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Die endliche Fourier- und Walsh-Transformation mit einer by Klaus Niederdrenk (auth.), Gisela Engeln-Müllges (eds.)

By Klaus Niederdrenk (auth.), Gisela Engeln-Müllges (eds.)

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Additional info for Die endliche Fourier- und Walsh-Transformation mit einer Einführung in die Bildverarbeitung: Eine anwendungsorientierte Darstellung mit FORTRAN 77-Programmen

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3 DER MEHRDIMENSIONALE FALL Die Erweiterung der in den letzten Abschnitten gemachten Aussagen auf reell- oder komplexwertige Funktionen mehrerer unabhangiger Veranderlicher bereitet keine Schwierigkeiten, wenn man die Erweiterung auf Funktionen von zwei unabhangigen Veranderlichen kennt. Da dies auBerdem der weitaus am meisten vorkommende mehrdimensionale Fall in der Praxis ist, wollen wir uns hier darauf beschranken. Eine wichtige Anwendung ist die Bildverarbeitung. Man kann ein in analoger Weise vorliegendes Bild durch eine Grauwertfunktion bei einem SchwarzWeiB-Bild bzw.

9: Die Werte der periodischen Funktionen fund 9 mit der gleichen Periode X seien in den Punkten xm = m~ , m=0,1, ... ,M-1 , im fundamentalen Intervall bekannt und beschrankt. Dann gilt: (i) Die diskrete zyklische Korre·l ation erfUllt und ist periodisch mit der Periode X. 8 bzw. 5. Sowohl bei der Faltung wie auch bei der Korrelation Ubertragen sich also die wichtigen Eigenschaften auf den diskreten Fall. 7 in den Punkten xm die Werte D(f of)(x ) annimmt. folgt insbesondere fUr Xo = 0 m M M-1 1.

5 ist SATZ 1. 9: Die Werte der periodischen Funktionen fund 9 mit der gleichen Periode X seien in den Punkten xm = m~ , m=0,1, ... ,M-1 , im fundamentalen Intervall bekannt und beschrankt. Dann gilt: (i) Die diskrete zyklische Korre·l ation erfUllt und ist periodisch mit der Periode X. 8 bzw. 5. Sowohl bei der Faltung wie auch bei der Korrelation Ubertragen sich also die wichtigen Eigenschaften auf den diskreten Fall. 7 in den Punkten xm die Werte D(f of)(x ) annimmt. folgt insbesondere fUr Xo = 0 m M M-1 1.

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