Digital Signal Processing Reference
In-Depth Information
Chapter 13
Digital Transmission Techniques III: Modulation
Digital signals at the output of an encoder are a sequence of numbers in the form of a bit
stream. In order to be able to transmit such bit patterns via a physical medium (cable or
space) they have to be converted into a modulated, continuous-time signal, which is, in
the final analysis, analog.
Bit patterns as a particular type of signal seem to consist of a random sequence of rectan-
gular impulses. These contain steps in quick succession and therefore their bandwidth is
very large. This is why prior to transmission the bandwidth needs to be restricted by
means of filters. According to the Uncertainty Principle this leads, however, to an exten-
sion in time of each bit-pulse whereby neighbouring bits may overlap (ISI Intersymbol
Interference).
A rectangular pulse always has a Si-like spectrum. This is also shown in Illustration 257.
A "black box" provides an arbitrary sequence of binary pulses. The spectrum has a
Si-shaped curve. The task is, by means of filters, to try and restrict the bandwidth in an
optimal way so that the receiver can still reconstruct the bit pattern.
Note: eye diagrams
The eye diagram in Illustration 257 provides information on the quality of a digital
signal. For this purpose the horizontal deflection of the screen is synchronized with
the clock of the (random) bit pattern. A more detailed, comparative analysis of the
diagrams leads to the following results:
• The curves of the "eyes" are the result of the curves of the pulse transitions.
• The horizontal lines passing through at the top and bottom are a measure of the
existence of rectangular pulses.
• If the openings of the eye diagram disappear the distortion of the bit pattern makes it
almost impossible to reconstruct the original transmission signal in the receiver.
• Eye diagrams make it possible to estimate the quality of ISI and of so- called phase
jitters (irregular phase fluctuations caused by instable oscillators) and overlaid noise.
ISI depends to a great extent on the type of filter used and above all on its edge steepness.
This is shown in Illustration 257 for four different types of filters where the cutoff
frequency of the filter is identical with the so-called NYQUIST-frequency (the minimum
frequency with which a band-limited signal is to be sampled according to the sensing
principle: f
N
= 2
<
f
max
(see Illustration 200). Illustration 257 shows two types of filters
where the eye diagrams are closed on the right hand side. BUTTERWORTH and
CHEBYCHEFF filters have a greater edge steepness than BESSEL filters (with the same
cutoff frequency and "quality"), but they have a pronounced non-linear phase curve. This
means that the sinusoidal oscillations at the output of the filter are in a different phase po-
sition towards each other than at the input of the filter. That is why the pulse form becomes
blurred and neighbouring bits overlap each other. It should hardly be possible to recon-
struct the original bit pattern in the receiver in these two cases.
