Das Rätsel um die Abtastrate
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Wenn ich ein Audiosignal digitalisiere, dann taste ich das Signal alle paar mal pro Sekunde ab und speichere diesen Wert. Wenn ich ein so digitalisiertes Signal wieder in ein analoges Signal zurückwandle, dann ähm…
Falsch.
Eine Treppenstufe ist eine kontinuierliche Zeitfunktion. Ein gesampeltes Signal ist zeitdiskret. Es hat nur einen Wert an einem Punkt in der Zeit, es ist nicht kontinuierlich.
Was bedeutet das jetzt?
Die Signalkurve *muss* den Weg zwischen den einzelnen Punkten nehmen, und es gibt nur genau diesen einen Weg.
Ergebnis: Keine Treppenstufen. Keine Treppenstufen.
Kei-i-n-e. Verdammten. Treppenstufen.
Die Kurve sieht genau so aus wie das ursprüngliche Signal.
Das funktioniert auch bei hohen Frequenzen.
Ah ja. Irgendwann hast du ein so hochfrequentes Signal (rote Linie), das so schnell schwingt, dass es durch die selben Samplingpunkte passieren könnte wie die schwarze Kurve. Der Digital-zu-Analog Wandler würde daraus genau die schwarze Kurve zeichnen.
Wie lösen wir dieses Problem?
Ganz einfach:
Wir sagen der Kurve: „Du darfst maximal so schnell schwingen.“
Wir begrenzen die Bandbreite, in der die Kurve (das Signal) schwingen darf (bandlimitiertes Signal). Alles, was schneller schwingt, schneiden wir ab (Tiefpassfilter; das Tiefe darf passieren).
Wenn wir diese Regel aufgestellt haben, gibt es nur eine Lösung, eine Kurve von Digital zu Analog. Das Signal wird, in dem definierten Frequenzbereich, verlustfrei wiedergegeben.
Und wenn sie auch nur einen Mikrometer davon abweicht, hat sie diese Regel gebrochen, wäre höherfrequentig als definiert und dann hätte sie wirklich mit einer höheren Abtastrate aufgezeichnet werden müssen.
Da wir aber den Frequenzbereich definiert haben, darf die Kurve das nicht.
Gut, und wie definieren wir den Frequenzbereich?
Das menschliche Hören
Das menschliche Ohr nimmt unterschiedliche Frequenzen unterschiedlich gut wahr. Tiefe Frequenzen eher schlecht, deshalb muss die Bassbox auch mehr Pfuus haben, damit wir davon noch etwas wahrnehmen. Bei den Höhen ist ab 22 kHz Schluss. Schwingungen, die höher als zweiundzwanzigtausendmal in der Sekunde schwingen, nimmt das Ohr nicht mehr wahr.
Somit haben wir die Bandbreite des menschlichen Hörens. 20 Hz bis 22 kHz.
Das Nyquist-Shannon-Abtasttheorem besagt, dass ich ein Signal mindestens doppelt so oft abtasten muss wie die höchste Frequenz, die ich aufzeichnen will.
Also:
2 * 22 kHz = 44 kHz.
„Mindestens“: 0.1
44 kHz + 0.1 = 44.1 kHz.
Das heisst also: Wenn ich einen Ton mit einer Abtastrate von 44.1 kHz aufzeichne, wird das Signal *perfekt* für das menschliche Gehör wiedergegeben.
Christopher Montgomery hat das alles anschaulich in einem Video zusammengefasst, mit nachvollziehbaren Experimenten und Messergebnissen:
Was für einen Sinn haben dann Abtastraten mit 192 kHz?
Christof von 24bit96.de erklärt es mir so:
Das mit den ganzen Theoremen ist sicherlich (teils) richtig, hängt aber auch immer davon ab wie man diese auslegt und was man wie misst.
Die ursprüngliche Frage lautete ja „96 kHz und höher sind somit Marketing?“ und bezog sich darauf ob das hörbar ist oder nicht. Und zum Hören benutzen wir jetzt mal keine Messgeräte sondern unsere Ohren 🙂
Dazu einfach mal ein einfaches Experiment das man leicht selbst machen kann.
- Man nehme einen sehr guten AD/DA-Wandler (REM/Lake People/Grace)
- ein analoges HighEnd-Laufwerk mit einer wirklich guten Aufnahme mit viel Dynamik (=Rumms)
- exzellente Elektronik (Verstärker/RIAA-Entzerrer bzw. MC-Vorstufe)
- möglichst aktive Abhörmonitore (Westlake/KS-Digital/Genelec) ohne Digital-Funktion bzw. einen hochwertigen Kopfhöhrer
- dann zeichnet man mit dem A/D-Wandler eine Aufnahme die man gut kennt mit 44.1/16, 96/16 und 96/24 auf
- das gibt man dann über den D/A-Wandler wieder
Man wir kaum einen Unterschied zwischen 44.1/16 bzw. 96/16 hören, bei 96/24 jedoch ist der Unterschied enorm.
Und ein selbst aufgezeichnetes/gewandeltes analoges Signal ist hier Pflicht, denn viele gekaufte „HD-Aufnahmen“ sind nur von 44.1/16 auf höhere Raten/Bittiefen upgesampelte Files, da hört man dann wirklich keinen Unterschied da das Ausgangsmaterial gleich ist und diese „Sample-Rate-Conversion“ immer verlustbehaftet ist.
Das Thema ist ähnlich umfangreich wie
- Röhre/Transistor (=harmonische/unharmonische Verzerrungen -- trotzdem gibt es grottige Röhren- und phantastische Transitorverstärker)
- Bauformen und Materialien der Widerstände/Kondensatoren (gleiche Kenndaten müssten ja gleich klingen, tun sie aber nicht)
- Schallplatte oder CD (Schallplatte! 😉 )
- oder um bei dem digitalen zu bleiben: asynchron oder adaptiv
Ein befreundeter Tontechniker meint dazu:
Mit der Abtastrate muss man sich das so vorstellen wie bei einem Fernseher mit der Auflösung (Pixel). Sofern das Originalsignal nicht gut genug ist, nützt diese auch nichts. Und irgendwann macht das menschliche Gehör auch nicht mehr mit. Der Mensch selbst nimmt auch höhere Frequenzen wahr, allerdings reagiert nicht jeder Mensch genau gleich darauf. Ebenfalls nehmen wir auch tieffrequente Schwingungen wahr, welche wir aber nicht hören sondern nur spüren.
Solange aber nicht entsprechendes Equipment zur Aufnahme und letztlich auch zur Wiedergabe genutzt wird nützt alles nichts.
Selbstverständlich ist z.B. bei Musikinstrumenten mehr da, als nur das hörbare. Der Grossteil der Menschen wird dies allerdings kaum beachten und für nötig empfinden (Alleine schon der Quatsch der da täglich im Radio läuft oder MP3 als Standard beweist dies zu genüge). Für die paar wenigen, welche dann doch ein feineres Gehör haben, darf es natürlich auch etwas mehr sein als CD-Qualität. Der Preis steigt aber entsprechend, da der Herstellungsaufwand und auch das Equipment teurer ist.
Zusammenfassend: 192kHz nützt nur dann, wenn vom Mikrofon bis zum Lautsprecher alle Teile ein Frequenzspektrum von mehr als 20-20’000Hz (Hörbereich) aufzeichnen/wiedergeben können.
Seufz. Also ganz so einfach ist es wohl doch nicht. Ich stehe nach wie vor vor einem Rätsel. Warum klingen Aufnahmen mit 96 kHz / 24-bit besser? Ich höre den Unterschied ja selber. Doch dieses Abtasttheorem besagt, dass es da gar keinen Unterschied geben dürfte. Tontechniker und HiFi Enthusiasten geben vor allem dem Equipment die Schuld.
Andere Frage: Was ist eigentlich, wenn mehrere Geräusche auf eine Aufnahme zusammenkommen? Wenn also ein Bach plätschert, eine Geige spielt, eine grosse Pauke trommelt und ein Triangel bimmelt -- das fliesst ja dann alles auf letztendlich *ein* Tonsignal zusammen. Wieviele Pauken, Bäche, Geigen können ächt gleichzeitig spielen, so dass man jedes Instrument auseinanderhalten und evtl. wieder extrahieren kann, und zwar originalgetreu und verlustfrei? Tausend Geigen? Vierzig Triangel? Inwiefern beeinflusst das tiefe pauken den Klang der Geigen? Irgendwann ist doch wirklich Schluss, und die arme Signalkurve kann nicht mehr Informationen aufzeichnen…
Ich stehe nach wie vor vor einem Rätsel.
