MATLAB: Calculating energy

energy frequency bands psd power spectral density

Hi,
I would appreciate your help and suggestions. I know this is a silly question for most of the readers, but this has been bugging me for sometime. I generated a PSD of a signal using spectrogram command (matlab signal processing toolbox). I used a 250 ms window. to calculate the energy for a frequency band in a certain time window, can i simply add up the power values of the individual frequencies or should i multiply power values * frequency then add up the results .. or … for example: WINDOW1: (freq 1 Hz power 20) (freq 2Hz power 20) (freq 3 Hz power 15) is the energy of 1-3 Hz band in WINDOW1 is 20 + 20 + 15 or is it 1 X 20 + 2 X 20 + 3 X 15 … Thanks a lot.

Best Answer

In order to obtain energy, do not even worry about the power. Just do this:
Using "*y*" and "*f*" from the output of spectrogram -
N = 250; % window length
Fs = 500; % sample frequency
df = Fs/N; % frequency increment
y_squared = (y/Fs)*conj(y/Fs);  % Fs is used to normalize the FFT amplitudes
energy_10Hz_to_90Hz = 2*sum(y_squared( f>=10 & f<=90,: ))*df;
If at any point the range of frequencies you want to calculate the energy over includes either 0Hz or the Nyquist frequency, then you will not be multiplying those amplitudes by 2. Otherwise the above should work. You need to multiply the sum of squared amplitudes by the frequency increment (df) as I do above because you are essentially performing discrete integration across the interval between 10Hz and 90Hz.
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