Digital Signal Processing Reference
In-Depth Information
1,00
1
0,75
2
0,50
0,25
0
0,00
-0,25
-0,50
-0,75
4
-1,00
0 0100
200
300
400
500
600
700
800
900
ms
Illustration 24:
Geometric model for the way in which a sinusoidal signal arises
Let a pointer rotate uniformly in anti-clockwise direction, beginning in the diagram at 0. When for
example the numbers express time values in ms the pointer is in position 1 after 70 ms, after 550ms in
position 4 etc. The period length (of 0 to 6.28) is T = 666ms, i.e. the pointer turns 1.5 times per second.
Only the projection of the pointer on to the vertical axis can be measured physically. The visible/
measurable sine course results from the pointer projections at any given moment. It should be noted that
the (periodic) sinusoidal signal existed before 0 and continues to exist after 1000 ms as it lasts for an
infinite length of time in theory! Only a tiny time segment can be represented, here slightly more than the
period length T.
There is a single form of AC voltage which only has one audible tone: the sinusoidal
signal! In these experiments it is only a question of time before we begin to feel
suspicious. Thus in the "sawtooth" of 100Hz there is an audible sine of 200Hz, 300Hz etc.
This means that if we could not see that a periodic sawtooth signal had been made audible
our ear would make us think that we were simultaneously hearing a sinusoidal signal of
100 Hz, 200Hz, 300Hz etc.
Preliminary conclusions:
(1) There is only one single oscillation which contains only one tone: the (periodic)
sinusoidal signal
(2) All the other (periodic) signals or oscillations - for instance tones and vowels contain
several tones.
(3) Our ear tells us
•
one tone = one sinusoidal signal
•
this means: several tones = several sinusoidal signals
•
All periodic signals/oscillations apart from the sine contain several
tones
