Books on waves with Fourier Transforms

[Joker93]

There are many waves and oscillations books out there that also include Fourier analysis but very few give the subject a thorough treatment, they just pass it in a few pages. If anybody has any sources(particularly books) that have Fourier analysis and particularly Fourier Transforms, I would appreciate if he could share his information with me.

Waves, Oscillations, Quantum Mechanics or Mathematics books are all ok if they have an intuitive Fourier analysis in them.

 

[Dr. Courtney]

http://arxiv.org/ftp/physics/papers/0605/0605154.pdf

http://arxiv.org/ftp/arxiv/papers/1211/1211.4832.pdf

http://arxiv.org/pdf/1507.01832v1.pdf

More practical than thorough, but you get the idea.

Books take lots of different paths. There are none I really like.

 

[jasonRF]

Adam Landos,

I'm not sure exactly what you are looking for. Have you tried the obvious google searches? For example "fourier transform notes physics" provided many pdf files of notes from physics faculty on Fourier analysis. Perhaps one is useful for you. This subject can be presented with many different viewpoints at many different levels. One book I like (but which is probably not what you want) is:
https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdfDr. Courtney,

Interesting papers. I do have a question: how does your EI method in the third paper compare with simple zero-padding prior to FFT? This would give you the higher sample rate in the frequency domain, effectively using sinc interpolation.

jason

 

[jasonRF]

Adam Landos,

Another idea is to look in typical "math methods for physics" or "advanced engineering mathematics" type books. Your library should have several to chose from. Examples:
https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20
https://www.amazon.com/dp/0471154962/?tag=pfamazon01-20
https://www.amazon.com/dp/0521679710/?tag=pfamazon01-20
I don't know these books well - they may not be great. So look in your library to see what works for you.

jason

 

[Dr. Courtney]

Dr. Courtney,

Interesting papers. I do have a question: how does your EI method in the third paper compare with simple zero-padding prior to FFT? This would give you the higher sample rate in the frequency domain, effectively using sinc interpolation.

jason

In all the cases we've tested, the results are equivalent to within rounding errors related to machine precision. The tradeoffs between zero padding and the EI method are discussed in detail on pp 17-18 of the paper, but we prefer the EI method for several reasons:

1. Taking smaller frequency steps continues to increase accuracy for steps as small as 1/100 th the FFT bin size. Zero padding a 100,000 point data set out to 10 million points does not make sense. If a time series was only sampled for 1 second (or 1 year), padding the data to 100 seconds (or 100 years) may be technically equivalent, but it seems dishonest.

2. It is better not to teach students to add data to a data set that is not actually measured. This is a very rare case in all of data analysis where doing so may be rigorously justified, and students and younger scientists may not appreciate the subtle distinctions between this rare case and scientific dishonesty.

3. If only a small number of peaks are of interest, the EI method can be more effficient, because the whole spectrum need not be computed.

4. The EI method does not require evenly sampled time series.

 

[Joker93]

Thank you all.Your suggestions where very helpful. If anyone else has anything more to suggest, please feel free.

 

[jasonRF]

Dr. Courtney,

Thanks for your reply. My apologies for obviously not carefully reading that part of the paper!

EDIT: the above is more honestly stated: my apologies for not reading that part of the paper!

jason