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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

This example computes the equivalent noise bandwidth of a Butterworth filter over 100 samples of the impulse response.

```Fs = 16; % Sampling rate
Fnyq = Fs/2; % Nyquist frequency
Fc = 0.5; % Carrier frequency
[num,den] = butter(2,Fc/Fnyq); % Butterworth filter
bw = noisebw(num,den,100,Fs)```

The output is below.

```bw =

1.1049
```

expand all

### 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.