Unformatted text preview: ve the second half of the samples of the DFT of , 4 £ £ 4
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egX ¨ g dcX % £ ¨© X § 4E7 §
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gX De5 dcX % £ ¨© X § 5 (3.25) In the last equation we apply the following substitution: and we end up with the following for £ After rewriting the last expression in terms of
mula: (3.26) (3.27) B E 4)
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" GFDA' § ) T© gX DIdcX ' % E § ¨ e5 as a function
Now we have two expression to compute the DFT of a series of length
of two time series of length . Good FFT algorithms repeat this trick until the ﬁnal
time series are series of length . The recursions given in (3.24) and (3.27) are applied 41 B 4 3.1. THE Z TRANSFORM AND THE DFT 69 to recover the DFT of the original time series. It can be proved that the total number of
operations of the FFT is proportional to
(for a time series of length ). This
is an impo...
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 Winter '12
 Sacchi
 Digital Signal Processing, DFT

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