From sbhatnag@aoc.nrao.edu Wed Feb  9 10:01:59 1994
Xref: pavo.csi.cam.ac.uk comp.dsp:5394 sci.image.processing:6162
Newsgroups: comp.dsp,sci.image.processing
Path: pavo.csi.cam.ac.uk!doc.ic.ac.uk!warwick!zaphod.crihan.fr!jussieu.fr!univ-lyon1.fr!swidir.switch.ch!scsing.switch.ch!xlink.net!howland.reston.ans.net!pipex!uunet!hearst.acc.Virginia.EDU!saips.cv.nrao.edu!saips.nrao.edu!sbhatnag
From: sbhatnag@aoc.nrao.edu (Sanjay Bhatnagar)
Subject: Re: Discrete Cosine Transform
In-Reply-To: siohan@judikael.loria.fr's message of 4 Feb 1994 10:24:48 GMT
Message-ID: <SBHATNAG.94Feb8070848@isleta.aoc.nrao.edu>
Sender: news@news.cv.nrao.edu
Organization: National Radio Astronomy Observatory
References: <2it7pg$bpu@muller.loria.fr>
Date: Tue, 8 Feb 1994 14:08:48 GMT
Lines: 36


Hi there !
	To your question which is as following my answer is ...


By definition, the discrete cosine transform X(k) of a signal x(n) is:

X(k) = \sum_{n=0}^{N} x(n).cos(pi.k.n/N)


In practice, the following form is often used:

X(k) = \sum_{n=0}^{N} x(n).cos(pi.k.(n+0.5)/N)


What are the advantages of this second form ? (using
(n+0.5) instead of n) ?



I think that , as this formula is a addition formula and you have to
calculte all the terms . Why you want to calculte the terms which are
going to vanish any way? See this Cos (pi.k(n+0.5)/N means that  you
are only considering the odd values of a numberline for all n.to
calculate the cosine. (for even values of n , the cos term will have a
odd multiple of pi which is going to vanish. So actually this second
form is just an acknowledgement that cosine is a ODD function by
nature.


Alka Dikshit.






