Power spectral density

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This document discusses power spectral density (PSD), which is a measure of the power of acceleration as a function of frequency, obtained via the Fourier transform of an acceleration time history. It provides the mathematical definitions and equations for calculating PSD from an acceleration Fourier amplitude spectrum, expressing PSD in units of micro G/sqrt(Hz) and decibels, and calculating the root-mean-square of PSD over a given frequency range.

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PSD Spectrum
Acceleration time history
)(tA
Fourier transform of




 dtetAfA ftj 2
)()(
Power Spectral Density



 dffAPSD 2
)(
Code: psd[i] =
Math.sqrt(2.0*accFamp[i]*accFamp[i]*df*0.0001)/9.8*1000000.;//micro G/sqrt(Hz)
In terms of dB
2
2
10
sec/1
))
)(
((log10
mAwhere
df
A
fA
PSD
ref
ref
dB


PSD_rms = Root-Mean-Square(PSD)*sqrt(1.6*(f2-f1)) for frequency range (f1~f2)
PSD_rms = Root-Mean-Square(PSD)*sqrt(f2-f1) for frequency range (f1~f2)

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