Digital Signal Processing Reference
In-Depth Information
Signals are regularly non-periodic signals.
The less their future
development can be predicted, the greater their information val-
ue may be
. Every signal has a "conserving tendency" which is de-
termined by the information-bearing pattern.
Stochastic noise is by contrast completely random, has no "con-
serving tendency" and is therefore not a signal in the true sense.
The future course cannot predicted. This seems to be, however, a
contradiction to the above statement!?
Noisy looking signals, despite their scarcely predictable pattern,
therefore can contain a lot of information, although the conserva-
tion trend is very difficult to detect.
From theoretical point of
view a pure noise is the limit value at which the conservation
tendency is no longer recognizable
.
Note: The discussion of the information content of noise is very difficult to conduct
and the scientific discussion even ventures into philosophical sphere. At the present
level the following questions may arise:
• If the conservation trend is characteristic of an existing information, how can we
decide whether a signal section shows conservation trend or not? Obviously, this
term already includes a degree of "unsharpness" because it is not precisely de-
fined mathematically. And how can we compare conservation tendency in time
and
frequency domain?
• Any information can be represented as a bit pattern. How long or short must it
be, to distinguish between a conservation tendency and pure randomness?
• And further: cryptography is the science of hiding the recognizable conserving
tendency of information, i.e. to pretend that something is purely random! Is there
any additional information?
• What is a noise filter? How is what is random filtered out? In this case, would a
noise filter not be a "conservation trend filter"? Does this also occur in data com-
pression, or is redundancy simply reduced?
The discussion of this issue will appear in this topic at various points over and over again
without, however, achieving definitive clarity. See also the text next to SHANNON's
picture at the beginning of the topic.
Stochastic noise should not be demonized. As it has such extreme properties and embo-
dies pure randomicity, it is of considerable interest. As we shall see, it is of great
importance as a test signal for (linear) systems.
Note: Computer-generated noise is significantly different from ideal, natural noise.
Among other things, the timing of each event is synchronized with the PC clock!
