ss

Convert discrete-time filter System object to state-space representation

Syntax

[A,B,C,D] = ss(sysobj)

[A,B,C,D] = ss(sysobj,Arithmetic=arithType)

Description

[A,B,C,D] = ss(sysobj) converts a filter System object™ to state-space representation given by:

$$\begin{array}{l}x(k+1)=Ax(k)+Bu(k),\\ y(k)=Cx(k)+Du(k),\end{array}$$

where x is the state vector, u is the input vector, and y is the output vector.

[A,B,C,D] = ss(sysobj,Arithmetic=arithType) analyzes the filter System object based on the arithmetic specified in arithType.

For more input options, see ss in Signal Processing Toolbox™.

Examples

State-Space Representation of Biquad Filter

Design a fourth-order, lowpass SOS filter object with a normalized cutoff frequency of 0.4.

[z,p,k] = ellip(4,1,60,.4);    % Set up the filter
[sosMatrix,scaleValues] = zp2sos(z,p,k);
[num,den] = sos2ctf(sosMatrix);
sosFilt = dsp.SOSFilter(Structure='Direct form I',...
    Numerator=num,Denominator=den,...
    ScaleValues=scaleValues)

sosFilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form I'
    CoefficientSource: 'Property'
            Numerator: [2x3 double]
          Denominator: [2x3 double]
       HasScaleValues: true
          ScaleValues: [0.0351 1 1]

  Use get to show all properties

Convert the designed filter into state-space form using the ss function.

[A,B,C,D] = ss(sosFilt)

A = 8×8

         0         0         0         0         0         0         0         0
    1.0000         0         0         0         0         0         0         0
    1.8116    1.0000    1.0095   -0.3954         0         0         0         0
         0         0    1.0000         0         0         0         0         0
    1.8116    1.0000    1.0095   -0.3954         0         0         0         0
         0         0         0         0    1.0000         0         0         0
    1.8116    1.0000    1.0095   -0.3954    1.1484    1.0000    0.5581   -0.7823
         0         0         0         0         0         0    1.0000         0

B = 8×1

    0.0351
         0
    0.0351
         0
    0.0351
         0
    0.0351
         0

C = 1×8

    1.8116    1.0000    1.0095   -0.3954    1.1484    1.0000    0.5581   -0.7823

D = 
0.0351

Input Arguments

sysobj — Input filter

filter System object

Input filter, specified as one of the following filter System objects:

• dsp.DCBlocker (since R2024b)

• dsp.Differentiator

• dsp.FilterCascade

• dsp.FIRFilter

• dsp.FourthOrderSectionFilter

• dsp.HighpassFilter

• dsp.IIRFilter

• dsp.LowpassFilter

• dsp.NotchPeakFilter

• dsp.ParallelFilter

• dsp.SOSFilter

• dsp.VariableBandwidthFIRFilter

• dsp.VariableBandwidthIIRFilter

arithType — Arithmetic type

'double' (default) | 'single' | 'Fixed'

Arithmetic used in the filter analysis, specified as 'double', 'single', or 'Fixed'. When the arithmetic input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. When the arithmetic input is not specified and the System object is locked, the function performs the analysis based on the data type of the locked input.

The 'Fixed' value applies to filter System objects with fixed-point properties only.

When the 'Arithmetic' input argument is specified as 'Fixed' and the filter object has the data type of the coefficients set to 'Same word length as input', the arithmetic analysis depends on whether the System object is unlocked or locked.

• unlocked –– The analysis object function cannot determine the coefficients data type. The function assumes that the coefficients data type is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

• locked –– When the input data type is 'double' or 'single', the analysis object function cannot determine the coefficients data type. The function assumes that the data type of the coefficients is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

To check if the System object is locked or unlocked, use the isLocked function.

When the arithmetic input is specified as 'Fixed' and the filter object has the data type of the coefficients set to a custom numeric type, the object function performs fixed-point analysis based on the custom numeric data type.

Output Arguments

A — State matrix

matrix

State matrix, returned as an N-by-N matrix, where N is the filter order.

Data Types: double

B — Input matrix

column vector

Input matrix, returned as an N-by-1 column vector, indicating that the number of inputs to the linear system is 1. N is the filter order.

Data Types: double

C — Output matrix

row vector

Output matrix, returned as a 1-by-N row vector, indicating that the number of outputs of the linear system is 1. N is the filter order.

Data Types: double

D — Feedthrough matrix

scalar

Feedthrough matrix, returned as a scalar, indicating that the number of inputs and outputs of the linear system is 1.

Data Types: double

Version History

Introduced in R2011a

R2024b: dsp.BiquadFilter object warns

The dsp.BiquadFilter object issues a warning and will be removed in a future release. Use the dsp.SOSFilter object instead.

Update Code

This table shows typical usage of the object and explains how to update existing code to use the dsp.SOSFilter object.

Discouraged Usage	Recommended Replacement
[z,p,k] = butter(10,2000/(8000/2)); [s,g] = zp2sos(z,p,k); biquad = dsp.BiquadFilter(Structure='Direct form I',... SOSMatrix=s,ScaleValues=g); [A,B,C,D] = ss(biquad)	[z,p,k] = butter(10,2000/(8000/2)); [s,g] = zp2sos(z,p,k); [num,den] = sos2ctf(s); sosFilter = dsp.SOSFilter(Numerator=num,... Denominator=den,... ScaleValues=g,... Structure="Direct form I"); [A,B,C,D] = ss(sosFilter)

R2024b: Support for dsp.DCBlocker object

Starting in R2024b, this function supports the dsp.DCBlocker object.

R2023b: Support for dsp.ParallelFilter Object

Starting in R2023b, the ss analysis function supports the dsp.ParallelFilter object.

R2023b: dsp.BiquadFilter object will be removed

The dsp.BiquadFilter object will be removed in a future release. Use the dsp.SOSFilter object instead.