Fundamentals - The MPEG - page 37

The non-linearity of the transfer function results in distortion, which produces harmonics. Unfortunately these
harmonics are generated after the anti-aliasing filter, and so any which exceed half the sampling rate will alias.
Figure 2.28 shows how this results in anharmonic distortion in audio. These anharmonics result in spurious tones
known as birdsinging.
Figure 2.28: Quantizing produces distortion after the anti-aliasing filter: thus the distortion products will fold back to
produce anharmonics in the audio hand. Here the fundamental of 15 kHz produces second and third harmonic
distortion at 30 and 45 kHz. This results in aliased products at 40-30 = 10 kHz and 40-45 = (-)5 kHz.
When the sampling rate is a multiple of the input frequency the result is harmonic distortion. Where more than one
frequency is present in the input, intermodulation distortion occurs, which is known as granulation.
As the input signal is further reduced in level, it may remain within one quantizing interval. The output will be silent
because the signal is now the quantizing error. In this condition, low-frequency signals such as airconditioning
rumble can shift the input in and out of a quantizing interval so that the quantizing distortion comes and goes,
resulting in noise modulation.
In video, quantizing error in luminance results in visible contouring on low-key scenes or flat fields. Slowly changing
brightness across the screen is replaced by areas of constant brightness separated by sudden steps. In colour
difference signals, contouring results in an effect known as posterization where subtle variations in colour are
removed and large areas are rendered by the same colour as if they had been painted by numbers.
[ 12 ] Roberts, L.G., Picture coding using pseudo-random noise. IRE Trans. Inform. Theory , IT-8 145-154 (1962)
2.13 Dither
At high signal level, quantizing error is effectively noise. As the level falls, the quantizing error of an ideal quantizer
becomes more strongly correlated with the signal and the result is distortion. If the quantizing error can be
decorrelated from the input in some way, the system can remain linear. Dither performs the job of decorrelation by
making the action of the quantizer unpredictable.
The first documented use of dither was in picture coding. [ 12 ] In this system, the noise added prior to quantizing was
subtracted after reconversion to analog. This is known as subtractive dither. Although subsequent subtraction has
some slight advantages [ 13 ] it suffers from practical drawbacks, since the original noise waveform must accompany
the samples or must be synchronously re-created at the DAC. This is virtually impossible in a system where the
signal may have been edited. Practical systems use non-subtractive dither where the dither signal is added prior to
quantization and no subsequent attempt is made to remove it. The introduction of dither inevitably causes a slight
reduction in the signal-to-noise ratio attainable, but this reduction is a small price to pay for the elimination of non-
linearities. As linearity is an essential requirement for digital audio and video, the use of dither is equally essential.
The ideal (noiseless) quantizer of Figure 2.27 has fixed quantizing intervals and must always produce the same
quantizing error from the same signal. In Figure 2.29 it can be seen that an ideal quantizer can be dithered by
linearly adding a controlled level of noise either to the input signal or to the reference voltage which is used to
derive the quantizing intervals. There are several ways of considering how dither works, all of which are valid.