Asked by 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.

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Answer by Elige Grant
on 1 Aug 2012

Accepted answer

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;

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Elige Grant
on 1 Aug 2012

Yeah... in your case, you would just need:

area_y = sum(abs(y))/N;

The frequency increment ( **df** ) comes into play only if you scaled your FFT amplitudes ( **y** ) by the time increment ( **dt** ) - since **dt*df** = 1/ **N**. If you do not scale your FFT amplitudes inside your **srs** function, then you should just divide your sum by **N** to get the area. If you want to find the area between a frequency range, you will have to do something a little different. See below:

Example:

N = 4096; fs = 2000; x = randn(1,N);

df = fs/N; Nyq = fs/2; y = fft(x); f = ifftshift(-Nyq : df : Nyq-df);

If your **y** represents both the negative and positive frequency amplitudes:

area_y_10_800 = sum(abs(y( abs(f) >= 10 & abs(f) <= 800 )))/N;

or if your **y** represents only the positive frequencies

area_y_10_800 = 2*sum(abs(y( f >= 10 & f <= 800 )))/N;

However, you do not want to double the amount if you are including either your 0 frequency or Nyquist frequency amplitude in the frequency range.

Answer by 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

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