Digital Signal Processing Reference
In-Depth Information
Chapter 6
System analysis
Gradually we are able to reap the fruits of our basic principles (FOURIER, the
Uncertainty and Symmetry Principles).
An important practical problem is measuring the properties of a circuit, component or
system from outside. You will be familiar with test reports which, for instance, compare
the features of different amplifiers. At issue is always the technical behaviour of transmis-
sion (“frequency response”, “distortion factor” etc). Let us first look at the frequency-
dependent behaviour of a system to be tested.
This is easy as long as we do not forget the
UP
: any frequency-dependent behaviour
necessarily triggers a certain time-dependent reaction. The FOURIER Principle says even
more precisely that the time-dependent reaction can be completely deduced from the
frequency-dependent behaviour and vice-versa.
The technical signal test of a circuit, a component or system is generally carried out by
comparing the output signal u
out
with the input signal u
in
. In the first instance it is imma-
terial (see above) whether the comparison of the signals is carried out in the time or
frequency domain.
Note:
It is however, pointless to look at the signal from your TV aerial (roof) on the screen
of a (rapid) oscilloscope. All you can see is a chaotic picture. All the radio and
television transmitters are broadcast in staggered frequencies. For this reason they
can only be represented separately on the screen of a suitable spectrum analyzer
(See Chapter 8: Traditional modulation procedures).
The standard procedure is based on the direct implementation of the FOURIER Principle:
If it is known how a given (linear) system reacts to sinusoidal
signals of different frequencies it is also clear how it reacts to all
other signals …because all other signals are composed of nothing
but sinusoidal signals.
This procedure is widely practised in school laboratories. The necessary equipment is:
• Sine wave generator with adjustable frequency or sweep mode.
• 2-channel oscilloscope
The properties in the time and frequency domain are to be established by comparing u
out
and u
in
. Then both signals should be represented simultaneously on the screen. For this
reason u
in
is connected not only to the input of the circuit but also to channel A of the
oscilloscope. The output signal reaches the screen via channel B.
