Digitalisation - Signals, Processes, and Systems - page 273

The PDM signal represents a rectangular time window whose pulse length depends on the
instantaneous measured value. This signal opens and closes a gate. At the input of the gate
there is a periodic needle pulse sequence with 32 times the frequency of the above
sampling process. Depending on the pulse length more or fewer pulses pass through the
gate and, to be precise, between (minimum) 0 and (maximum) 32. The number of pulses
is always discrete, i.e. 16 or 17 but never 16.23 ... . Now the information on the instanta-
neous measurement is no longer present in analog continuous form but in discrete form.
This is the process of quantization , as explained in Illustration 148 and Illustration 149.
In the present case a maximum of 32 different measurements can be taken and registered.
The pulse groups in the lower series - not shown here- are connected with a binary
counter which gives the number of impulses as a dual number, for example 13 pulses are
equivalent to the dual number 01101. This is the coding process.
Note:
• In practice the “gate” described here is merely an AND circuit which is set at “high”
at the output when (instantaneously) both inputs are at “high“.
• This simulation is a 5 bit A/D converter (2 5 = 32) for 32 different numbers can be
coded using equivalent 5 bit combinations.
• The process of number coding described here is very simple but it is hardly ever used
in practice. In the case of a 16 bit A/D converter as used in audio technology the pulse
frequency would have to be 2 16 = 65536 times as high as the sampling frequency.
• There are two possibilities in the case of the A/D of outputting strings of dual numbers:
• Parallel output : here there is an output for every bit. In the case of a 5
bit combination there would be 5 outputs. Parallel output is usually
internal in chips or systems, for instance between the A/D converter
and the signal processor.
• Serial output : using a shift register the bit combination is connected
with a single channel. As a result the pulse frequency in the above
example is increased to five times the sampling frequency. In transmis-
sion technology serial outputting is used almost exclusively.
• The digital signal is present in serial form on an audio CD, that is the entire music
consists of a sequence of 0 and 1 (“low” and “high”) which seems more or less
random.
Principle of a D/A converter
At the inputs of a D/A converter there is a dual number which is converted internally into
a discrete analog value. The output signal of a D/A converter is thus, to be precise, a step-
like signal. In the case of a 5 bit D/A converter 32 different “steps” would be possible.
The “jump height” at the edges of the steps is always an integer multiple of the minimum
value defined by the quantization process (see in this connection Illustration 148 and
Illustration 149).