# ZP2TF

## Purpose:

Converts zeros, poles and gain to transfer function form.

## Syntax:

ZP2TF(z, p, k)

(b, a) = ZP2TF(z, p, k)

 z - A series, the zeros. p - A series, the poles. k - Optional. A scalar, the gain. Defaults to 1.0

## Returns:

A Nx2 array where the first column contains the numerator coefficients and the second column contains the denominator coefficients.

(b, a) = ZP2TF(z, p, k) returns the numerator and denominator coefficients in two separate series.

## Example:

W1: zp2tf({0}, {0.5}, 1)

W1 == {{1, 0}, {1, -0.5}}

W1 contains two columns, where the first column is {1, 0}, the numerator coefficients and the second column is {1, -0.5}, the denominator coefficients. The coefficients represent the system: ## Example:

(b, a) = zp2tf({0}, {0.5}, 1)

b == {1, 0}

a == {1, -0.5}

Same as above except the coefficients are returned in two separate variables.

## Example:

z = {0.0, 2.0};

p = {0.5, 0.2};

k = 1.0;

(b, a) = zp2tf(z, p, k);

b == {1, -2, 0};

a == {1, -0.7, 0.1};

The coefficients represent the system: ## Remarks:

For zp2tf(z, p, k), the input series represent the zeros, poles and gain of the rational polynomial H(z) = b(z) / a(z) where: z = e jω complex frequency N = number of numerator terms M = number of denominator terms

ZP2TF returns the numerator coefficients b(z) and the denominator coefficients a(z).

ZP2TF also works for continuous systems with a transfer function in decreasing powers of s.

See TF2ZP to convert a continuous S plane transfer function to zeros, poles and gain.

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

RESIDUEZ

ROOTS

TF2CAS

TF2ZP

TF2ZPK

ZFREQ

ZP2CAS

ZPLANE