I u 5 h 3 3 t0 p note that the central frequency

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: rtant saving with respect to the standard DFT which involves a number of . operations proportional to ¥ 4 ¡ X £¢¡4 4 X 4 A small modification to formulas (3.24) and (3.27) will permit us to compute the inverse DFT. 3.1.4 Working with the DFT/FFT Symmetries 4 Let us start with a the DFT of a real time series of length (3.28)  BGEF4D) &   4 5 "" ) 44" 0' § 7 ) © D5  dcX ' %  3 © § ¤ e the frequency in radians is given by B E 4 "" )B) ) 4 3 5 " GFD) 44" #CA' § 7 @C 7 1 § 60 Using the following property (3.29) ©  ' § ©  h ¨© & % &  e IdcX % e 5 dcX 5 g we can re-write equation (3.28) as follows: 1) E)  ©) ¦)B) ¦)  D#B C0) §0¨#IA§0 &1 §      &    ¨© ¤5  " ¥ § © e h 5 ¨ © g  dcX & %  ¨ © § © e h 5 ¨© g  dcX ' %  ¨ © § 5 The following example is used to illustrate the last point. The time series is The DFT is given by (3.30) "    r &0 e #  0 1 #! $" 3UH  U  5 !d Hc¡i(%U d 5 555 55  ¤¤¤5 d 3  5¤¤&5 d   3UH d  ...
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