# ss

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

## Description

## Examples

### State-Space Representation of Biquad Filter

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); biquad = dsp.BiquadFilter(s,g,'Structure','Direct form I')

biquad = dsp.BiquadFilter with properties: 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,B,C,D] = ss(biquad)

`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:

`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**

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