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:

 

image\zplane01.gif

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:

 

image\zplane03.gif

 

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.

See Also:

DADiSP/Filters

RESIDUEZ

ROOTS

TF2CAS

TF2ZP

TF2ZPK

ZFREQ

ZP2CAS

ZPLANE