Function Reference |

Quick access to transfer function data

**Syntax**

**Description**

```
[num,den] = tfdata(sys)
```

returns the numerator(s) and denominator(s) of the transfer function for the TF, SS or ZPK model (or LTI array of TF, SS or ZPK models) `sys`

. For single LTI models, the outputs `num`

and `den`

of tfdata are cell arrays with the following characteristics:

`num`

and`den`

have as many rows as outputs and as many columns as inputs.- The
`(i,j)`

entries`num{i,j}`

and`den{i,j}`

are row vectors specifying the numerator and denominator coefficients of the transfer function from input`j`

to output`i`

. These coefficients are ordered in*descending*powers of or .

For arrays `sys`

of LTI models, `num`

and `den`

are multidimensional cell arrays with the same sizes as `sys`

.

If `sys`

is a state-space or zero-pole-gain model, it is first converted to transfer function form using `tf`

. See Table 11-15, "LTI Properties," on page 11-194 for more information on the format of transfer function model data.

For SISO transfer functions, the syntax

forces `tfdata`

to return the numerator and denominator directly as row vectors rather than as cell arrays (see example below).

```
[num,den,Ts] = tfdata(sys)
```

also returns the sample time `Ts`

.

You can access the remaining LTI properties of `sys`

with `get`

or by direct referencing, for example,

**Example**

Given the SISO transfer function

you can extract the numerator and denominator coefficients by typing

This syntax returns two row vectors.

If you turn `h`

into a MIMO transfer function by typing

now returns two cell arrays with the numerator/denominator data for each SISO entry. Use `celldisp`

to visualize this data. Type

and MATLAB returns the numerator vectors of the entries of `H`

.

Similarly, for the denominators, type

**See Also**

`get`

` `

Get properties of LTI models

`ssdata`

` `

Quick access to state-space data

`tf`

` `

Specify transfer functions

`zpkdata`

` `

Quick access to zero-pole-gain data

tf | totaldelay |