dsp.FourthOrderSectionFilter
Implement cascade of fourth-order section filter
Description
The dsp.FourthOrderSectionFilter
implements a cascade of
fourth-order section filters.
Creation
Syntax
Description
returns a
fos
= dsp.FourthOrderSectionFilterFourthOrderSectionFilter
object, fos
, that
implements a cascade of fourth order filter sections.
returns a fos
= dsp.FourthOrderSectionFilter(num
,den
)FourthOrderSectionFilter
object with the
Numerator
property set to num
and the
Denominator
property set to den
.
returns a fos
= dsp.FourthOrderSectionFilter(Name,Value
)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
Description
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 |
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 rad/sample and the stopband frequency to be 0.25 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
See Also
Functions
Objects
Blocks
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