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# powerbw() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

bw = powerbw(x) returns the 3-dB (half-power) bandwidth, bw, of the input signal, x. examplebw = powerbw(x,fs) returns the 3-dB bandwidth in terms of the sample rate, fs. examplebw = powerbw(pxx,f) returns the 3-dB bandwidth of the power spectral density (PSD) estimate, pxx. The frequencies, f, correspond to the estimates in pxx. bw = powerbw(sxx,f,rbw) computes the 3-dB 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 = powerbw(___,freqrange,r) specifies the frequency interval over which to compute the reference level, using any of the input arguments from previous syntaxes. freqrange must lie within the target band.If you also specify r, the function computes the difference in frequency between the points where the spectrum drops below the reference level by r dB or reaches an endpoint. example[bw,flo,fhi,power] = powerbw(___) also returns the lower and upper bounds of the power bandwidth and the power within those bounds. powerbw(___) with no output arguments plots the PSD or power spectrum in the current figure window and annotates the bandwidth.

bw = powerbw(x)bw = powerbw(x,fs) examplebw = powerbw(pxx,f) examplebw = powerbw(sxx,f,rbw)bw = powerbw(___,freqrange,r)[bw,flo,fhi,power] = powerbw(___) examplepowerbw(___)

3-dB 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 3-dB bandwidth of the signal and annotate it on a plot of the power spectral density (PSD).powerbw(x,Fs) ans = 4.4386e+04 Generate another chirp. Specify an initial frequency of 200 kHz, a final frequency of 300 kHz, and and 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 3-dB bandwidth of each channel.y = powerbw([x x2],Fs) y = 1.0e+04 * 4.4386 9.2208 Annotate the 3-dB bandwidths of the two channels on a plot of the PSDs.powerbw([x x2],Fs); Add the two channels to form a new signal. Plot the PSD and annotate the 3-dB bandwidth.powerbw(x+x2,Fs) ans = 9.2243e+04 3-dB 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 3-dB bandwidth of the signal and annotate it on a plot of the PSD.[Pxx,f] = periodogram(x,kaiser(nSamp,38),[],Fs); powerbw(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 3-dB bandwidth.[Pyy,f] = periodogram([x x2],kaiser(nSamp,38),[],Fs); y = powerbw(Pyy,f) y = 1.0e+03 * 3.1753 3.3015 Annotate the 3-dB bandwidths of the two channels on a plot of the PSDs.powerbw(Pyy,f); Add the two channels to form a new signal. Estimate the PSD and annotate the 3-dB bandwidth.[Pzz,f] = periodogram(x+x2,kaiser(nSamp,38),[],Fs); powerbw(Pzz,f); 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 rad/sample and rad/sample. d = fir1(88,[0.25 0.45]); Compute the 3-dB occupied bandwidth of the signal. Specify as a reference level the average power in the band between rad/sample and rad/sample. Plot the PSD and annotate the bandwidth.powerbw(d,[],[0.2 0.6]*pi,3); Output the bandwidth, its lower and upper bounds, and the band power. Specifying a sample rate of is equivalent to leaving the rate unset.[bw,flo,fhi,power] = powerbw(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 = 0.200*pi, flo = 0.250*pi, fhi = 0.450*pi power = 96.9% of totalAdd a second channel with normalized cutoff frequencies rad/sample and 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 6-dB bandwidth of the two-channel signal. Specify as a reference level the maximum power level of the spectrum.powerbw(d,[],[],6); Output the 6-dB bandwidth of each channel and the lower and upper bounds.[bw,flo,fhi] = powerbw(d,[],[],6); bds = [bw;flo;fhi]; fprintf('One: bw = %.3f*pi, flo = %.3f*pi, fhi = %.3f*pi \n',bds(:,1)/pi) fprintf('Two: bw = %.3f*pi, flo = %.3f*pi, fhi = %.3f*pi \n',bds(:,2)/pi) One: bw = 0.198*pi, flo = 0.252*pi, fhi = 0.450*pi Two: bw = 0.294*pi, flo = 0.503*pi, fhi = 0.797*pi