Discrete cosine transform

A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions.

In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. DCTs are equivalent to DFTs 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 DCT variants, of which four are common.

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The Bottle And The Cross

by: Jaya The Cat

Last night on the 2, ride home. I swear man I saw an angel.
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Temptation, redemption, the Bottle and the Cross.
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And somewhere out there,
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Temptation, redemption, the Bottle and the Cross.
Life's illusion, from everything you've done.
And somewhere out there over the airwaves,
I hear a SCREAM!
And when the music takes control, it's allright by me.
Ooh another moon rise competing with the lights of the bright city.
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