FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math
A series related to the Hilbert transform
Post new topic   Reply to topic Page 1 of 1 [1 Post] View previous topic :: View next topic
Author Message
larryhammick@telus.net
science forum Guru Wannabe


Joined: 14 Feb 2006
Posts: 217

PostPosted: Fri Jul 21, 2006 3:28 am    Post subject: A series related to the Hilbert transform Reply with quote

This thing is not new, but it struck me as surprising and interesting,
so I thought I'd pass it along.

Define a function f on the integers by
f(n) = 1/(2n-1) if n > 0
f(n) = - f(1-n) if n <= 0.
For any fixed integer m, the family of numbers
f(n)f(n+m)
is absolutely summable, and its sum is zero if m is nonzero.

This result is essentially a special case of the fact that the
"discrete Hilbert transform" (google) preserves orthogonality between
square-summable sequences.
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [1 Post] View previous topic :: View next topic
The time now is Fri Jun 23, 2017 12:07 pm | All times are GMT
Forum index » Science and Technology » Math
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Function from Taylor series? Nathan Urban Research 1 Thu Jul 20, 2006 12:48 am
No new posts Fourier Transform / Decay / Canot set don11154 Math 11 Wed Jul 19, 2006 9:41 pm
No new posts Complex Analysis question, Taylor series James1118 Math 6 Tue Jul 18, 2006 2:17 pm
No new posts inverting a cubic polynomial as a series pluton Math 6 Tue Jul 18, 2006 4:54 am
No new posts why are the polynomials in this series all solvable by ra... Lee Davidson Symbolic 5 Mon Jul 17, 2006 4:34 pm

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0172s ][ Queries: 16 (0.0040s) ][ GZIP on - Debug on ]