sos2zp() - Signal Processing

sos2zp converts a second-order section representation
of a given digital filter to an equivalent zero-pole-gain representation.[z,p,k] = sos2zp(sos) returns
the zeros z, poles p, and gain k of
the 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 in its
rows.sos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L].Column vectors z and p contain
the zeros and poles of the transfer function H(z).H(z)=k(z−z1)(z−z2)⋯(z−zn)(p−p1)(p−p2)⋯(p−pm)where the orders n and m are
determined by the matrix sos. [z,p,k] = sos2zp(sos,g) returns
the zeros z, poles p,
and gain k of the system given
by sos in second-order section form with gain g.H(z)=g∏k=1LHk(z).

Syntax

[z,p,k] = sos2zp(sos)[z,p,k] = sos2zp(sos,g)

Example

Zeros, Poles, and Gain of a SystemOpen This Example
Compute the zeros, poles, and gain of a simple system in second-order section form.
sos = [1  1  1  1  0 -1; -2  3  1  1  10  1];
[z,p,k] = sos2zp(sos)

z =

  -0.5000 + 0.8660i
  -0.5000 - 0.8660i
   1.7808 + 0.0000i
  -0.2808 + 0.0000i


p =

   -1.0000
    1.0000
   -9.8990
   -0.1010


k =

    -2

Output / Return Value

Limitations

Alternatives / See Also

Reference