# Documentation

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# bandwidth

Frequency response bandwidth

## Syntax

``fb = bandwidth(sys)``
``fb = bandwidth(sys,dbdrop) ``

## Description

example

````fb = bandwidth(sys)` returns the bandwidth of the SISO dynamic system model `sys`. The bandwidth is the first frequency where the gain drops below 70.79% (-3 dB) of its DC value.```

example

````fb = bandwidth(sys,dbdrop) ` returns the bandwidth for a specified gain drop.```

## Examples

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Compute the bandwidth of the transfer function` sys = 1/(s+1)`.

```sys = tf(1,[1 1]); fb = bandwidth(sys)```
```fb = 0.9976 ```

This result shows that the gain of `sys` drops to 3 dB below its DC value at around 1 rad/s.

Compute the frequency at which the gain of a system drops to 3.5 dB below its DC value. Create a state-space model.

```A = [-2,-1;1,0]; B = [1;0]; C = [1,2]; D = 1; sys = ss(A,B,C,D);```

Find the 3.5 dB bandwidth of `sys`.

```dbdrop = -3.5; fb = bandwidth(sys,dbdrop)```
```fb = 0.8348 ```

Find the bandwidth of each entry in a 5-by-1 array of transfer function models. Use a `for` loop to create the array, and confirm its dimensions.

```sys = tf(zeros(1,1,5)); s = tf('s'); for m = 1:5 sys(:,:,m) = m/(s^2+s+m); end size(sys)```
```5x1 array of transfer functions. Each model has 1 outputs and 1 inputs. ```

Find the bandwidths.

`fb = bandwidth(sys)`
```fb = 1.2712 1.9991 2.5298 2.9678 3.3493 ```

`bandwidth` returns an array in which each entry is the bandwidth of the corresponding entry in `sys`. For instance, the bandwidth of `sys(:,:,2)` is `fb(2)`.

## Input Arguments

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Dynamic system, specified as a SISO dynamic system model or an array of SISO dynamic system models. Dynamic systems that you can use include:

• Continuous-time or discrete-time numeric LTI models such as `tf`, `zpk`, or `ss` models.

• Frequency-response data models such as `frd` models. For such models, `bandwidth` uses the first frequency point to approximate the DC gain.

If `sys` is an array of models, `bandwidth` returns an array of the same size, where each entry is the bandwidth of the corresponding model in `sys`. For more information on model arrays, see Model Arrays.

Gain drop in dB, specified as a real negative scalar.

## Output Arguments

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Frequency response bandwidth, returned as a scalar or an array. If `sys` is:

• A single model, then `fb` is the bandwidth of `sys`.

• A model array, then `fb` is an array of the same size as the model array `sys`. Each entry is the bandwidth of the corresponding entry in `sys`.

`fb` is expressed in `rad/TimeUnit`, where `TimeUnit` is the `TimeUnit` property of `sys`.