Function Reference
tfdata

Syntax

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

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

• ```[num,den] = tfdata(sys,'v')
```

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,

• ``````sys.Ts
``````sys.variable
``````

Example

Given the SISO transfer function

• ```h = tf([1 1],[1 2 5])
```

you can extract the numerator and denominator coefficients by typing

• ```[num,den] = tfdata(h,'v')
num =
0     1     1

den =
1     2     5
```

This syntax returns two row vectors.

If you turn `h` into a MIMO transfer function by typing

• ```H = [h ; tf(1,[1 1])]
```

the command

• ```[num,den] = tfdata(H)
```

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

• ``````celldisp(num)
``````

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

• ```num{1} =
0     1     1

num{2} =
0     1
```

Similarly, for the denominators, type

• ```celldisp(den)
den{1} =
1     2     5

den{2} =
1     1
```

`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