# eqtflength

Equalize lengths of transfer function numerator and denominator

## Description

[b,a] = eqtflength(num,den) modifies the vector num or the vector den so that the resulting output vectors b and a have the same length. b and a represent the same discrete-time transfer function as num and den, but are of equal length.

example

[b,a,n,m] = eqtflength(num,den) returns the numerator order n and the denominator order m, not including any trailing zeros.

## Examples

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Consider the following discrete-time SISO transfer function model:

$H\left(z\right)=\frac{2{z}^{-2}}{4+3{z}^{-2}-{z}^{-3}}$.

Equalize the numerator and denominator polynomial lengths. Determine the polynomial orders.

num = [0 0 2];
den = [4 0 3 -1];

[b,a,n,m] = eqtflength(num,den)
b = 1×4

0     0     2     0

a = 1×4

4     0     3    -1

n = 2
m = 3

Visualize the poles and zeros of the transfer function.

zplane(b,a)

Convert the transfer function with equalized numerator and denominator to state-space form. b and a must have equal lengths to find the state-space representation of the discrete-time transfer function.

[A,B,C,D] = tf2ss(b,a)
A = 3×3

0   -0.7500    0.2500
1.0000         0         0
0    1.0000         0

B = 3×1

1
0
0

C = 1×3

0    0.5000         0

D = 0

## Input Arguments

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Numerator polynomial coefficients of discrete-time transfer function, specified as a vector.

Data Types: double
Complex Number Support: Yes

Denominator polynomial coefficients of discrete-time transfer function, specified as a vector.

Data Types: double
Complex Number Support: Yes

## Output Arguments

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Numerator polynomial coefficients of discrete-time transfer function, returned as a row vector. b has the same length as a.

Denominator polynomial coefficients of discrete-time transfer function, returned as a row vector. a has the same length as b.

Numerator order, returned as an integer. Any trailing zeros in b are excluded when computing n.

Denominator order, returned as an integer. Any trailing zeros in a are excluded when computing m.

## Tips

• Use eqtflength to obtain a numerator and denominator of equal length before applying transfer function conversion functions such as tf2ss and tf2zp to discrete-time models.

## Algorithms

eqtflength(num,den) appends zeros to either num or den as necessary. eqtflength removes any trailing zeros that num and den have in common.

## Version History

Introduced before R2006a