Documentation

# 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

collapse all

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 ```

## 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

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