The Engineer's Guide to Standards Conversion - Snell

2.6 Quantizing error
It is possible to draw a transfer function for such an ideal quantizer followed by
an ideal DAC, and this is shown in Fig 2.6.1. A transfer function is simply a graph
of the output with respect to the input. In circuit theory, when the term linearity is
used, this generally means the overall straightness of the transfer function. Linearity
is a goal in video, yet it will be seen that an ideal quantizer is anything but linear.
The transfer function is somewhat like a staircase, and blanking level is half way up
a quantizing interval, or on the centre of a tread. This is the so-called mid-tread
quantizer which is universally used in digital video and audio.
Output
Input
Quantisng
error
Fig 2.6.1
Transfer function of an ideal ADC followed by an ideal DAC is a
staircase as shown here. Quantizing error is a saw tooth-like
function of input voltage.
Quantizing causes a voltage error in the video sample which is given by the
difference between the actual staircase transfer function and the ideal straight line.
This is shown in Fig 2.6.1 to be a saw-tooth like function which is periodic in Q.
The amplitude cannot exceed +/-1/2Q peak-to-peak unless the input is so large that
clipping occurs. Quantizing error can also be studied in the time domain where it is
better to avoid complicating matters with any aperture effect. For this reason it is
assumed here that output samples are of negligible duration. Then impulses from
the DAC can be compared with the original analogue waveform and the difference
will be impulses representing the quantizing error waveform. This has been done in
Fig 2.6.2.
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