ss
Convert discrete-time filter System object to state-space representation
Description
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:
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 R2011aR2024b: 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.
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