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# sos2tf() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

sos2tf converts a second-order section representation of a given digital filter to an equivalent transfer function representation.[b,a] = sos2tf(sos) returns the numerator coefficients b and denominator coefficients a of the transfer function that describes a discrete-time system given by sos in second-order section form. The second-order section format of H(z) is given byH(z)=∏k=1LHk(z)=∏k=1Lb0k+b1kz−1+b2kz−21+a1kz−1+a2kz−2.sos is an L-by-6 matrix that contains the coefficients of each second-order section stored in its rows.sos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L].Row vectors b and a contain the numerator and denominator coefficients of H(z) stored in descending powers of z.H(z)=B(z)A(z)=b1+b2z−1+⋯+bn+1z−na1+a2z−1+⋯+am+1z−m[b,a] = sos2tf(sos,g) returns the transfer function that describes a discrete-time system given by sos in second-order section form with gain g.H(z)=g∏k=1LHk(z).

[b,a] = sos2tf(sos)[b,a] = sos2tf(sos,g)

Transfer Function Representation of a Second-Order Section SystemOpen This Example Compute the transfer function representation of a simple second-order section system. sos = [1 1 1 1 0 -1; -2 3 1 1 10 1]; [b,a] = sos2tf(sos) b = -2 1 2 4 1 a = 1 10 0 -10 -1