Python Power Spectral Density


The scripts on this page require the utility modules

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PSD of a Time History

The PSD of a time history may be calculated using

The script uses the FFT function.

from scipy.fftpack import fft

It includes options for retangular and Hanning windows.

A GUI version which uses Tkinter is given at:

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Spectrogram PSD

A script for a spectrogram PSD of a time history is given at:

The script uses the Matplotlib function specgram.

This function is useful for tracking the frequency change with time.

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Overall GRMS Level

The overall GRMS level for a PSD function can be calculated via:

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Synthesize a Time History to Satisfy a Specified PSD

A sample time history can be synthesized via:

This script also requires:

Note that a given PSD does not have a unique time history, because it discards the phase angle.

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SDOF Response

This script calculates the response of a single-degree-of-freedom system to an acceleration PSD base input:

The method is more accurate than Miles equation, because it performs a point-by-point multiplication of the power transmissibility function times the base input PSD. It thus allows the PSD to vary with frequency.

This script calculates the vibration response spectrum (VRS) for a PSD base input:

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– Tom Irvine

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