2( y1);

Extended Capabilities

See Also

System Objects


Introduced in R2014b