Information Technology Reference
In-Depth Information
Figure 5.30:
A one-dimensional inverse transform. See text for details.
Statistically, the further from the top-left corner of the wave table the coefficient is, the smaller will be its magnitude.
Coding gain (the technical term for reduction in the number of bits needed) is achieved by transmitting the low-
valued coefficients with shorter wordlengths. The zero-valued coefficients need not be transmitted at all. Thus it is
not the DCT which compresses the data, it is the subsequent processing. The DCT simply expresses the data in a
form which makes the subsequent processing easier.
Higher compression factors require the coefficient wordlength to be further reduced using requantizing. Coefficients
are divided by some factor which increases the size of the quantizing step. The smaller number of steps which
results permits coding with fewer bits, but of course with an increased quantizing error. The coefficients will be
multiplied by a reciprocal factor in the decoder to return to the correct magnitude.
Inverse transforming a requantized coefficient means that the frequency it represents is reproduced in the output
with the wrong amplitude. The difference between original and reconstructed amplitude is regarded as a noise
added to the wanted data. Figure 5.10 showed that the visibility of such noise is far from uniform. The maximum
sensitivity is found at DC and falls thereafter. As a result the top-left coefficient is often treated as a special case
and left unchanged. It may warrant more error protection than other coefficients.
Transform coding takes advantage of the falling sensitivity to noise. Prior to requantizing, each coefficient is divided
by a different weighting constant as a function of its frequency. Figure 5.31 shows a typical weighting process.
Naturally the decoder must have a corresponding inverse weighting. This weighting process has the effect of
reducing the magnitude of high-frequency coefficients disproportionately. Clearly different weighting will be needed
for colour difference data as colour is perceived differently.
