6 5 5 e h 5 g dcx 310 the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: §  ¡ (3.9) ¢ ¡ ¡ where the coefficients must be determined. This formula is analogous to the one use to invert the Fourier transform, however it is important to note that because the discrete nature of the problem we have interchanged the integration symbol by a summation. The parameters are our unknowns. In order to find our unknowns we proceed as follows, first we replace the last equation into equation (3.6), ¢ 5 ¢       5 " © e h 5  g  dcX & % ¨ © ¨ © § ¤ ¡ (3.10) ¢ ¡ ¡ The last equation can be rewritten as     )     5 " ¨ © § © e h 5  g  dcX & % ¨ © ¨ © § ¤   5 ¡ ¢ ¡ ¢ ¡ ¡ ¡ ¡ is given by     " © e h 5  g  dcX & % ¨ © § 5 "  5" ¡ where the sequence (3.11) ¡ (3.12) ¡ At this point we realize the the last equation is a geometric series1 with a sum given by 1 We have used a geometric series to find the inverse of a dipole in Chapter 2 CHAPTER 3. DISCRETE FOURIER TRANSFORM ¤ ¡ ¥ ¦¤ 4 £¢  ©h  &am...
View Full Document

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.

Ask a homework question - tutors are online