Re: FFT VS DCT

cincydsp@xxxxxxxxx writes:

On Apr 26, 3:51 pm, glen herrmannsfeldt <g...@xxxxxxxxxxxxxxxx> wrote:
senthil_lsk wrote:
I see that all are asking why DCT is better than FFT or DFT.
Where FFT is prepered than DCT? Why ? Is it only for phase information?

The difference is boundary conditions. FFT (or DFT) has periodic
boundary conditions. DST has f(0)=f(L)=0, DCT has f'(0)=f'(L)=0.
For image processing the DCT boundary conditions are less noticeable.

(There is an explanation in Numerical Recipes, among others.)

-- glen

I've read that the DCT is preferable for data compression applications
because it has good energy-compaction properties; that is, when
applying the DCT to a signal, a higher ratio of the energy is
concentrated in a small number of coefficients relative to the DFT or
other similar transforms. Therefore, it's possible to throw away more
frequency bins at the DCT output, resulting in better compression. I'm
not sure if this is something that is mathematically proven, or if
it's just an empirical observation.

I've heard this as well. The Wikipedia article

http://en.wikipedia.org/wiki/Discrete_cosine_transform

seems to have some relevent information on this aspect.
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Relevant Pages

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