From: "Ken Davis" <kendavis.nospam@alum.mit.edu>
Path: news.mathworks.com!newsfeed-00.mathworks.com!webcrossing
Newsgroups: comp.soft-sys.matlab
Subject: Re: Dummies guide to DCT
Message-ID: <461D3FB5D24D3F2E648AAD6FC6CFC05A@in.webcrossing.raydaftYaTP>
Date: Thu, 16 Nov 2006 18:46:18 -0500
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"James Turner" <james_turner_81@hotmail.co.uk> wrote in message 
news:ef462d4.2@webcrossing.raydaftYaTP...
> sturlamolden wrote:
>>
>>
>>
>> James Turner wrote:
>>
>>> I was wondering if someone could explain to me the Discrete
>> Cosine
>>> Transform, in as simple as possible English.
>>
>> In the DCT the signal is decomposed into a sum of cosines, as
>> opposed
>> to the Discrete Fourier transform (DFT) where the signal is
>> decomposed
>> into a sum of sines and cosines.
>>
>>
>
>
> Thanks for the respone guys, but I think I need even more reading. I
> am lost at "the signal is decomposed into a sum of cosines". I don't
> understand what a sum of cosines is! Is there not a way of explaining
> DCT assuming that a person ONLY understands what a digital image is
> (i.e. a collection of pixels described using bits)? I'm talking
> simple so a kid could understand it kind of stuff!

I fear you may be in over your head. You really need a little linear algebra 
and maybe a little signal/image processing to understand this stuff.

That said, the short answer is that you decompose your image into a weighted 
sum of "primitive" images. These primitive images are just sinusoidal waves 
of different frequencies in both the x and y directions. When you do a DCT 
you are calculating what the values of the weights are. You can transmit the 
complete set of weights (or a selected subset of them) and reconstruct the 
original image by applying the weights to the appropriate primitive images 
and adding them all together.

When you encode information into an image by perturbing the weights, the 
effect of the perturbation may be very difficult to see in the reconstructed 
image.