Digitalisation - Signals, Processes, and Systems - page 281

• A television picture and any film conveys the impression of a continuous “analog”
change in the sequence of movement although only 50 individual (half) pictures are
transmitted per second in the case of television.

It is a good idea - as in Chapter 2 - to begin with periodic digital signals. Basic features
of digital signals and sources of error in the computer-based processing of digital signals
will now be explored step by step using suitable experiments.

The period length of digital signals
How can the processor or the computer know whether the signal is in fact periodic or non-
periodic as it only stores the data or measurements of a given “block length”? Can it sense
what the signal was originally like and what it would have been like later? Of course not.
For this reason we will now examine experimentally without a great deal of prior
conjecturing how the computer or DASY Lab copes with this problem.

Note:

• The block length n does not indicate a time but only the number of the intermediate
stored measurements

• Only the inclusion of the sampling frequency f S results in something like the “signal
length”

t. If T S is the period of time between two sampling values, f S = 1/T S
applies. Hence

Δ

“Signal length” Δ t = n < T S = n/f S

For Illustration 190 for instance “signal length” Δ t = n < T S = n/ f S = 32/32 = 1 s

• The block length and sampling rate are set with DASY Lab by the menu item A/D

• The signal length t will always be 1 s if the sampling rate and the block length are

set at the same level in the menu item A/D

Δ

• It is striking that the block length n in the menu item A/D is always to the power of 2

e.g. n = 2 4 , 2 5 , .......2 10 , ........2 13 or n = 16, 32, ……..1024…..8192. There is an
important reason for this. Only than the frequency spectrum can be calculated very
quickly via the FFT algorithm (FFT: Fast FOURIER transformation).

In Illustration 190 both the block length n and the sampling frequency f S are set at 32. A
(periodic) sawtooth of 1 Hz was selected as a signal as we are very familiar with its
spectrum from Chapter 2. At the top the signal is to be seen in the time domain and at the
bottom in the frequency domain. The length of the signal

Δ t is the same as the period

length.