Calculate GRMS from a narrow band PSD curve

H I have PSD values extracted from a narrowband PSD curve, PSD (amplitudes) & Freqeuncy values stored as a array values, generated using plwech function. PSD are G^2/Hz), The whole profile for 20 seconds run would look like below got over 60,000 PSD values. i have a set of data selected from it below.

PSD = [ 0.000250 0.000250 0.000249 0.000248 0.000247 0.000246 0.000245 0.000244 0.000242 0.000241 0.00023];

Freq = [ 0.949 0.999 1.049 1.099 1.149 1.199 1.249 1.299 1.349 1.399 1.449];

How can i calculate GRMS ?

Answer 1

[Dheeraj]

Hi Sud Mudiyanselage,

To calculate from the given Power Spectral Density data, please follow the below steps

1. Calculate Frequency resolution between each frequency bin. Since the bins have non-uniform spacing calculate average frequency resolution.
2. Use the formula, to calculate . where ​ is the power spectral density at the i-th frequency bin and is the frequency resolution.

Here is an example to do the same:

deltaF = mean(diff(Freq)); %mean frequency resolution
G_RMS = sqrt(sum(PSD * deltaF));

Thank you.

[Sud Mudiyanselage]

Thank you heaps Dheeraj.

why do you say, the bins have non-uniform spacing ?