sos
Convert to second order sections
Description
Examples
Convert an IIR discrete-time filter object to an SOS filter object that contains the corresponding SOS sections.
Design a 10th order lowpass Butterworth filter using the butter function.
N = 10; Fc = 0.4; [b,a] = butter(N,Fc);
Create a dsp.IIRFilter object and assign the designed coefficients to the Numerator and the Denominator properties of the object.
iir = dsp.IIRFilter(Numerator=b,Denominator=a)
iir =
dsp.IIRFilter with properties:
Structure: 'Direct form II transposed'
Numerator: [4.9945e-04 0.0050 0.0225 0.0599 0.1049 0.1259 0.1049 0.0599 0.0225 0.0050 4.9945e-04]
Denominator: [1 -1.9924 3.0195 -2.8185 2.0387 -1.0545 0.4144 -0.1157 0.0225 -0.0027 1.4876e-04]
InitialConditions: 0
Show all properties
Use the sos function to convert the IIR filter object into an SOS filter that contains the corresponding SOS sections.
sosFilt = sos(iir)
sosFilt =
dsp.SOSFilter with properties:
Structure: 'Direct form II transposed'
CoefficientSource: 'Property'
Numerator: [5×3 double]
Denominator: [5×3 double]
HasScaleValues: true
ScaleValues: [4.9945e-04 1 1 1 1 1]
Show all properties
You can obtain the SOS matrix and scale values from the SOS filter object.
sMatrix = [sosFilt.Numerator,sosFilt.Denominator]
sMatrix = 5×6
1.0000 2.0958 1.0984 1.0000 -0.3187 0.0313
1.0000 2.0576 1.0602 1.0000 -0.3345 0.0826
1.0000 1.9981 1.0005 1.0000 -0.3695 0.1958
1.0000 1.9412 0.9436 1.0000 -0.4317 0.3969
1.0000 1.9073 0.9097 1.0000 -0.5380 0.7410
sValues = sosFilt.ScaleValues
sValues = 1×6
0.0005 1.0000 1.0000 1.0000 1.0000 1.0000
Compare these values to the values obtained using the tf2sos function and verify that they are the same.
[sMatrixfn,g] = tf2sos(b,a)
sMatrixfn = 5×6
1.0000 2.0958 1.0984 1.0000 -0.3187 0.0313
1.0000 2.0576 1.0602 1.0000 -0.3345 0.0826
1.0000 1.9981 1.0005 1.0000 -0.3695 0.1958
1.0000 1.9412 0.9436 1.0000 -0.4317 0.3969
1.0000 1.9073 0.9097 1.0000 -0.5380 0.7410
g = 4.9945e-04
isequal(sMatrix,sMatrixfn)
ans = logical
1
isequal(sValues(1),g)
ans = logical
1
Input Arguments
IIR discrete-time filter object, specified as a dsp.IIRFilter
System object.
Pole direction flag, specified as either:
'up'–– The first row contains the poles closest to the origin, and the last row contains the poles closest to the unit circle.'down'–– The sections are ordered in the opposite direction. The zeros are always paired with the poles closest to them.
Output Arguments
Second order section filter object, returned as a dsp.SOSFilter
System object. The sos function converts the input IIR filter
numerator and denominator coefficients into SOS matrix and scale values, and assigns
these values to the dsp.SOSFilter object.
Version History
Introduced in R2011aThe dsp.BiquadFilter object and the
UseLegacyBiquadFilter flag will be removed in a future
release.
The dsp.BiquadFilter object and the
UseLegacyBiquadFilter flag will be removed in a future
release.
The sos function now generates a dsp.SOSFilter object
instead of the dsp.BiquadFilter object.
Initialize a dsp.IIRFilter object. Use the
sos function to convert the IIR filter object into a biquadratic filter
that contains the corresponding SOS sections. The output is a dsp.SOSFilter
filter object.
iirFilt = dsp.IIRFilter convFilt = sos(iirFilt)
convFilt =
dsp.SOSFilter with properties:
Structure: 'Direct form II transposed'
CoefficientSource: 'Property'
Numerator: [1 1 0]
Denominator: [1 0.1000 0]
HasScaleValues: false
Show all properties
To design a dsp.BiquadFilter object instead of the
dsp.SOSFilter object, you can use the
UseLegacyBiquadFilter flag and set it to
true.
convFilt = sos(iirFilt,UseLegacyBiquadFilter=true)
convFilt =
dsp.BiquadFilter with properties:
Structure: 'Direct form II transposed'
SOSMatrixSource: 'Property'
SOSMatrix: [1 1 0 1 0.1000 0]
ScaleValues: [2×1 double]
InitialConditions: 0
OptimizeUnityScaleValues: true
Show all properties
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