Re: Query DCT and DFT

MJ wrote:
Hi
This is true that in DCT,it real value exponetioal function and in DFT
, it is complex value exponentioal function. 

I don't understand this sentence, it's garbled.

But how DCT is more
useful in compression


DCT is better for lossy compression. To see that, you need to recall that both DCT and DFT stem from fourier series that analyze functions mapping from R ->R and are periodic. The input of DCT and DFT, however, is finite sequence of samples. So to compute the fourier series, it is necessary to continue the function onto R by assuming what the values outside the given range are. For DFT, the assumption is thath the finite sequence repeats. For DCT, the sequence is mirrored and then repeated. So if you have an input signal like this:

^
|   .
|  .
| .
|.
-------------->

this is the assumption of DFT:

^
|   .   .   .
|  .   .   .
| .   .   .
|.   .   .
-------------->


whereas DCT assumes

^
|   .     .
|  . .   . .
| .   . .   .
|.     .     .
-------------->


If you are a bit familiar with fourier series, you know, that the dsicontinuity at DFT's assumption is evil and leads to very bad convergence of the series. However, quantizing means suppressing small coefficents. It's clear, that this will distort the signal more in the case with discontinuities.

So DCT is more robust against quantization because it avoids the discontinuites at the edges. You can look at this also from the viewpoint of phase shifts: In DCT all cosine waves have always the same phase, whereas, if you treat DFT's coefficients individually, it may change the phase which has a strong impact.

	Christian
.

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