Processing for compression - The MPEG - page 99

arranged to be generated at frequencies where it will not be perceived, or on signal values which occur relatively
infrequently.
Shortening the wordlength of a sample from the LSB end reduces the number of quantizing intervals available
without changing the signal amplitude. As Figure 3.70 shows, the quantizing intervals become larger and the
original signal is requantized with the new interval structure. It will be seen that truncation does not meet the above
requirement as it results in signal-dependent offsets because it always rounds in the same direction. Proper
numerical rounding is essential for accuracy. Rounding in two's complement is a little more complex than in pure
binary.
Figure 3.70: Shortening the wordlength of a sample reduces the number of codes which can describe the voltage
of the waveform. This makes the quantizing steps bigger, hence the term requantizing. It can be seen that simple
truncation or omission of low-order bits does not give analogous behaviour. Rounding is necessary to give the
same result as if the larger steps had been used in the original conversion.
If the parameter to be requantized is a transform coefficient the result after decoding is that the frequency which is
reproduced has an incorrect amplitude due to quantizing error. If all the coefficients describing a signal are
requantized to roughly the same degree then the error will be uniformly present at all frequencies and will be noise-
like.
However, if the data are time-domain samples, as in, for example, an audio sub-band coder, the result will be
different. Although the original audio conversion would have been correctly dithered, the linearizing random
element in the low-order bits will be some way below the end of the shortened word. If the word is simply rounded
to the nearest integer the linearizing effect of the original dither will be lost and the result will be quantizing
distortion. As the distortion takes place in a bandlimited system the harmonics generated will alias back within the
band. Where the requantizing process takes place in a sub-band, the distortion products will be confined to that
sub-band as shown in Figure 3.71 .
Figure 3.71: Requantizing a band-limited signal causes harmonics which will always alias back within the band.
In practice, the wordlength of samples should be shortened in such a way that the requantizing error is converted
to noise rather than distortion. One technique which meets this requirement is to use digital dithering prior to
rounding. [ 24 ]
Digital dither is a pseudo-random sequence of numbers. If it is required to simulate the analog dither signal of
Figure 2.28, then it is obvious that the noise must be bipolar so that it can have an average voltage of zero. Two's
complement coding must be used for the dither values.