Discrete Cosine Transform

See also: Compression | JPEG | Run Length Encoding | Huffman Encoding

A type of lossy compression.

The Discrete Cosine Transform (DCT) tranforms a signal from the spacial domain to the frequency domain. It is often used in JPEG with a quantization table. DCT is lossy to begin with, and using quantization exacerbates this. The lossiness is due (essentially) to the fact that on a computer, if we start with A, let B = cos(A), then let C = arccos(B), C != A (although it is very close). Quantization exacerbates this by removing the precision of B.

DCT was chosen for JPEG because within the 8×8 pixel size the DCT operates on in JPEG, there is usually very little variation in chroma, so the quantized DCT of the region has a few values near the beginning, then many 0’s (zeros) following. This property lends itself to Run Length Encoding of the DCT values, which compresses the data.

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