Signal Processing Toolbox

tf2zp

Convert transfer function filter parameters to zero-pole-gain form.

Syntax

[z,p,k] = tf2zp(b,a) 

Description

tf2zp finds the zeros, poles, and gains of a transfer function.

[z,p,k] = tf2zp(b,a) finds the matrix of zeros z, the vector of poles p, and the associated vector of gains k from the transfer function parameters b and a:

• The numerator polynomials are represented as columns of the matrix b.
• The denominator polynomial is represented in the vector a.

Given a SIMO continuous-time system in polynomial transfer function form

or

you can use the output of tf2zp to produce the single-input, multioutput (SIMO) factored transfer function form

or

The following describes the input and output arguments for tf2zp:

• The vector a specifies the coefficients of the denominator polynomial A(s) (or A(z)) in descending powers of s (z^-1).
• The ith row of the matrix b represents the coefficients of the ith numerator polynomial (the ith row of B(s) or B(z)). Specify as many rows of b as there are outputs.
• For continuous-time systems, choose the number nb of columns of b to be less than or equal to the length na of the vector a.
• For discrete-time systems, choose the number nb of columns of b to be equal to the length na of the vector a. You can use the function eqtflength to provide equal length vectors in the case that b and a are vectors of unequal lengths. Otherwise, pad the numerators in the matrix b (and, possibly, the denominator vector a) with zeros.
• The zero locations are returned in the columns of the matrix z, with as many columns as there are rows in b.
• The pole locations are returned in the column vector p and the gains for each numerator transfer function in the vector k.

The tf2zp function is part of the standard MATLAB language.

Example

Find the zeros, poles, and gains of the discrete-time system

b = [2 3];
a = [1 0.4 1];
[b,a] = eqtflength(b,a);% Make lengths equal.
[z,p,k] = tf2zp(b,a)    % Obtain the zero-pole-gain form.
z =
         0
   -1.5000
p =
   -0.2000 + 0.9798i
   -0.2000 - 0.9798i
k =
   2

See Also

sos2zp	Convert digital filter second-order sections parameters to zero-pole-gain form.
ss2zp	Convert state-space filter parameters to zero-pole-gain form.
tf2sos	Convert digital filter transfer function parameters to second-order sections form.
tf2ss	Convert transfer function filter parameters to state-space form.
zp2tf	Convert zero-pole-gain filter parameters to transfer function form.

tf2ss

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