Calculate area under power spectrum for certain frequency range

Question

Below I present my code how I calculate power spectrum for my signal:

Fs=100;
n = length(x) (in my example always n=160);

whann = window(@hann,n).';
x = whann.*x';

xdft = fft(x);
xdft = (2/length(x))*xdft(1:length(x)/2+1);
xdft = abs(xdft);
xdft=xdft.^2;
freq = 0:Fs/length(x):Fs/2;

Now, I would like to calculate area under power spectrum but only for frequency range 4-6 Hz. The 32 first elements of vector freq look like this:

freq = [0,00    0,28    0,56    0,83    1,11    1,39    1,67    1,94    2,22    2,50    2,78    3,06    3,33    3,61    3,89    4,17    4,44    4,72    5,00    5,28    5,56    5,83    6,11    6,39    6,67    6,94    7,22    7,50    7,78    8,06    8,33]

So, I can find only area between 4,17 Hz- 6,11 Hz.

Could you advice me, how to calculate area under spectrum for specific frequency range (as I mentioned above for example 4-6 Hz)?

Thanks in advance for any help

Answer 1

I would proceed as follows:

idx = find(freq>=4 & freq<=6);

trapz(freq(idx),spectrum(idx))

If I understood your question right, what stated above should lead you to the results you wanna estimate.

EDIT

Since you don't have spectrum values for freq=4Hz and freq=6Hz, I would suggest to interpolate values like this:

int_spec = exp(interp1(log(freq),log(spec),log(4:.1:6),'linear','extrap'))

and then call

trapz(4:.1:6,int_spec)