# Area of a Spectrum

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Lisa Justin on 1 Aug 2012
What matlab command can give me the area of a spectrum. I have shock response spectrum but i need to find the area under the curve.

Dr. Seis on 1 Aug 2012
The area under your curve should just be:
N = numel(x);
dt = 1/fs;
df = fs/N;
y = fft(x)*dt;
area_y = sum(abs(y))*df; % which is also equal to: sum(abs(fft(x)))/N
energy_y = sum(abs(y).^2)*df;
If you really want "energy", then energy_y should be equal to energy_x:
energy_x = sum(x.^2)*dt;
Lisa Justin on 2 Aug 2012
Thanks.

Wayne King on 1 Aug 2012
Hi Lisa, If you have the Signal Processing Toolbox, you can use the avgpower() method of a spectrum object.
For example:
Fs = 1000;
t = 0:1/Fs:1-(1/Fs);
x = cos(2*pi*50*t)+sin(2*pi*100*t)+randn(size(t));
psdest = psd(spectrum.periodogram,x,'Fs',Fs,'NFFT',length(x));
avgpower(psdest,[25 75])
The final line above integrates under the PSD from 25 to 75 Hz.
Note you can get the fraction of the total power in the specified interval with:
avgpower(psdest,[25 75])/avgpower(psdest)
Lisa Justin on 1 Aug 2012
Thanks Wayne. But it is like this: I calculated the shock response spectrum Y and plotted between frequencies 10-500. I need the peaks and the area under the curve max(Y) gives me the peak and i tried area(Y) and i get a shaded plot again but what i really want is the value of the area of Y.