Digital Signal Processing Reference
In-Depth Information
Illustration 27:
FOURIER synthesis: the more the better!
Here the first N = 32 sinusoidal signals were added from which a sawtooth signal is composed. At the jump
position of the "sawtooth" the deviation is greatest. The cumulative function can never change faster than
the sinusoidal signal with the greatest frequency (it is practically visible as "ripple content"). As the
"sawtooth" at the jump position can theoretically "change infinitely rapidly", the deviation can only have
disappeared when the cumulative function also contains an "infinitely rapidly changing" sinusoidal signal
(i.e. f
−>
∝
). As that doesn't exist, a perfect sawtooth signal cannot exist either. In nature every change
takes time!
Terms such as "frequency range" or "frequency response" are well-known. Both concepts
are only meaningful in the context of sinusoidal signals:
Frequency range
: the frequency range which is audible for human beings lies in a
range of roughly 30 to 20,000Hz (20 kHz). This means that our ear (in conjunction
with the brain) only hears acoustic sinusoidal signals between 30 and 20,000Hz
Frequency response
: if a frequency response for a bass loudspeaker is given as 20
to 2500 Hz this means that the loudspeaker can only transmit acoustic waves which
contains sinusoidal waves between 20 and 2500 Hz.
Note: In contrast to the term
frequency range
the term
frequency response
is only
used in connection with a system capable of oscillation.
The other two - also important properties - of a sinusoidal signal are:
•
amplitude
and
•
phase angle
