The Fourier Transform: A Tutorial Introduction Annotated Edition

I wish I had this little gem when I was in college. Not only does it clearly explain the Fourier transform, deriving it from basic principles, it sets the foundation for understanding texts on signal processing. Having completely forgotten everything from school about Fourier transformations, I put off revisiting the topic for years because I did not like the way it was covered in any of my old college texts. Within 30 pages I was able to decompose a composite signal and about 2/3 of the way through the book (60 pages), transform more complicated signals back and forth between time and frequency domains. Taking the example code apart and putting it back together was very instructive. I especially enjoyed the derivation of the sinc function, which now makes much more sense. By the time I was done with the book I was left with a many questions - most of which I was able to answer myself based on the foundation provided.

I wish I had this little gem of a book in my undergrad physics courses, it summarizes things very well and shows exactly the kind of plots that I wish I had seen to make sense of what the transform does and how it works. The notation might be different than how other authors use it, but that's to be expected when trying to simplify matters. Worth the purchase if you're interested.