BIOL 335 Lecture 18: solFouriercoefs

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20 Oct 2017
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The following identities are useful when working with the fourier fre- quencies p = 2 p/n : (a) for each p = 1, 2, . Xt=1 sin ( pt) = 0. (b) for each p, q = 0, 1, 2, . , n/2, sin ( pt) cos ( qt) = 0. Xt=1 (c) (d) cos ( pt) cos ( qt) = sin ( pt) sin ( qt) = 0 p 6= q p = q 6= 0, n. 2 p 6= q p = q 6= 0, n. , xn } be a sequence of n numbers. Now by the above, for each t = 1, . , n , it must be possible to write xt = Xq=0 (aq cos ( qt) + bq sin ( qt)) (1) for some constants {aq, bq : q = 0, . , n/2} . we aim to nd these constants, starting with the terms {aq} .

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