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13 the fast fourier transform fft r x y a yr

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Unformatted text preview: re (3.1) we have the original time series and the associated DFT (the real and imaginary part). In Figure (3.2) the original time series after zero padding ( zeros) is used to compute the DFT. ' 1 In the following example I show how to pad with zeros a time series. This codes was utilized to generate Figures (3.1) and (3.2). d GF  £¥©£¥b [email protected]"[email protected]¦¨A4 )¨©T(B¨¦9AQ¦¨&$ )0  § S§¥£R E§ ¥£P I GF £CB E§ CB£8 @4¨)4AD))[email protected] 5 cu¢&¨¦¢)i†4¦¨4 v8 E S§¥£R CB… b 6 e CB£ 1 Wr ‡#))@A¦' 20 6„ur ƒ8€ U W&¨¦@‚# y1 # w1 cu eS§¥£R € x 6U v8 E 6 %tsf# 1 # d 6W¦ r r dU 5 g ¦U ¨qW)pihgd H f&S 1 #  e g © e  6 V VU a`0YXUWQ1  65H 7¤91 8 653 1 7&420 £'©$#! © §¥£¡ )(&%" ¤¦¨¨¦¤¢ 41 The FFT is not a new transform; the FFT is just a fast algorithm to compute DFTs. The FFT is based on the halving trick, that is a trick to compute the DFT of length N time series using the DFT of two sub-series of length N/2. Let’s start assuming that we a have :...
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