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# upsample

Upsample discrete-time models

## Syntax

```sysl = upsample(sys,L) ```

## Description

`sysl = upsample(sys,L)` resamples the discrete-time dynamic system model `sys` at a sampling rate that is `L`-times faster than the sample time of `sys` (Ts0). `L` must be a positive integer. When `sys` is a TF model, H(z), `upsample` returns `sysl` as H(zL) with the sample time Ts0 / `L`.

The responses of models `sys` and `sysl` have the following similarities:

• The time responses of `sys` and `sysl` match at multiples of Ts0.

• The frequency responses of `sys` and `sysl` match up to the Nyquist frequency π / Ts0.

### Note

`sysl` has `L` times as many states as `sys`.

## Examples

collapse all

Create a transfer function with sample time 2.25 seconds.

`sys = tf(0.75,[1 10 2],2.25)`
```sys = 0.75 -------------- z^2 + 10 z + 2 Sample time: 2.25 seconds Discrete-time transfer function. ```

Create a transfer function with a sample time that is 14 times faster than `sys`.

```L = 14; sys1 = upsample(sys,L)```
```sys1 = 0.75 ------------------ z^28 + 10 z^14 + 2 Sample time: 0.16071 seconds Discrete-time transfer function. ```

The sample time of `sys1` is 0.16071 seconds, which is 14 times faster than the sample time of `sys`.