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discrete cosine transformation (encoding) (DCT)

The discrete cosine transform(DCT) is a method for converting time-related signals into frequency-related ones. The difference with the Fourier transform is that in the DCT transform, the conversion is in two dimensions, and not all frequencies are treated equally.

Lower frequencies, which represent a slow increase or decrease inbrightness, are treated differently than higher frequencies, which represent a rapid change in brightness and thus resolution and contour. The distinction between lower and higher frequencies is important because it can affect image sharpness.

In terms of the procedure, the DCT transformation splits the individual images into 8x8 blocks.

DCT partial spectra

DCT partial spectra

Each block is considered as a two-dimensional vector with 64 pixel values containing the brightness and color values, where each block also represents a certain 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 (top left) 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 up to the center and then back to the edge; the value thus reflects a bifurcated axis. In the vertical, the same criteria are applied, but for the vertical axis of the image.

From this data, a coefficient matrix is created, the data of which is compressed in JPEG by means of quantization. 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.

Informations:
Englisch: discrete cosine transformation (encoding) - DCT
Updated at: 25.10.2012
#Words: 301
Links: digital cordless telephony (mobile communications) (DCT), method, frequency (f), conversion, brightness
Translations: DE
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