Digital Signal Processing Reference
In-Depth Information
In this case the
-coded signal has a smaller amplitude than the original signal. In other
words: the probability for measurements around zero rises. Far fewer measurements will
be far away from zero.
Δ
These are favourable conditions for HUFFMAN encoding as described above. If the orig-
inal signal does not change or rise linearly the
-coded signal has a sequence of the same
bit patterns. They occur most frequently. A typical prodedure is therefore after (lossy)
Δ
Δ
-encoding to use the HUFFMAN or RLE encoding as loss-free entropy encoding.
In Illustration 226 the schematic block diagram of the
Δ
-encoder (often also called
Δ
-encoder consists of
a feedback loop. The 1 bit ADC (analog digital converter) has only two states: + and
-modulator), the transmission route and the
Δ
-decoder are shown.
Δ
.
If the difference signal at the input of the 1 bit ADC is greater than zero at the output, for
instance +1, otherwise -1 (corresponding to low and high). In the final analysis the 1 bit
ADC is simply a special comparator.
−
In Illustration 226 the "zero decision line" can be seen around which the difference signal
fluctuates. It can be clearly recognised (see arrows A, B and C) that: as soon as the
difference signal is above the zero line, the
Δ
-coded signal is "high"; otherwise it is low.
What is the - here sinusoidal - input signal compared with? In this connection you should
recapitulate what an integrator does (see Illustration 137 and Illustration 139). If there is
a positive signal segment at the imput of the integrator - here on the right - the integrator
moves upwards, otherwise downwards. This can be clearly seen in Illustration 226 and
Illustration 227. Where the
Δ
-coded signal has the value +1 steps rise; in the case of -1
they lead downwards.
In the centre of Illustration 226 the realisation of the schematic block diagram using
DASY
Lab
is to be seen. The "digital integrator" is a feedback analog adder. In the last
output value +1 is added or -1 subtracted. This produces the step-like curve. In the case
of DASY
Lab
and similar programs a delay is part of all the feedback circuits. This makes
sure that the causal principle is adhered to. The reaction of a process at the output can only
be fed back to the input with a delay (first the cause, then the result). Before the analog
adder two arithmetic modules (creating a multiplicative and additive constant) makes cer-
tain that the curve of the input signal and that of the difference signal are roughly in the
same area. The real 1 bit ADC is the trigger or comparator. The subsequent component
serves the correct signal setting of the
Δ
-encoder.
As the output signal has only two states, a kind of
pulse length modulation
takes place.
The quantisation error which occurs in this connection can be reduced almost at will by
oversampling. The smaller the interval between two sampling values the smaller is also
the difference.
A characteristic of
-encoding is oversampling. The factor n is important
by which the sampling frequency lies above the limit defined by the Sampling Principle.
As nowadays in the case of these
-modulation or
Δ
Δ
-procedures sampling frequencies of 1 MHz and more
are used, n may have a value of around 25. As a result of oversampling the noise is
distributed over a greater frequency range (Illustration 231).
Δ
