dsp.FourthOrderSectionFilter

Implement cascade of fourth-order section filter

Description

The dsp.FourthOrderSectionFilter implements a cascade of fourth-order section filters.

Creation

Syntax

fos = dsp.FourthOrderSectionFilter

fos = dsp.FourthOrderSectionFilter(num,den)

fos = dsp.FourthOrderSectionFilter(Name,Value)

Description

fos = dsp.FourthOrderSectionFilter returns a FourthOrderSectionFilter object, fos, that implements a cascade of fourth order filter sections.

fos = dsp.FourthOrderSectionFilter(num,den) returns a FourthOrderSectionFilter object with the Numerator property set to num and the Denominator property set to den.

fos = dsp.FourthOrderSectionFilter(Name,Value) returns a FourthOrderSectionFilter object with each specified property name set to the specified value. You can specify additional name-value pair arguments in any order.

Example: fos = dsp.FourthOrderSectionFilter('Numerator',num,'Denominator',den)

Properties

num — Numerator coefficients of filter

[1 0.1 0.2 0.3 0.4] (default) | row vector | matrix

Numerator coefficients of the filter, specified as an L-by-5 matrix, where L is the number of filter sections. The size of this property cannot change when the object is locked. However, the values can be modified.

Tunable: Yes

Data Types: single | double
Complex Number Support: Yes

den — Denominator coefficients of filter

[1 0.1 0.2 0.3 0.4] (default) | row vector | matrix

Denominator coefficients of the filter, specified as an L-by-5 matrix or an L-by-4 matrix, where L is the number of filter sections. The leading denominator coefficients are assumed to be 1 always. If the denominator is of size L-by-4, one(s) are appended to make the size L-by-5. If the denominator is of size L-by-5, the first column values are ignored and appended with 1s. The size of this property cannot change when the object is locked. However, the values can be modified.

Tunable: Yes

Data Types: single | double
Complex Number Support: Yes

Usage

Syntax

y = fos(x)

Description

y = fos(x) filters the input signal using the specified fourth-order section filter to produce the filtered output, y.

Input Arguments

x — Input signal

vector | matrix

Input signal, specified as a vector or a matrix.

The input can be a variable-sized signal, that is, the frame size of each channel (number of rows) can change even after the object is locked. However, the number of channels (number of columns) cannot change.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

y — Filtered output

vector | matrix

Filtered output, returned as a vector or a matrix. The output has the same size, data type, and complexity as the input signal.

Data Types: single | double
Complex Number Support: Yes

Object Functions

Specific to dsp.FourthOrderSectionFilter

filterAnalyzer	Analyze filters with Filter Analyzer app
freqz	Frequency response of discrete-time filter System object
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
grpdelay	Group delay response of discrete-time filter System object
outputDelay	Determine output delay of single-rate or multirate filter

Common to All 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
clone	Create duplicate System object
isLocked	Determine if System object is in use

Examples

Filter Noisy Signal Using Fourth-Order Section (FOS) Filter

Filter a noisy sinusoidal signal using the dsp.FourthOrderSectionFilter object. Visualize the original and filtered signals using a spectrum analyzer.

Input Signal

The input signal is the sum of two sine waves with frequencies 100 Hz and 350 Hz. Add zero-mean white Gaussian noise with a standard deviation of 1e-4 to the sum of sine waves. The sample rate is 1000 Hz.

frameSize = 1024;
fs = 1000;
Sine1 = dsp.SineWave(5,100,'SamplesPerFrame',1024,'SampleRate',fs);
Sine2 = dsp.SineWave(2,350,pi/2,'SamplesPerFrame',1024,...
    'SampleRate',fs);
x = Sine1()+Sine2()+1e-4.*randn(Sine1.SamplesPerFrame,1);

Fourth-Order Section (FOS) Filter Coefficients

The numerator and denominator coefficients for the FOS filter are obtained using designParamEq which is part of Audio Toolbox:

%N = [2,4];
%gain = [5,10];
%centerFreq = [0.025,0.75];
%bandwidth = [0.025,0.35];
%mode = 'fos';
%[num,den] = designParamEQ(N,gain,centerFreq,bandwidth,mode,'Orientation','row');

num = [1.0223   -1.9368    0.9205         0         0
    1.5171    2.3980    1.4317    0.6416    0.2752];

den = [-1.9368    0.9428         0         0
    2.0136    1.9224    1.0260    0.3016];

Initialize Filter and Spectrum Analyzer

Construct the FOS IIR filter using the num and den coefficients. Construct a spectrum analyzer to visualize the original sinusoidal signal and the filtered signal.

fos = dsp.FourthOrderSectionFilter('Numerator',num,...
    'Denominator',den);

scope = spectrumAnalyzer(...
    'SampleRate',fs,...
    'PlotAsTwoSidedSpectrum',false,...
    'FrequencyScale','linear',...
    'Method','welch',...
    'Title','Original and Filtered Signals',...
    'ShowLegend',true,...
    'ChannelNames',{'Original Signal','Filtered Signal'});

Filter the input signal, and visualize the original and filtered spectrums.

for i = 1:10000
    y = fos(x);
    scope([x,y]);
end
release(scope);

Lowpass Fourth-Order Section (FOS) Filter

Design a lowpass fourth-order section (FOS) filter using the fdesign function. Using this filter, filter a noisy sinusoidal signal with two tones, one at 3 kHz, and the other at 12 kHz.

Design a fifth-order filter using the elliptic method in the 'df2tsos' structure. Use L-infinity norm scaling in the frequency domain. Specify the passband frequency to be 0.15$\pi$ rad/sample and the stopband frequency to be 0.25$\pi$ rad/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB.

Fp = 0.15; 
Fst = 0.25;
Ap = 1; 
Ast = 60;

The filter coefficients are scaled using an fdopts.sosscaling object. The scaling object is defined to have no numerator constraints, and the ScaleValueConstraint is set to 'unit', specifying the scaling to be unity scaling.

fdo = fdopts.sosscaling;
fdo.NumeratorConstraint='none';
fdo.ScaleValueConstraint='unit';

f = fdesign.lowpass('Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast);
hFilter = design(f,'ellip','SystemObject',true,...
    'FilterStructure','df2tsos','SOSScaleNorm','Linf',...
    'SOSScaleOpts',fdo)

hFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Property'
            Numerator: [3x3 double]
          Denominator: [3x3 double]
       HasScaleValues: true
          ScaleValues: [1 1 1 1.0000]

  Use get to show all properties

Visualize the lowpass frequency response of the designed filter.

freqz(hFilter)

Convert the lowpass filter to a bandpass filter using the iirlp2bp function.

[num,den] = iirlp2bp(hFilter.Numerator,hFilter.Denominator,Fp,[0.25,0.75])

num = 3×5

    0.2456         0   -0.2456         0         0
    0.4175   -0.0000   -0.4206   -0.0000    0.4175
    0.4281   -0.0000   -0.6433   -0.0000    0.4281

den = 3×5

    1.0000   -0.0000    0.5088         0         0
    1.0000   -0.0000    0.0060   -0.0000    0.8657
    1.0000   -0.0000    0.5160   -0.0000    0.5283

Create a fourth-order section filter using these numerator and denominator coefficients.

fos = dsp.FourthOrderSectionFilter(num,den)

fos = 
  FourthOrderSectionFilter with properties:

      Numerator: [3x5 double]
    Denominator: [3x5 double]

Visualize the frequency response of the fourth-order section filter.

freqz(fos);

Filter a noisy input signal with the fourth-order section filter. Visualize the spectra of the original signal and the filtered signal using the spectrum analyzer.

The input is a sum of two sine waves with frequencies 3 kHz and 12 kHz, respectively. The input sample rate is 44.1 kHz, and the frame size is set to 1024 samples.

fs = 44100;
FrameLength = 1024;

SINE1 = dsp.SineWave('SamplesPerFrame',FrameLength,'SampleRate',fs,'Frequency',3000);
SINE2 = dsp.SineWave('SamplesPerFrame',FrameLength,'SampleRate',fs,'Frequency',12000);

Initialize a spectrum analyzer to visualize the signal spectra.

scope = spectrumAnalyzer(...
    'SampleRate',fs,...
    'PlotAsTwoSidedSpectrum',false,...
    'Title','Original and Filtered Signals',...
    'ShowLegend',true,...
    'YLimits',[-180 50],...
    'ChannelNames',{'Original Signal','Filtered Signal'});
for index = 1:1000    
    x = SINE1() + SINE2()+ 0.001*randn(FrameLength,1);    
    y = fos(x);
    scope([x,y]);    
end

Version History

Introduced in R2019a