22 we can rewrite the last equation in terms of two

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Unformatted text preview: a time series of length 3.1.3 The Fast Fourier Transform (FFT) r © &$" x ¦ %&Y£ A¦' Yr © „ ¦@¥ x ¦£(i¤e '¨A¦' # W¤ e ¦ Xƒ…fA@uS „#!  $ ©e ' P 6   $§ © £P 6 rr  $ € e $£B 6 3U e B§'© Wr i3 a%¤(&P I S r © &#$" x '¤¨eY£ A¦' 6Yr © „ ¦@¥ x ¦(i§¤e ¨PA¦' # Wr¤ Y¤@ƒ¥ƒ…fA@uS „ ! £ © ' P  £$ © '£  6 r e'£ € e $£B 6 rHU e B§'© W¨u3 a%¤(&P I S 6 © © '£  6 © e P ' 6 € e B§' Wr ‡#eY¨P ¦' Wr `©Y'£ A¦¨# Wr ƒ#fqaA¤(© 6 UU e B§'© Wr¦¤3 a%¤(&P I S SB S£ B§'b (A' I @¥2%¤(4 6 sg© H 0 (i)pig 91 … d (¦¥¢c¤(¦ d¨&E ¨¤B ¨B I &$i¨¢ S   S # §£¥ £C £ © §¡ 6Wr ‡#)¤E 2 F¥£ £ £ ©$§ )¦¤¨C¤B ¨B I &i¨¡¢ e BE 1 6 A£  6 V VU a`0YXUWQ1  0¢ Figure 3.2: A time series and the real and imaginary parts of the DFT. In this case the time series was padded with zeros in order to decrease the frequency interval . −2 0 1 2 3 0 1 2 3 ω [rad] 4 5 6 7 4 5 6 7 −1 Imag[Xk] 0 1 2 −1 ω [rad] −0.5 Real...
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