MATLAB: Power estimation using PWelch

psdpwelch

I have the psd estimate using the Pwelch function in Matlab. I need to convert the PSD values from db/Hz to abosute power to dBm. The understanding that I have is from the PSD value at a particular frequency point do the following.

Power at frequency point=PSD value@ freq point+10*log10(frequency resolution)

Do we also have to add the correction factor for the windowing to get the absolute power?

Best Answer

If you want the power spectrum as simple uints of power as a function of frequency, use the fft function. To convert amplitude to power, square the signal either before or after doing the fft on it. To convert the power values to decibels:

pwr = amplitude.^2;
dBpwr = 10*log10(pwr);

Related Solutions

MATLAB: What is the difference between the functions PSD and PWELCH

We highly recommend that you use PWELCH for Welch's method of estimation rather than PSD. Although PSD was an implementation of Welch's method, PWELCH was added for the following reasons:

The name of the function PWELCH reflects much better the method used to obtain the spectral estimate. PSD is too generic, in fact there are several different algorithms for psd estimation.

Also, PSD does not scale the data by a factor of Fs (sampling frequency). Thus, PSD was actually more of a power spectrum estimate (yielding units of power or db) whereas PWELCH and our other functions return a power spectral density estimate (yielding units of power/freq or db/freq).

The units are of importance because a density (from PWELCH) can be integrated to obtain an estimate of the average power over a given frequency interval. When you integrate you will get units of power not power/freq.

Moreover, PWELCH returns a single sided spectrum by default (for real signals). This means that the total power of the signal is contained in half the spectrum [0 to Fs/2]. In other words, if you integrate the single-sided PSD estimate from [0 to Fs/2], you will get the average power estimate over the entire Nyquist interval. You will get the same result of integrating the double-sided PSD estimate over the interval [-Fs/2 Fs/2].

MATLAB: Amplitude spectrum

There are a couple things you can do. Let x be your speech signal and fs your sampling frequency. The following two are power estimates.

    plot(psd(spectrum.periodogram,x,'Fs',fs));
If you do not want it in dB:
    psdest = psd(spectrum.periodogram,x,'Fs',fs);
    plot(psdest.Frequencies,psdest.Data);
    xlabel('Hz'); grid on;

Finally, just using fft()

      xdft = fft(x);
      % assume x is even length
      xdft = xdft(1:length(x)/2+1);
      freq = 0:fs/length(x):fs/2;
      plot(freq,abs(xdft));
      xlabel('Hz');

Best Answer

Related Solutions

MATLAB: What is the difference between the functions PSD and PWELCH

MATLAB: Amplitude spectrum

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