sos

Convert to second order sections

Syntax

sysobjsos = sos(sysobj)

sysobjsos = sos(sysobj,dir_flag)

Description

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

Convert IIR Discrete-time Filter to SOS Form

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

sysobj — IIR discrete-time filter object

dsp.IIRFilter System object

IIR discrete-time filter object, specified as a dsp.IIRFilter System object.

dir_flag — Pole direction flag

'up' | 'down'

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

sysobjsos — Second order section filter object

dsp.BiquadFilter System object

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.