
106 Image Processing for Cinema
[0, 255] to [−127, 128]. This operation reduces the dynamic range in the sub-
sequent processing.
4.3.1 Discrete cosine transform
Next, the DCT (Discrete Cosine Transform) is applied to the block. The
DCT is, like the discrete Fourier transform, a linear transform that expresses
a signal as a linear combination of basis functions.
FIGURE 4.2: JPEG’s DCT basis functions. Figure from [16].
A very basic property of all linear transforms is that both the signal and
its transform have the same number of samples. For example, the DCT of an
8 × 8 block will consist of 64 transform coefficients, each being the sum of
the pixel-by-pixel ...