eqtflength

Equalize lengths of transfer function numerator and denominator

Syntax

[b,a] = eqtflength(num,den)

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

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.

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

Examples

Equalize Transfer Function Numerator and Denominator Lengths

Consider the following discrete-time SISO transfer function model:

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

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

num — Numerator coefficients

vector

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

Data Types: double
Complex Number Support: Yes

den — Denominator coefficients

vector

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

Data Types: double
Complex Number Support: Yes

Output Arguments

b — Numerator coefficients

row vector

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

a — Denominator coefficients

row vector

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

n — Numerator order

integer

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

m — Denominator order

integer

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a