sos2zp

Signal Processing Toolbox

Second-order section to zero-pole-gain conversion.

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

Description

sos2zp converts a second-order section representation of a given system 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 by

where L is the number of rows of sos. sos is an L-by-6 matrix which contains the coefficients of each second-order section stored in its rows:

Column vectors z and p contain the zeros and poles of the transfer function H(z):

where the orders N and M are determined by the matrix sos.

Example

Compute the poles, zeros, 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
  -0.2808

p =

   -1.0000
    1.0000
   -9.8990
   -0.1010

k =

    -2

Algorithm

sos2zp finds the roots and poles of each second-order section using the roots command. sos2zp returns the roots and poles with conjugate pairs in consecutive locations, with the order of the pairs determined by their row in the sos matrix. The gain k is the product of the gains of the sections:

`sos2ss`	Second-order section to state-space conversion.
`sos2tf`	Second-order section to transfer function conversion.
`ss2sos`	State-space to second-order section conversion.
`zp2sos`	Zero-pole-gain to second-order section conversion.