Note that freq axis is given in radians 1 3 2a in

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Unformatted text preview: owed by zeros, 4E  ¨ ' §¦¥ ) © ' ) ¤ 3© ) ) )  )  & § " " 4" X "  D) " 4" AD0' © The new time series is an -points time series with a DFT given by (3.21)   BE ) &  4 &    5 ") 4" " A' § 7 ) © D5  dcX ' %    © § © D5  dcX ' %  ¨ © § ¤ e e The sampling interval of the frequency axis is now 3 " 1 4 3 §0 1 ¢$¢ In general, the trick of zero padding is used to oversample the frequency axis at the time of plotting the DFT. It is also important to pad with zeros at the time of performing discrete convolution using the DFT. CHAPTER 3. DISCRETE FOURIER TRANSFORM 66 0.4 x 0.2 0 −0.2 0 5 10 15 n 20 25 30 Real[Xk] 1 0.5 0 −0.5 0 1 2 3 0 1 2 3 ω [rad] 4 5 6 7 4 5 6 7 Imag[Xk] 2 1 0 −1 −2 ω [rad] Figure 3.1: A time series and the real and imaginary parts of the DFT. Note that freq. axis is given in radians 1) ¥ 3 2A' ¡ In Figures (3.1) and (3.2) we portray the effect of padding a time series. In Figu...
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This note was uploaded on 11/29/2012 for the course GEOPHYSICS 426 taught by Professor Sacchi during the Winter '12 term at University of Alberta.

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