My laptop crashed 10 days back and I had to make do with out one till the new one arrives. After a looooong time, staying completely away from system allowed me some time to think on some aspects which I had not focused on . Managed to read some terrific books on Fourier series in the last 10 days. Fourier series is something that I learnt in undergrad and conveniently forgot it as I never came across a practical application(may be bhag daud ki zindagi mein, never took time to understand i guess), until I came across Vol Modeling.

There is a vast amount of literature where FFT (Fast Fourier transformation) is used for option valuation and the math is beautiful . A combination of sines and cosines can do wonders. For those who would want to get down to basics and see what a fourier transform looks like, where one can use it and how is it related to math finance, here is a list of books that I recommend(purely from my own experience after making false starts on a set of literature) :

whoisfourier

This book is a gem . It is like HeadFirst Series for Fourier. If you have not read any of HeadFirst Series books, then you are missing something !. Ironically HeadFirst Books were first suggested to me by a High school teacher who was kicked about the way things are communicated.Head First books are books on Technology and the way High Schoole teacher applied Head First principles for her curriculum is amazing, when I first heard about it.

FFP

Title is misleading. This book is more than a pedestrian introduction to Fourier. I guess some knowledge of fourier would be good before you embark on this book

introappmath

One should read the chapter on fourier from this book to enjoy the great way the author talks about Fourier. Gilbert Strang is very popular for his ways of teaching as he makes any subject intuitive and easily understandable. This book has to be read after you think that you know pretty well some stuff on Fourier. What this book will tell you is that, your knowledge is no good for real life apps. It proceeds to show where one can exactly use it

After reading the above 3 books ,you would be in a better shape to code/program/understand FFTs use in Option valuation. Once you take an effort in understanding the basics, rest of math and application is BEAUTIFUL.