Spectral Analysis: alternatives to Fourier Transforms?

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The discussion focuses on seeking alternatives to Fourier transforms for spectral analysis, particularly for those familiar with FFT but looking for less noisy methods. Participants suggest exploring various approaches, including Laplace transforms, wavelet transforms, and Kramers-Kronig transforms. One contributor shares their experience with FTIR spectroscopy, indicating the challenges of finding superior methods. The conversation emphasizes the importance of understanding different spectral analysis techniques. Overall, the thread serves as a resource for learning about diverse computational methods in spectral analysis.
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
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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