What is the big difference in using DCT and DFT?

[naresh850]

Why DCT is used instead of DFt?

What is the big differenc to use DCT then DFT?

Regards?

 

[shakeelsultan]

jpeg dct

well the advatage of DCT over DFT is complexity, the kernal of DFT is having a complex exponential with it which makes the computations comlplex

 

[vadkudr]

dct dft

1. The best compression of signal is achieved by using its eigen-transform (karhunen-Loeve transform). But it depends on signal, so inconvenient to use.
2. Many of signals in real world can be approximated by first order Markov process. So that is good idea to use eigen-transform of first order Markov process. ( By the way it has parameter 'beta', so let choose some value )
3. DCTII is eigentransform of processes which correlation matrix is very similar to first order Markov processes, when 'beta' close to 1.


Vetterli M., Kovacevic J.(1995) Wavelets and Subband Coding(488s).djvu
see page 375

N. Ahmed, T. Natarajan. and K. R Rao. Discrete cosine transform. IEEE Trans. on Computers, 23:88-93. January 1974.

If you want to see method of computing DCT through DFT and vice cersa - see h**p://vadkudr.boom.ru/Algorithms/vadkudr_Algorithms_eng.html#DTT

 

[vacikel]

dft vs dct

when using dft you have to keep complex numbers also you have to perform complex computation however by using dct you all deal with real numbers you perform your computation with real numbers and you keep real coefficients. So, you gain memory locations and your computational cost decrease. ( if your signal is real )

 

[salma ali bakr]

dft and dct

the DC term of the 8-point DCT represents a 1/8 scale of the input sequence and each following AC term adds another 1/8 as well...so the frequency info is concentrated in the first terms...and thus lossy compression can be done with minimal distortion in DCT...by simply discarding the higher frequency components...

also...the number of multiplications needed for DCT is less than DFT...since DCT multiplications are real...

 

[soloktanjung]

relation between dct and dft

Hi,

I think this is a good paper describing DCT and DFT by James Blinn.

Link:

 

[smile2dhamu]

dft dct relation

dct coding

 

[xulfee]

jpeg-dct

dft contains both real and imaginery part of fourior transform,where as dct contains only real part