I am really unaware about wavelet transforms and rather curious to know their relevance and advantage over Fourier and Laplace transform. What edge do the wavelet transforms provide over the well known Fourier or Laplace transforms?
Hello Arghya, you may try with Stéphane Mallat's "A Wavelet Tour of Signal Processing": it is a complete survey about the theory of wavelets and Gabor frames, from an engineering point of view, with detailed mathematical insights.
For a broad range of applications, the good time-frequency concentration of these functions provides a higher readability to the decompositions obtained with the related transforms, if compared to those given by decompositions with complex exponentials.
https://www.ceremade.dauphine.fr/~peyre/wavelet-tour/
Dear Arghya, If you want to know from basics, then the book by Walker "A primer on Wavelets and their Scientific applications" is good. If you are from an electronics background and would like to understand it from a filter bank perspective then the book by Vetterli " Wavelets and subband coding" would be good.On the other hand you would like to learn about wavelet transform from the concepts of bases,frames and wavelet system design then the book by Sidney Burrus et al "Introduction to wavlets and wavelet transforms- A primer" would be good. The book by Nguyen and strang on Wavelets and Filter banks is good from an engineering perspective.
@thank you Sudheer. My background is Applied mathematics, with specialization in Fluid Mechanics that includes mainly Oceanography (Dynamics point of view).
I also recommend the classic book "Ten Lectures on Wavelets" by Ingrid Daubechies.
(perhaps it need more mathematical background, I'm not sure)
Thank you Pablo. I had the opportunity to have a long chat with Daubechies at ICM , 2010 in Hyderabad, India (where she became the president of IMU), I didn't know about this book of her.
For a short introduction see Torrence and Gilbert (1997), "A Practical Guide to Wavelet Analysis". Here is the link: http://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf.
The idea behind wavelet analysis of time series is to find which frequencies where important at any moment in time.
Dear Arghya
A nice online material for you
http://alexandria.tue.nl/repository/books/612762.pdf
with regards
J. Dhar
@Dr. Dhar, thank u..... but the link is not working and showing a 404 error. If you have already downloaded the book , would you please send it to my email id: [email protected]
David F. Walnut: An Introduction to Wavelet Analysis
is also a nice introductory book.
The bible "Ten Lectures" is, overall, rather advanced but always useful as reference book.
There indeed appears to be a glitch when one follows the link of Joydip. Here's another attempt to post this link which worked for me: http://alexandria.tue.nl/repository/books/612762.pdf
- Badges
- Science topic
- Similar topics
- Mathematics
- Applied Mathematics