From fc941c6ac3c4be56edbd2ddbb2959aed2e62f34d Mon Sep 17 00:00:00 2001 From: Michael Czechowski Date: Thu, 14 May 2026 11:25:50 +0200 Subject: [PATCH] =?UTF-8?q?223015b=20phase=203:=20nyquist-diagram=20demo?= =?UTF-8?q?=20(kap1=20folie=2035=20nyquist-theorem).=20drei=20vergleichs-c?= =?UTF-8?q?ases=20mit=20derselben=20grundwelle=20(8=20cycles=20=C3=BCber?= =?UTF-8?q?=20880px=20svg):=20(1)=20aliasing=20rot=20f=5Fs=3D0.9f,=208=20s?= =?UTF-8?q?ample-punkte=20sitzen=20mathematisch=20korrekt=20auf=20der=20we?= =?UTF-8?q?lle=20und=20ergeben=20verbunden=20eine=20ganz=20andere=20langsa?= =?UTF-8?q?mere=20kurve,=20(2)=20nyquist-grenze=20gelb=20f=5Fs=3D2f,=2016?= =?UTF-8?q?=20punkte=20exakt=20auf=20peak/tal=20und=20zigzag-verbindung=20?= =?UTF-8?q?zeigt=20mathematisches=20minimum,=20(3)=20=C3=BCberabtastung=20?= =?UTF-8?q?gr=C3=BCn=20f=5Fs=3D8f=20mit=2064=20dichten=20punkten=20die=20d?= =?UTF-8?q?er=20welle=20treu=20folgen=20wie=20eine=20CD.=20punkte=20mit=20?= =?UTF-8?q?python=20berechnet=20(y=20=3D=2070=20-=2045*sin(2=CF=80*(x-20)/?= =?UTF-8?q?105)=20f=C3=BCr=20jede=20sample-position).=20verdict=20erkl?= =?UTF-8?q?=C3=A4rt=2044,1=20khz:=20ohr=20h=C3=B6rt=20bis=2020=20khz,=202x?= =?UTF-8?q?20=3D40=20plus=204,1=20sicherheitsmarge?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../223015b/assets/demos/nyquist-diagram.html | 232 ++++++++++++++++++ .../223015b/assets/demos/nyquist-diagram.png | Bin 0 -> 143186 bytes 2 files changed, 232 insertions(+) create mode 100644 slides/223015b/assets/demos/nyquist-diagram.html create mode 100644 slides/223015b/assets/demos/nyquist-diagram.png diff --git a/slides/223015b/assets/demos/nyquist-diagram.html b/slides/223015b/assets/demos/nyquist-diagram.html new file mode 100644 index 0000000..b2d7ece --- /dev/null +++ b/slides/223015b/assets/demos/nyquist-diagram.html @@ -0,0 +1,232 @@ + + + + +Nyquist-Shannon — wie oft muss man messen? + + + +

Nyquist-Shannon — wie oft müssen wir messen?

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Dieselbe Welle, drei Sample-Raten. Eine fällt durch, eine reicht knapp, eine ist sicher.
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Zu wenig
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Aliasing
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fs = 0,9 · f
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Die Sample-Punkte sitzen auf der Welle — aber verbunden sehen sie aus wie eine ganz andere, langsamere Welle.
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Genau
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Nyquist-Grenze
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fs = 2 · f
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Sample exakt auf Peak und Tal. Mathematisch reicht das — visuell sieht es kaputt aus.
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Sicher
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Überabtastung
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fs = 8 · f
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Genug Punkte — die Welle wird Punkt für Punkt nachgezeichnet. So macht es eine CD.
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fs ≥ 2 · fmax. So einfach. So endgültig.
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Das Ohr hört bis 20 kHz. 2 × 20 = 40 kHz. Die CD nimmt 44,1 kHz — die 4,1 sind Sicherheits-Marge.
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