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# tfdata

Access transfer function data

## Syntax

```[num,den] = tfdata(sys) [num,den,Ts] = tfdata(sys) [num,den,Ts,sdnum,sdden]=tfdata(sys) [num,den,Ts,...]=tfdata(sys,J1,...,Jn) ```

## 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 s or z.

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`. For more information on the format of transfer function model data, see the `tf` reference page.

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`.

`[num,den,Ts,sdnum,sdden]=tfdata(sys)` also returns the uncertainties in the numerator and denominator coefficients of identified system `sys`. `sdnum{i,j}(k)` is the 1 standard uncertainty in the value `num{i,j}(k)` and `sdden{i,j}(k)` is the 1 standard uncertainty in the value `den{i,j}(k)`. If `sys` does not contain uncertainty information, `sdnum` and `sdden` are empty (`[]`).

`[num,den,Ts,...]=tfdata(sys,J1,...,Jn)` extracts the data for the `(J1,...,JN)`entry in the model array `sys`.

You can access the remaining LTI properties of `sys` with `get` or by direct referencing, for example,

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

## Examples

### Example 1

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) ```

This command 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 ```

### Example 2

Extract the numerator, denominator and their standard deviations for a 2-input, 1 output identified transfer function.

`load iddata7`

transfer function model

`sys1 = tfest(z7, 2, 1, 'InputDelay',[1 0]);`

an equivalent process model

```sys2 = procest(z7, {'P2UZ', 'P2UZ'}, 'InputDelay',[1 0]); [num1, den1, ~, dnum1, dden1] = tfdata(sys1); [num2, den2, ~, dnum2, dden2] = tfdata(sys2);```