Digital Signal Processing Reference
In-Depth Information
Illustration 26:
FOURIER synthesis of the sawtooth oscillation
It is worth looking very carefully at this picture. It shows all the cumulative curves beginning with a
sinusoidal oscillation (N = 1) and ending with N = 8. Eight appropriate sinusoidal oscillations can
"model" the sawtooth oscillation much more accurately than for example three (N = 3.) Please note - the
deviation from the ideal sawtooth signal is apparently greatest where this oscillation changes most rapidly.
First find the cumulative curve for N = 6
If it is known how a given system reacts to sinusoidal signals of
different frequencies it is also clear how it reacts to all other
signals because all other signals are made up of nothing but
sinusoidal oscillations.
Suddenly the entire field of communications engineering seems easier to understand
because it is enough to to look more closely at the reaction of communications enginee-
ring processes and systems to sinusoidal signals of different frequencies.
It is therefore important for us to know everything about sinusoidal signals. As can be seen
from Illustration 24 the value of the frequency f results from the angular velocity
ω
/ t of the rotating pointer. If the value of the full angle (equivalent to 360°) is given
in rad,
=
ϕ
ω
= 2
π
/ T or
ω
= 2
π
f applies.
In total a sinusdoidal signal has three properties. The most important property is quite
definitely the frequency. It determines acoustically the height of the tone.
