# tf

Constructs a transfer function model

## Syntax

SYS = tf()

SYS = tf('s')

SYS = tf('z', Ts)

SYS = tf(S)

SYS = tf(SYSIN)

SYS = tf(NUM, DEN)

SYS = tf(NUM, DEN, Ts)

SYS = tf(NUM, DEN, Ts, 'variable', 'var')

## Inputs

S
A scalar (static gain).
NUM
The numerator polynomial coefficients, stored as a row vector or as a cell array of row vectors.
DEN
The denominator polynomial coefficients, stored as a row vector or as a cell array of row vectors.
SYSIN
State-space or transfer function model.
Ts
Sampling time Ts (in seconds).
Ts = -1 leaves the sampling time unspecified.
Ts = 0 by default.
var
A string, either 'z^-1' or 'z' (default) to indicate the displayed polynomial variable.

## Outputs

SYS
The transfer function model.

## Examples

Transfer function model for a discrete time system:
num = [3 4];
den = [3 1 5];
Ts = 0.2;
sys = tf(num, den, Ts)
Transfer function for input 1, output 1

3 z + 4
-------------
3 z^2 + z + 5

Sampling Time: 0.2 s
Transfer function model for a discrete time system, but with z^-1 as the variable:
num = [3 4];
den = [3 1 5];
Ts = 0.2;
sys = tf(num, den, Ts, 'variable', 'z^-1')
Transfer function for input 1, output 1

3 z^-1 + 4 z^-2
-----------------
3 + z^-1 + 5 z^-2

Sampling Time: 0.2 s
State-space model as an input to the function tf:
sys = ss(1,2,3,4);
sys_tf = tf(sys)
Transfer function for input 1, output 1

4 s + 2
-------
s - 1

## Comments

SYS = tf(NUM, DEN) constructs a continuous-time transfer function model with numerator NUM and denominator DEN.

Adding Ts parameter allows you to define the discrete-time transfer function.

Ts = -1 leaves the sampling time unspecified. In this case, the input arguments are considered to be continuous-time.

When NUM and DEN have different lengths, the shorter vector is treated as having implicit leading zeros. See filt for comparison.

For MIMO systems, the cell arrays of polynomials will have the dimension q x p, where q is the number of outputs and p is the number of inputs.