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.

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