I want to self-study Fourier Transforms followed by signal analysis and Wavelets.

Question

I want to self-study Fourier Transforms followed by signal analysis and Wavelets.

I am considering buying the books: "Fourier Analysis: An Introduction" and "A First Course in Fourier Analysis".

My question is, are these at my level or are they over my head? Are these books good choices or are there other subjects that I need to study first?

The titles of the books sound perfect, but glancing at the table of contents and the first few pages (on Amazon preview), these books look pretty advanced.

I currently am very comfortable with a standard 2-3 semester sequence of calculus, one semester of differential equations, linear algebra (including eigenvalues/vectors, vector spaces, basic fourier series, etc). I know all those subjects fairly well and am more than willling to review any areas that I am weak in.

Thanks in advance for any advice!

Answer 1

I am not familiar with the two books you mentioned, as I learned Fourier analyis over 50 years ago. Judging by the knowledge of calculus, you should have no problem with the subject. The titles of the books indicate that they probably will provide a good introduction.

Usually Amazon provides reader reviews of books; sometimes they are written by people who are not impartial, but it's worth checking anyway.

Answer 2

This link should take you to six Amazon reviews of the first book. http://www.amazon.com/Fourier-Analysis-Introduction-Princeton-Lectures/product-reviews/069111384X/ref=dp_top_cm_cr_acr_txt?ie=UTF8&showViewpoints=1

Answer 3

Thanks so much for the response.

I ordered the books. I bought two books in case one isn't a good fit.

My main concern was that there is some other theoretical prerequisites that I'm not aware of that I should be studying before diving into Fourier analysis.

Thanks!

Answer 4

Based on your description of your current background, it seems like you have a solid foundation in the necessary mathematical subjects to understand Fourier Transforms and signal analysis. However, to determine if the books you mentioned are suitable for you, a closer look at their contents is necessary.

If you found the table of contents and the initial pages of these books to be challenging, chances are they might be more advanced than what you are looking for as a starting point. It's important to select resources that are appropriate for your current level of understanding to build a strong foundation.

Here are a few suggestions to help you get started with self-studying Fourier Transforms and signal analysis:

1. "Introduction to Fourier Analysis and Wavelets" by Mark A. Pinsky: This book is aimed at undergraduate students. It covers the basics of Fourier analysis and introduces wavelets, making it a good starting point for your journey.

2. "A Friendly Introduction to Fourier Analysis" by Gerald Folland: This book presents Fourier analysis in an accessible and friendly manner. It assumes familiarity with basic calculus and provides a solid introduction to Fourier Transforms.

3. "Signals and Systems" by Alan V. Oppenheim and Alan S. Willsky: Although not exclusively focused on Fourier Transforms, this widely-used textbook covers the fundamentals of signals and systems. It includes a solid introduction to Fourier analysis and its applications.

Before diving into these books, it's recommended to review your knowledge of basic calculus, especially complex numbers, integration techniques, and ordinary differential equations. Having a strong understanding of these topics will greatly aid your study of Fourier Transforms.

Remember, it is always advisable to start with resources that match your current level of understanding and gradually progress to more advanced material as you become comfortable with the concepts. Happy studying!