Digital Signal Processing Reference
In-Depth Information
Zeitbereich
Kurzer Kammerton “a”
(440Hz) einer Klarinette
Ausschnitt aus dem oberen Bild: Fastperiodizität erkennbar
Frequenzbereich
Beweis für Fastperiodizität: “Linienähnliches” Spektrum und nur
die ganzzahlig Vielfachen der Grundfrequenz vorhanden!
Illustration 56:
Tone, pitch and sound
The near-periodicity of all tones is illustrated by means of a short clarinet tone (440 Hz = concert pitch
"A"). In the time domain it is possible to perceive "similar events" at the same distance T from each other.
Use a ruler to measure 10 T (why not simply T?), define T and calculate the inverse value 1/T = f
A
.
The result ought to be the basic frequency f
A
= 440 Hz. As our ear is a FOURIER analyzer - see Chapter 2
- we are able to recognise the (base) pitch. If you are not entirely unmusical you can also sing this tone
after it has been played.
The "concert pitch" of a clarinet sounds different from that of a violin., i.e. every instrument has its own
timbre. These two tones differ in the amplitude of the overtones and not in the basic pitch ( = f
A
). As a
violin sounds "sharper" than a clarinet there are more overtones than in the spectrum of the clarinet.
A short tone/sound purposely wa chosen because it demonstrates a small "defect" in the near-periodic
segment. The actual tone lasts roughly 250 ms and produces a near-periodic spectrum. One thus arrives at
the following rule of thumb: every uniform tone/sound which lasts at least 1 s produces a practically
periodic spectrum!
