Processing for compression - The MPEG - page 53

Chapter 3: Processing for compression
Virtually all compression systems rely on some combination of the basic processes outlined in this chapter. In order
to understand compression a good grasp of filtering and transforms is essential along with motion estimation for
video applications. These processes only express the information in the best way for the actual compression stage,
which almost exclusively begins by using requantizing to shorten the word- length. In this chapter the principles of
filters and transforms will be explored, along with motion estimation and requantizing. These principles will be
useful background for the subsequent chapters.
3.1 Introduction
In compression systems it is very important to remember that the valuable commodity is information. For practical
reasons the way information is represented may have to be changed a number of times during its journey. If
accuracy or realism is a goal these changes must be well engineered. In the course of this topic we shall explore
changes between the continuous domain of real sounds and images, the discrete domain of sampled data and the
discrete spatial and temporal frequency domains. A proper understanding of these processes requires familiarity
with the principles of filters and transforms.
Figure 3.1 shows an optical system of finite resolution. If an object containing an infinitely sharp line is presented to
this system, the image will be an intensity function known in optics as a point spread function . Such functions are
almost invariably symmetrical in optics. There is no movement or change here, the phenomenon is purely spatial. A
point spread function is a spatial impulse response. All images passing through the optical system are convolved
with it.
Figure 3.1: In optical systems an infinitely sharp line is reproduced as a point spread function (a) which is the
impulse response of the optical path. Scanning either object or image produces an analog time-variant waveform
(b). The scanned object waveform can be converted to the scanned image waveform with an electrical filter having
an impulse response which is an analog of the point spread function. (c) The object and image may also be
sampled or the object samples can be converted to the image samples by a filter with an analogous discrete
impulse response.
Figure 3.1 (b) shows that the object may be scanned by an analog system to produce a waveform. The image may
also be scanned in this way. These waveforms are now temporal. However, the second waveform may be obtained
in another way, using an analog filter in series with the first scanned waveform which has an equivalent impulse
response. This filter must have linear phase, i.e. its impulse response must be symmetrical.
Figure 3.1 (c) shows that the object may also be sampled in which case all samples but one will have a value of
zero. The image may also be sampled, and owing to the point spread function, there will now be a number of non-
zero sample values. However, the image samples may also be obtained by passing the input sample into a digital
filter having the appropriate impulse response. Note that it is possible to obtain the same result as (c) by passing
the scanned waveform of (b) into an ADC and storing the samples in a memory.
Clearly there are a number of equivalent routes leading to the same result. One consequence is that optical
systems and sampled systems can simulate one another. This gives us considerable freedom to perform
processing in the most advantageous domain which gives the required result. There are many parallels between
analog, digital and optical filters, which this chapter treats as a common subject.
It should be clear from Figure 3.1 why video signal paths need to have linear phase. In general, analog circuitry
and filters tend not to have linear phase because they must be causal which means that the output can only occur
after the input. Figure 3.2 (a) shows a simple RC network and its impulse response. This is the familiar exponential