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I am a student taking engineering course and wish to learn more about Fourier Transforms. It seems very useful. Would highly appreciate it if anyone could advise me where to start.

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It would be helpful to mention what kind of engineering course you are taking, since there are books for various engineering specialties, e.g. books.google.com/books?id=WoRZyjM6iREC – Baudrillard Nov 21 '10 at 14:12
I am taking electrical engineering course. I didn't specify because I thought Fourier could be applied on various areas. I even saw a book of Fourier Transform for Finance. =O – learnwhatever Nov 21 '10 at 14:36
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Well, that's because of 1. a lot of things in applications can be couched in terms of Fourier transforms, and 2. there exists a speedy algorithm called the "fast Fourier transform" (FFT), and if you have a sleek-looking hammer, you tend to start looking for nails... – J. M. Nov 21 '10 at 14:42

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I first learned Fourier techniques from Bracewell's The Fourier Transform and Its Applications, but I'm digging the non-conventional treatment in Meikle's A New Twist to Fourier Transforms.

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wao..the first book is a long one. Is this the best for beginners? – learnwhatever Nov 21 '10 at 14:17
@learn: Well, there is the assumption that your calculus is solid... and you didn't mention your mathematical background. – J. M. Nov 21 '10 at 14:20
M.: I took calculus module last semester in my uni. that was the first time I learn about line integral, surface integral etc. so I dare not to say I am solid in those... but for basic differentiation and integration I am sure I can handle them. – learnwhatever Nov 21 '10 at 14:32
I suppose that ought to be okay. In any event, if you're unclear about something, that's what teachers and this site are for... – J. M. Nov 21 '10 at 14:36
thanks mate! =) – learnwhatever Nov 21 '10 at 14:39
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For a general engineering perspective, Erwin Kreyszig's book "Advanced Engineering Mathematics" would have some chapters on Fourier and other integral transforms.

For a more mathematical approach, but still with applications in mind, Sneddon's book Fourier Transforms is recommended. It has a lot of physics applications.

The book of Taub and Schilling on Principles of Communication Systems is very good from an electrical engineering point of view. I particularly liked this last book.

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If you have an interest in engineering optics or linear systems, try Gaskill's book. It's good to start from.

David Kammler's book is also a a good introduction. The first part explains the connections between Fourier Series, Fourier Transform, DTFT, DFT very clearly which other books often gloss over.

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This link is really, really good!

Fourier Transform in one day http://www.dspdimension.com/admin/dft-a-pied/

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