# TF2ZP

## Purpose:

Converts S plane transfer function form to zeros, poles and gain.

## Syntax:

TF2ZP(b, a)

(z, p, k) = TF2ZP(b, a)

 b - A series. The numerator (i.e. zero) coefficients in descending powers of s. a - A series. The denominator (i.e. pole) coefficients in descending powers of s.

## Returns:

A Nx3 array where the first column contains the zeros, the second column contains the poles and the third column contains the gain.

(z, p, k) = TF2ZP(b, a) returns the zeros, poles and gain as three separate arrays.

## Example: W1: tf2zp({1}, {1, 0.5})

W1 contains two columns, where the first column is a pole at s = -0.5 and the second column is the gain of 1.0. The system has no zeros.

## Example:

(z, p, k) = tf2zp({1}, {1, 0.5});

z == {}

p == {-0.5}

k == 1

Same as above except the values are returned in three separate variables.

## Example: b = {1, 2, 0};

a = {1, 0.7, 0.1};

(z, p, k) = tf2zp(b, a);

z == {0, -2.0)

p == {-0.5, -0.2}

k == 1

## Remarks:

For tf2zp(b, a), the input series represent the terms of the rational polynomial H(s) = b(s) / a(s) where: s = jω complex frequency N = number of numerator terms M = number of denominator terms

See TF2ZPK to convert a discrete Z plane transfer function to zeros, poles and gain.

See ZP2TF to convert zeros, poles and gain to transfer function form.

RESIDUE

ROOTS

SFREQ

SPLANE

TF2CAS

TF2SOS

TF2ZPK

ZP2TF

ZPLANE