# noisebw

Equivalent noise bandwidth of digital lowpass filter

## 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.

## References

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

## Version History

Introduced before R2006a