ss

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

Description

example

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

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

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

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

[z,p,k] = ellip(4,1,60,.4);    % Set up the filter
[s,g] = zp2sos(z,p,k);

Structure: 'Direct form I'
SOSMatrixSource: 'Property'
SOSMatrix: [2x6 double]
ScaleValues: 0.0351
NumeratorInitialConditions: 0
DenominatorInitialConditions: 0
OptimizeUnityScaleValues: true

Show all properties

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

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

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

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

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

Data Types: double

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

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

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

Data Types: double 