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sos

Convert to second order sections

Description

example

sysobjsos = sos(sysobj) converts a IIR discrete-time filter System object™ to second-order section (SOS) form. The sysobjsos output is a dsp.BiquadFilter System object.

sysobjsos = sos(sysobj,dir_flag) rearranges the second-order sections according to proximity to the origin of the poles of the sections.

Examples

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Convert an IIR discrete-time filter object to a biquadratic 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: [1x11 double]
          Denominator: [1x11 double]
    InitialConditions: 0

  Show all properties

Use the sos function to convert the IIR filter object into a biquadratic filter that contains the corresponding SOS sections.

biquad = sos(iir)
biquad = 
  dsp.BiquadFilter with properties:

                   Structure: 'Direct form II transposed'
             SOSMatrixSource: 'Property'
                   SOSMatrix: [5x6 double]
                 ScaleValues: [6x1 double]
           InitialConditions: 0
    OptimizeUnityScaleValues: true

  Show all properties

You can access the SOS matrix and the scale value properties of the biquadratic filter.

sMatrix = biquad.SOSMatrix
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 = biquad.ScaleValues
sValues = 6×1

    0.0005
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000

To verify, compare these values to the values obtained using the tf2sos function.

[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

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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

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Second order section filter object, returned as a dsp.BiquadFilter 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.BiquadFilter object.

Introduced in R2011a