Figure 3 - from "jpeg"

Figure 2. DCT-Based Decoder Processing Steps

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The DCT is related to the Discrete Fourier Transform (DFT). Some simple intuition for DCT-based compression can be obtained by viewing the FDCT as a harmonic analyzer and the IDCT as a harmonic synthesizer. Each 8x8 block of source image samples is effectively a 64-point discrete signal which is a function of the two spatial dimensions x and y. The FDCT takes such a signal as its input and decomposes it into 64 orthogonal basis signals. Each contains one of the 64 unique two-dimensional (2D) “spatial frequencies’’ which comprise the input signal's “spectrum.” The ouput of the FDCT is the set of 64 basis-signal amplitudes or “DCT coefficients” whose values are uniquely determined by the particular 64-point input signal. At the input to the encoder, source image samples are grouped into 8x8 blocks, shifted from unsigned integers oe Nap [0, 2 - 1] to signed integers with range -1], and cB to the Forward DCT (FDCT). At the output from the decoder, the Inverse DCT (IDCT) outputs 8x8 sample blocks to form the reconstructed image. The following equations are the idealized mathematical definitions of the 8x8 FDCT and 8x8 IDCT:

Figure 1. DCT-Based Encoder Processing Steps

$Figure 3. Preparation of Quantized Coefficients for Entropy Coding After quantization, the DC coefficient is treated separately from the 63 AC coefficients. The DC coefficient is a measure of the average value of the 64 image samples. Because there is usually strong correlation between the DC coefficients of adjacent 8x8 blocks, the quantized DC coefficient is encoded as the difference from the DC term of the previous block in the encoding order (defined in the following), as shown in Figure 3. This special treatment is worthwhile, as DC coefficients frequently contain a significant fraction of the total image energy.$

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