tf2zp

Signal Processing Toolbox

Transfer function to zero-pole-gain conversion.

[z,p,k] = tf2zp(num,den)

Description

tf2zp finds the zeros, poles, and gains of a system in polynomial transfer function form.

[z,p,k] = tf2zp(num,den)

finds the single-input, multi-output (SIMO) factored transfer function form:

given a SIMO system in polynomial transfer function form:

Vector den specifies the coefficients of the denominator in descending powers of s. Matrix num indicates the numerator coefficients with as many rows as there are outputs. The zero locations are returned in the columns of matrix z, with as many columns as there are rows in num. The pole locations are returned in column vector p and the gains for each numerator transfer function in vector k.

tf2zp also works for discrete systems. The function zp2tf is the inverse of tf2zp.

Example

Find the zeros, poles, and gains of the system

num = [2 3];
den = [1 0.4 1];
[z,p,k] = tf2zp(num,den) 

z =

   -1.5000

p =

   -0.2000 + 0.9798i
   -0.2000 - 0.9798i

k =

   2

Algorithm

The system is converted to state-space using tf2ss and then to zeros, poles, and gains using ss2zp.

`ss2tf`	State-space to transfer function conversion.
`ss2zp`	State-space to zero-pole-gain conversion.
`tf2ss`	Transfer function to state-space conversion.
`zp2ss`	Zero-pole-gain to state-space conversion.
`zp2tf`	Zero-pole-gain to transfer function conversion.