# noisebw

Equivalent noise bandwidth of digital lowpass filter

## Syntax

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

## Description

example

````bw = noisebw(num,den,N,Fs)` returns the two-sided equivalent noise bandwidth of a digital lowpass filter in Hz. Specify the filter coefficients in descending polynomial powers by numerator `num` and denominator `den`. Input `N` is the number of samples of the impulse response. `Fs` is the sampling rate for the filtered signal. For more information on the two-sided equivalent noise bandwidth computation, see Algorithms.```

## Examples

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

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

Generate a Butterworth filter.

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

Compute the equivalent noise bandwidth of the filter over 100 samples of the impulse response.

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

## Input Arguments

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Numerator coefficients of the filter in descending polynomial powers, specified as a numeric row vector.

Data Types: `double`

Denominator coefficients of the filter in descending polynomial powers, specified as a numeric row vector.

Data Types: `double`

Number of samples of the impulse response to use when calculating the bandwidth, specified as a positive integer.

Data Types: `double`

Sampling rate for the filtered signal, specified as a positive integer. The function uses this input value as a scaling factor to convert a normalized unitless quantity into a bandwidth in Hz.

Data Types: `double`

## Output Arguments

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Equivalent noise bandwidth in Hz, returned as a numeric scalar.

## Algorithms

This formula specifies the two-sided equivalent noise bandwidth computation.

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

h is the impulse response of the filter and is specified by input arguments `num` and `den`.

 Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan. Simulation of Communication Systems. Second edition. Boston, MA: Springer US, 2000.