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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Noise Equivalent Bandwidth of Butterworth Filter

Open Live Script

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

$\frac{Fs \sum_{i = 1}^{N} {| h (i) |}^{2}}{{| \sum_{i = 1}^{N} h (i) |}^{2}}$

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.

Introduced before R2006a

Documentation