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Welch Spectrum Estimates

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Create a signal consisting of three noisy sinusoids and a chirp, sampled at 200 kHz for 0.1 second. The frequencies of the sinusoids are 1 kHz, 10 kHz, and 20 kHz. The sinusoids have different amplitudes and noise levels. The noiseless chirp has a frequency that starts at 20 kHz and increases linearly to 30 kHz during the sampling.

Fs = 200e3; 
Fc = [1 10 20]'*1e3; 
Ns = 0.1*Fs;

t = (0:Ns-1)/Fs;
x = [1 1/10 10]*sin(2*pi*Fc*t)+[1/200 1/2000 1/20]*randn(3,Ns);
x = x+chirp(t,20e3,t(end),30e3);

Compute the Welch PSD estimate and the maximum-hold and minimum-hold spectra of the signal. Plot the results.

[pxx,f] = pwelch(x,[],[],[],Fs);
pmax = pwelch(x,[],[],[],Fs,'maxhold');
pmin = pwelch(x,[],[],[],Fs,'minhold');

plot(f/1000,pow2db(pxx))
hold on
plot(f/1000,pow2db([pmax pmin]),':')
hold off
xlabel('Frequency (kHz)')
ylabel('PSD (dB/Hz)')
legend('pwelch','maxhold','minhold')
grid

Figure contains an axes object. The axes object with xlabel Frequency (kHz), ylabel PSD (dB/Hz) contains 3 objects of type line. These objects represent pwelch, maxhold, minhold.

Repeat the procedure, this time computing centered power spectrum estimates.

[pxx,f] = pwelch(x,[],[],[],Fs,'centered','power');
pmax = pwelch(x,[],[],[],Fs,'maxhold','centered','power');
pmin = pwelch(x,[],[],[],Fs,'minhold','centered','power');

plot(f/1000,pow2db(pxx))
hold on
plot(f/1000,pow2db([pmax pmin]),':')
hold off
xlabel('Frequency (kHz)')
ylabel('Power (dB)')
legend('pwelch','maxhold','minhold')
title('Centered Power Spectrum Estimates')
grid

Figure contains an axes object. The axes object with title Centered Power Spectrum Estimates, xlabel Frequency (kHz), ylabel Power (dB) contains 3 objects of type line. These objects represent pwelch, maxhold, minhold.

See Also

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