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# obw() - Signal Processing

```bw = obw(x) returns
the 99% occupied bandwidth, bw, of the input
signal, x.
examplebw = obw(x,fs) returns
the occupied bandwidth in terms of the sample rate, fs.

examplebw = obw(pxx,f) returns
the 99% occupied bandwidth of the power spectral density (PSD) estimate, pxx.
The frequencies, f, correspond to the estimates
in pxx.
bw = obw(sxx,f,rbw) computes
the occupied bandwidth of the power spectrum estimate, sxx.
The frequencies, f, correspond to the estimates
in sxx. rbw is the resolution
bandwidth used to integrate each power estimate.

bw = obw(___,freqrange,p) specifies
the frequency interval over which to compute the occupied bandwidth,
using any of the input arguments from previous syntaxes.This syntax also specifies p, the percentage
of the total signal power contained in the occupied band.

example[bw,flo,fhi,power]
= obw(___) also returns the lower and upper
bounds of the occupied bandwidth and the occupied band power.

obw(___) with no output arguments
plots the PSD or power spectrum in the current figure window and annotates
the bandwidth.```

### Syntax

```bw = obw(x)bw = obw(x,fs) examplebw = obw(pxx,f) examplebw = obw(sxx,f,rbw)bw = obw(___,freqrange,p)[bw,flo,fhi,power]
= obw(___) exampleobw(___)```

### Example

```Occupied Bandwidth of ChirpsOpen This Example
Generate 1024 samples of a chirp sampled at 1024 kHz. The chirp has an initial frequency of 50 kHz and reaches 100 kHz at the end of the sampling. Add white Gaussian noise such that the signal-to-noise ratio is 40 dB. Reset the random number generator for reproducible results.
nSamp = 1024;
Fs = 1024e3;
SNR = 40;
rng default

t = (0:nSamp-1)'/Fs;

x = chirp(t,50e3,nSamp/Fs,100e3);
x = x+randn(size(x))*std(x)/db2mag(SNR);
Estimate the occupied bandwidth of the signal and annotate it on a plot of the power spectral density (PSD).obw(x,Fs)

ans =

5.5377e+04

Generate another chirp. Specify an initial frequency of 200 kHz, a final frequency of 300 kHz, and an amplitude that is twice that of the first signal. Add white Gaussian noise.x2 = 2*chirp(t,200e3,nSamp/Fs,300e3);
x2 = x2+randn(size(x2))*std(x2)/db2mag(SNR);
Concatenate the chirps to produce a two-channel signal. Estimate the occupied bandwidth of each channel.y = obw([x x2],Fs)

y =

1.0e+05 *

0.5538    1.0546

Annotate the occupied bandwidths of the two channels on a plot of the PSDs.obw([x x2],Fs);

Add the two channels to form a new signal. Plot the PSD and annotate the occupied bandwidth.obw(x+x2,Fs);

Occupied Bandwidth of SinusoidsOpen This ExampleGenerate 1024 samples of a 100.123 kHz sinusoid sampled at 1024 kHz. Add white Gaussian noise such that the signal-to-noise ratio is 40 dB. Reset the random number generator for reproducible results.nSamp = 1024;
Fs = 1024e3;
SNR = 40;
rng default

t = (0:nSamp-1)'/Fs;

x = sin(2*pi*t*100.123e3);
x = x + randn(size(x))*std(x)/db2mag(SNR);
Use the periodogram function to compute the power spectral density (PSD) of the signal. Specify a Kaiser window with the same length as the signal and a shape factor of 38. Estimate the occupied bandwidth of the signal and annotate it on a plot of the PSD.[Pxx,f] = periodogram(x,kaiser(nSamp,38),[],Fs);

obw(Pxx,f);

Generate another sinusoid, this one with a frequency of 257.321 kHz and an amplitude that is twice that of the first sinusoid. Add white Gaussian noise.x2 = 2*sin(2*pi*t*257.321e3);
x2 = x2 + randn(size(x2))*std(x2)/db2mag(SNR);
Concatenate the sinusoids to produce a two-channel signal. Estimate the PSD of each channel and use the result to determine the occupied bandwidth.[Pyy,f] = periodogram([x x2],kaiser(nSamp,38),[],Fs);

y = obw(Pyy,f)

y =

1.0e+03 *

7.2001    7.3777

Annotate the occupied bandwidths of the two channels on a plot of the PSDs.obw(Pyy,f);

Add the two channels to form a new signal. Estimate the PSD and annotate the occupied bandwidth.[Pzz,f] = periodogram(x+x2,kaiser(nSamp,38),[],Fs);

obw(Pzz,f);

Occupied Bandwidth of Bandlimited SignalsOpen This Example
Generate a signal whose PSD resembles the frequency response of an 88th-order bandpass FIR filter with normalized cutoff frequencies
d = fir1(88,[0.25 0.45]);
Compute the 99% occupied bandwidth of the signal between
rad/sample. Plot the PSD and annotate the occupied bandwidth and measurement interval.obw(d,[],[0.2 0.6]*pi);

Output the occupied bandwidth, its lower and upper bounds, and the occupied band power. Specifying a sample rate of
is equivalent to leaving the rate unset.[bw,flo,fhi,power] = obw(d,2*pi,[0.2 0.6]*pi);

fprintf('bw = %.3f*pi, flo = %.3f*pi, fhi = %.3f*pi \n',[bw flo fhi]/pi)
fprintf('power = %.1f%% of total',power/bandpower(d)*100)
bw = 0.217*pi, flo = 0.240*pi, fhi = 0.458*pi
power = 99.0% of totalAdd a second channel with normalized cutoff frequencies
rad/sample and an amplitude that is one-tenth that of the first channel.d = [d;fir1(88,[0.5 0.8])/10]';
Compute the 50% occupied bandwidth of the signal between
rad/sample. Plot the PSD and annotate the occupied bandwidth and measurement interval.obw(d,[],[0.3 0.9]*pi,50);

Output the occupied bandwidth of each channel. Divide by
.bw = obw(d,[],[0.3 0.9]*pi,50)/pi

bw =

0.0705    0.1412```