sos2zp

Convert digital filter second-order section parameters to zero-pole-gain form

Syntax

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

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

Description

[z,p,k] = sos2zp(sos) returns the zeros, poles, and gain of a system whose second-order section representation is given by sos.

[z,p,k] = sos2zp(sos,g) returns the zeros, poles, and gain of a system whose second-order section representation is given by sos with gain g.

Examples

Zeros, Poles, and Gain of a System

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 = 4×1 complex

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

p = 4×1

   -1.0000
    1.0000
   -9.8990
   -0.1010

k = 
-2

Input Arguments

sos — Second-order section representation

matrix

Second-order section representation, specified as a matrix. sos is an L-by-6 matrix

$$\text{sos}=\left[\begin{array}{cccccc}{b}_{01}& b_{11}& b_{21}& 1& a_{11}& a_{21}\\ b_{02}& b_{12}& b_{22}& 1& a_{12}& a_{22}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ b_{0L}& b_{1L}& b_{2L}& 1& a_{1L}& a_{2L}\end{array}\right]$$

whose rows contain the numerator and denominator coefficients b_ik and a_ik of the second-order sections of H(z):

$$H(z)=g{\displaystyle \prod _{k=1}^L{H}_k}(z)=g{\displaystyle \prod _{k=1}^L\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}}{1+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}}}.$$

Example: [2 4 2 6 0 2;3 3 0 6 0 0] specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: single | double
Complex Number Support: Yes

g — Overall system gain

real scalar

Overall system gain, specified as a real scalar.

Data Types: single | double

Output Arguments

z — Zeros

vector

Zeros of the system, returned as a vector.

p — Poles

vector

Poles of the system, returned as a vector.

k — Scalar gain

scalar

Scalar gain of the system, returned as a scalar.

Algorithms

sos2zp finds the poles and zeros of each second-order section by repeatedly calling tf2zp.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• The complexity of outputs, z, p, and k, might be different in MATLAB^® and the generated code.

• The order of outputs, z and p, might be different in MATLAB and the generated code.

Version History

Introduced before R2006a