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# sos2ss() - Signal Processing

```sos2ss converts a second-order section representation
of a digital filter to an equivalent state-space representation.[A,B,C,D] = sos2ss(sos) converts sos,
a system expressed in second-order section form, to a single-input,
single-output state-space representation:x(n+1)=Ax(n)+Bu(n),y(n)=Cx(n)+Du(n).The discrete transfer function in second-order section form
is given byH(z)=∏k=1LHk(z)=∏k=1Lb0k+b1kz−1+b2kz−21+a1kz−1+a2kz−2.sos is a L × 6 matrix
organized assos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L].The entries of sos must be real for proper
conversion to state space. The returned matrix A is
of size 2L × 2L, B is
a 2L × 1 column vector, C is
a 1 × 2L row
vector, and D is a 1 × 1 scalar.[A,B,C,D] = sos2ss(sos,g) converts
to state space a system sos in second-order section
form with gain g:H(z)=g∏k=1LHk(z).```

### Syntax

`[A,B,C,D] = sos2ss(sos)[A,B,C,D] = sos2ss(sos,g)`

### Example

```State-Space Representation of a Second-Order Section SystemOpen This Example
Compute the state-space representation of a simple second-order section system with a gain of 2.
sos = [1  1  1  1   0  -1 ;
-2  3  1  1  10   1];
[A,B,C,D] = sos2ss(sos,2)

A =

-10     0    10     1
1     0     0     0
0     1     0     0
0     0     1     0

B =

1
0
0
0

C =

42     4   -32    -2

D =

-4```