Fourier Transform of Stochastic Data

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SUMMARY

The discussion focuses on transforming stochastic signals into the frequency domain using the Fourier Transform to create a periodogram. The user, Tei, aims to identify the signal with the most stable frequency by comparing the power of the dominant frequency to the integral of other frequencies with non-zero power. The inquiry also touches on the comparison between the standard Fourier Transform and the Short-Time Fourier Transform (STFT) for analyzing these signals.

PREREQUISITES
  • Understanding of Fourier Transform principles
  • Familiarity with periodograms and their applications
  • Basic knowledge of stochastic processes
  • Mathematical background in signal processing
NEXT STEPS
  • Research the implementation of Fourier Transform in Python using libraries like NumPy and SciPy
  • Explore the concept and application of Short-Time Fourier Transform (STFT)
  • Learn about periodogram estimation techniques and their statistical properties
  • Investigate methods for comparing frequency stability across multiple signals
USEFUL FOR

This discussion is beneficial for data scientists, signal processing engineers, and researchers working with stochastic data who need to analyze frequency characteristics of signals.

teilhardo
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Hi,

I have several sets of stochastic signals that oscillate about the x-axis over time. I would like to transform these signals into the frequency domain (make a periodogram) so that I can which signal has the most stable frequency. I was thinking about using taking the Fourier transform of each data set, finding the frequency with the max power, then comparing the power of this frequency to the integral of all the other frequencies with power greater than zero. With my somewhat limited mathematical background, this is all that I could come up with, maybe somebody might know something less complicated and more developed. How would this compare to a short time Fourier transform?

Thanks,
Tei
 
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