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.

ZP2TF

Purpose:

Syntax:

Returns:

Example:

Example:

Example:

Remarks:

See Also: