Text on Discrete Fourier Analysis & FFT

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Several users are seeking recommendations for texts on Discrete Fourier Analysis and the Fast Fourier Transform (FFT). Audrey Terras's "Fourier Analysis on Abelian Groups and Applications" is suggested as a valuable resource. Participants are uncertain about the appropriate forum for this topic, debating between Homework Help and General Math sections. The discussion highlights the need for quality educational materials in this area of mathematics. Overall, the search for comprehensive texts on FFT and Discrete Fourier Analysis continues.
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Does anyone know of any good texts that cover Discrete Fourier Analysis and the Fast Fourier Transform?

*I don't know if this belongs here in the HW help or in General Math section.
 
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AUdrey Terras, Fourier Analysis on abelian groups and applications from the LMS.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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