Digital Signal Processing Reference
In-Depth Information
0,006
Time domain
Zeitbereich
0,005
0,004
0,003
0,002
0,001
0,000
-0,001
-0,002
500
525
550
575
600
625
650
ms
0,00150
Frequency domain
Frequenzbereich
1204 Hz
0,00125
0,00100
0,00075
597 Hz
600 Hz
1617 Hz
1544 Hz
0,00050
1195 Hz
1686 Hz
1953 Hz
338 Hz
1005 Hz
0,00025
0,00000
0
250
500
750
1000
1250
1500
1750
2000
Hz
Illustration 58:
Sound of a wine glass as a quasi-periodic signal
In the time domain it is very difficult to detect periodicity. The signal appears to change constantly. Only
the distance between the maximum values in the right-hand half appears to be practically constant.
On the other hand, the frequency domain displays clear lines. The frequencies were measured on the
screen using the cursor. As you will easily establish, not all lines are integer multiples of a basic frequency.
The signal is therefore not near-periodic. We term this type of signal quasi-periodic. The physical cause of
quasi-periodic signals is the oscillations of a membrane for example. A wine glass is a kind of deformed
membrane. Waves, so-called oscillation modes with certain wave-lengths or frequencies, are formed on the
membrane depending on its size and shape. These frequencies then appear in the spectrum.
An analysis of this kind can be used, for example, in automation technology in the manufacture of glasses
or roof tiles to find defective objects, for instance those with cracks. Their spectrum differs considerably
from that of an intact glass or roof tile.
Tones or sounds must therefore last for a longer period of time in order to be recognised
as such. For this reason tones/sounds are near-periodic or quasi-periodic!
