dicsrete cosine transform

[shanmugavel]

what is discrete cosine transform..
how is that used in compression. any practical idea on that .
what are its advantages.

 

[vamshi]

DCT is used in compression standards ,
1) it converts time domain to frequency domain
2) by doing DCT the signal energy is concerntrated at DC(most) , Low frequency and high frequency

 

[shanmugavel]

what is the compression rate compared to others transform

 

[vadkudr]

I can not give you exact numbers of compressing effectivity. May be you can find them in books on signal compreesing (some of them are in my electronic library).

You should only keep in mind that
"DCT (namely, DCT of type 2) was was developed as an approximation for the KLT of a first-order Gauss-Markov process with a large positive correlation coefficient"
It is citation from M.Vetterli "Wavelets and subband processing", p.375

Another citation from the same page
"Even if the assumptions do not hold exactly (images are not first-order Gauss-Markov) DCT has proven to be a robust approximation for KLT"

 

[boeysue]

You can find the detailed explaination on the Rao's book.
The discrete cosine Transform

 

[Kevinloo]

In fact, DCT comes from DFT. When we take IDFT, the resulting signal may have some discontinued points. To delete it, we extend the signal as a even-symmetric signal and derive the DCT format

 

[ArjunSC]

what is discrete cosine transform..
how is that used in compression. any practical idea on that .
what are its advantages.

DCT (Discrete cosine transform) takes it's name because of the fact all signals can be interpreted as a sine/cosine wave. MP3 coding mainly uses DCT for compression. DCT is more effective than DFT for compression. FACT: ~85% of data is reduced by using DCT, but the signal will be perceivably of same quality.

Refer Fundamentals of Multmedia - Li & Drew.

 

[sinu_gowde]

DCT:
The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. It is equivalent to a DFT of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sample. (There are eight standard variants, of which four are common.)

The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT"; its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT".

Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data.

For more information checkout these links:
1) http://en.wikipedia.org/wiki/Discrete_cosine_transform
2) **broken link removed**
3) http://www.bretl.com/mpeghtml/DCxfrm.HTM
4) **broken link removed**

 

[saudrehman]

the most useful feature of DCT which makes it attractive for use in Image compression applications is that it takes correalated input data and concentrates its energy in a few transform coefficients i.e. the DC and Low frequency components.

Other components are usually zero or negligibly small and can be neglected or quantized.

and in image compression it is well known fact that adjacent pixels are highly correalated