I am trying to learn fft, since few problems in CodeChef seem to need it. I am reading CLRS, but it’s a difficult topic and I need more reference. If nothing else, please share your experience on how you learned fft 
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http://e-maxx.ru/algo/fft_multiply
Use google chrome to translate whole of the article at one go to english. The algo is properly described along with codes.
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This is great. Made me understand the concept behind FFT