# Documentation

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# noisebw

Equivalent noise bandwidth of filter

## Syntax

```bw = noisebw(num, den, numsamp, Fs) ```

## Description

```bw = noisebw(num, den, numsamp, Fs) ``` returns the two-sided equivalent noise bandwidth, in Hz, of a digital lowpass filter given in descending powers of z by numerator vector `num` and denominator vector `den`. The bandwidth is calculated over `numsamp` samples of the impulse response. `Fs` is the sampling rate of the signal that the filter would process; this is used as a scaling factor to convert a normalized unitless quantity into a bandwidth in Hz.

## Examples

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Computes the equivalent noise bandwidth of a Butterworth filter over 100 samples of the impulse response.

Set the sampling rate, Nyquist frequency, and carrier frequency.

```fs = 16; fNyq = fs/2; fc = 0.5; ```

Generate the Butterworth filter.

```[num,den] = butter(2,fc/fNyq); ```

Determine the noise bandwidth.

```bw = noisebw(num,den,100,fs) ```
```bw = 1.1049 ```

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### Algorithms

The two-sided equivalent noise bandwidth is

`$\frac{\text{Fs}\sum _{i=1}^{N}{|h\left(i\right)|}^{2}}{{|\sum _{i=1}^{N}h\left(i\right)|}^{2}}$`

where h is the impulse response of the filter described by `num` and `den`, and N is `numsamp`.

## References

[1] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan, Simulation of Communication Systems, New York, Plenum Press, 1992.