17 318 4 s s s where is an identity matrix finally

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Unformatted text preview: p; e 5 g  dcX % § (3.13) ¡ if if , therefore ) 7¢§ § © 7 ¢§ © ' 4 ¡  4 §  3 ©  In equation (3.12) we can identify if if B §§ B ¨ § 64 (3.14)  §5 " £¢ ¡ after introducing the final result into equation (3.11) we obtain the following expression for our unknown coefficients 5 ¢ B E 4 "" ) 5 " GFD) 44" A' § 7 ) 5 4 § ¤ (3.15) ¢ our inversion formula becomes:   4  " © e  dcX & % 3 © B §  ¡ (3.16) ¡ ¡ This equation can also be written as follows:  " r s B § u  4 . It is clear that the 4 s 4  s The matrix is the Hermitian transpose of the matrix matrix is an orthogonal matrix, (3.17) (3.18) ) © 4 § s s   s where is an identity matrix. Finally we have a pair of transforms, the DFT and the IDFT (inverse DFT) , given by (3.19)  ) BGEF4D) &    " 4" A' § 7 ) © e  CdcX ' %  ¨ © § 5 ") 5 4 4  © 3.1. THE Z TRANSFORM AND THE DFT 65   4 BE4 ") " GFD) " 4" A' §  © e  IdcX & % ¤ ¨ 5 © B §  5 5  (3.20) The DFT is used to map a discrete signa...
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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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