Fourier Time Series: Breaking Down Data Into Sines & Cosines

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SUMMARY

The discussion centers on the application of Fourier Series to decompose random time series data into sine and cosine components. It confirms that this decomposition is indeed possible, even for random datasets, resulting in spectral components that are also random. A recommended tool for visualizing this process is the online Fourier series demonstrator available at falstad.com, which allows users to explore the sine and cosine parts of random noise.

PREREQUISITES
  • Understanding of Fourier Series and their mathematical foundations
  • Familiarity with time series data analysis
  • Basic knowledge of signal processing concepts
  • Experience with online simulation tools for data visualization
NEXT STEPS
  • Explore the mathematical principles of Fourier Series decomposition
  • Learn about the limitations of Fourier Series in analyzing non-periodic signals
  • Investigate the use of Python libraries such as NumPy for Fourier transformations
  • Experiment with the Fourier series demonstrator at falstad.com to visualize data breakdown
USEFUL FOR

Data scientists, signal processing engineers, and researchers working with time series data who seek to understand the decomposition of signals into their fundamental frequency components.

islandtrader
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Hi,
I have a question regarding Fourier Series. I have a random set of time series data. Is there anyway to break this down into sines and cosines. From the literature I have read it seems like you can break down a function into sines and cosines but I need to do this for a random set of data or is this even possible(limitations of a Fourier Series). Any help on how to start on this will be greatly appreciated.
 
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Yes you can do it and each spectral component (set of coefficients) will also be random.
 
I found a nice online Fourier series demonstrator

http://www.falstad.com/fourier/"

You can select random noise and display the sine and cosine parts (unfortunately the scale factor is small), or display it in magnitude/phase with a log view.
 
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