s 5 now the dft is a transformation of a points

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Unformatted text preview: VVW `` X & X © feIdcX &' % B VVVV § ```` ¤ e %dcX % UVVV a```Y  p& © ae9cdX ' % efCcdB X % X B . . . . . . " 4" " " 4" " " 4" " . . . . . .  ¨© © ih¨© ih¨© '   & b b e g dcX % g & ``` X VVVW " ``` © e ih ¨© qgIdcX & ' % X ``` VVV ``` © e ih3B© dcX ' % g a```Y  UVVV a```Y 4 . . . § S 5 Now the DFT is a transformation of a points signal into Fourier coefficients . We can also write down our transform in matrix form . . . . . . (3.7) UVVV VVV VVVW The last equation can be written in compact form as follows: (3.8) s qu" t§ r 3.1. THE Z TRANSFORM AND THE DFT 63 It is clear that the DFT can be interpreted as a matrix that maps an -dimensional vector into another -dimensional vector. The remaining problem entails the invertivility of the DFT. We need a transform to come back from the frequency domain to the time . domain, in other words we need   s 3.1.1 Inverse DFT We propose the following inverse    " © e  dcX & % 3...
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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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