Accurately calculate the spectrum energy (scaling, window and other concerns)

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Bach 2012-7-26

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https://ww2.mathworks.cn/matlabcentral/answers/44628-accurately-calculate-the-spectrum-energy-scaling-window-and-other-concerns

Hi,

I am studying on how to calculate the energy within a frequency band. I tried to use the psd function as well as the fft function. The code is as follows.

h = spectrum.periodogram('Hann');
Hpsd = psd(h,xframe,'NFFT',2^13,'Spectrumtype','Twosided','Fs',Fs);

and

frame_fft = abs(fft(xframe.*hann(length(xframe)),2^13));
frame_psd = frame_fft.^2/Fs/length(xframe);

I found that the Hann window used in each function has a different gain, which leads to the different results.

So my question is how to get a PSD with accurate values (w/wo window function)? In addition, could anybody please explain why we need to divide the Fs and frame length to normalize the scale? I tried to look into the psd function but couldn't understand the 'KMU' variable which is the 'Normalizing scale factor'.

Any help will be appreciated, Bach