Spectral Analysis: alternatives to Fourier Transforms?

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SUMMARY

This discussion focuses on alternatives to Fourier Transforms for computational spectral analysis. Key methods mentioned include Laplace transforms, wavelet transforms, and Kramers-Kronig transforms. The user expresses a desire to explore various approaches beyond the Fast Fourier Transform (FFT), which they find produces excessive noise. Recommendations for further reading emphasize wavelet transforms as a particularly valuable alternative.

PREREQUISITES
  • Understanding of Fast Fourier Transform (FFT)
  • Basic knowledge of spectral analysis concepts
  • Familiarity with Laplace transforms
  • Introduction to wavelet transforms
NEXT STEPS
  • Research wavelet transforms and their applications in spectral analysis
  • Explore Kramers-Kronig transforms and their relevance in signal processing
  • Study the mathematical foundations of Laplace transforms
  • Investigate noise reduction techniques in FFT applications
USEFUL FOR

This discussion is beneficial for computational scientists, signal processing engineers, and anyone interested in advanced methods for spectral analysis beyond traditional Fourier techniques.

wimms
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hi,

Could someone point me to some good material that relates to problems of (computational) spectral analysis? I understand FFT well enough, and although I'm not very good with math I'm willing to chew. What I'm seeking is some alternative approach to Fourier transformation (ie. from time-domain into dynamic frequency domain).

I'm not even sure what exactly I'm after, for now I just want to learn all approaches that have been tried. I don't even know what to google for. FFT gives too much noise..

thanks for pointers.
 
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There's several 'kernels' you can pick. Popular ones are Fourier transforms, laplace transforms and wavelet transforms.

I suggest reading up on the latter
 

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