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# sos2ss() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

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### Reference

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).

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

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