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discrete cosine transformation (DCT)

The discrete cosine transform (DCT) is a method for converting time-related signals into frequency-related ones. The difference to the Fourier transform is that in the DCT transform the conversion takes place in two dimensions, whereby not all frequencies

are treated equally. Lower frequencies, which represent a slow increase or decrease in brightness

, aretreated differently than higher frequencies, which represent a rapid change in brightness and thus resolution

andcontour. The distinction between lower and higher frequencies is important because it can affect image sharpness.

In termsof procedure, the DCT transform breaks up the frames into 8x8 blocks

.

DCT partial spectra

DCT partial spectra

Each block is considered as a two-dimensional vector of 64 pixel values containing the brightness and color values, where each block also represents a specific frequency range

. The brightness and color blocks are treated separately.

DCT transformation of an 8x8 pixel block into a coefficient matrix in JPEG

DCT transformation of an 8x8 pixel block into a coefficient matrix in JPEG

As can be seen from the DCT basis functions, the first value (topleft ) contains the average value for the brightness of all 64 pixels

of the 8x8 block. The other values in the horizontal represent the brightness changes, starting with small changes and increasing to the shortest changes. So that the second value (2) in the horizontal is a measure of the brightness progression from left to right. The third (3) indicates whether the brightness changes to the center and then back to the edge; thus, the value reflects a bifurcated axis. Thesame criteria are applied vertically, but for the vertical axis of the image.

This data is used to create a coefficient matrix, the data of which is compressed using quantization in JPEG. The DCT transformation itself does not cause any data compression. The disadvantage is that images encoded with DCT no longer correspond to the original signal after decoding.

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Englisch: discrete cosine transformation - DCT
Updated at: 25.10.2012
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