Spectral Analysis: alternatives to Fourier Transforms?

In summary, the conversation discusses the topic of computational spectral analysis and the speaker's request for good material on the subject. They mention being familiar with FFT but wanting to learn alternative approaches, and ask for pointers on where to start. Another person suggests reading up on wavelet transforms and Kramers-Kronig transforms, and shares their experience with FTIR spectroscopy.
  • #1
wimms
496
0
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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  • #2
There's several 'kernels' you can pick. Popular ones are Fourier transforms, laplace transforms and wavelet transforms.

I suggest reading up on the latter
 
  • #3
There's also Kramers-Kronig transforms.

http://www.galactic.com/Algorithms/kk_trans.htm

I did a couple years of FTIR spectroscopy, millimeter waves really, not IR. It is hard to beat.

Njorl
 

1. What is spectral analysis and why do we use it?

Spectral analysis is a mathematical tool that is used to analyze and extract information from signals and data in the frequency domain. It is used in a variety of scientific fields, such as physics, engineering, and astronomy, to study and understand complex systems and phenomena.

2. What are the alternatives to Fourier transforms in spectral analysis?

Some of the alternatives to Fourier transforms in spectral analysis include wavelet transforms, Hilbert transforms, and empirical mode decomposition. These methods offer different advantages and are used in specific applications depending on the type of data being analyzed.

3. When should I use a different method instead of a Fourier transform?

Fourier transforms are best suited for analyzing stationary signals with a well-defined frequency spectrum. If the signal is non-stationary or contains transient components, other methods such as wavelet transforms or empirical mode decomposition may be more suitable.

4. What are the benefits of using alternative methods in spectral analysis?

Alternative methods can offer better time-frequency resolution and can handle non-stationary signals more effectively. They may also be able to capture nonlinear relationships between variables and provide a more detailed analysis of signal components.

5. Are there any limitations to using alternative methods in spectral analysis?

Like any mathematical tool, alternative methods in spectral analysis have their own limitations. Some methods may not be suitable for certain types of data or may require more computational resources. It is important to understand the strengths and weaknesses of each method and choose the most appropriate one for the specific application.

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