Beispiel: Wavelet-Transformation

Funktionen > Transformationen und Filter > Beispiel: Wavelet-Transformation

Verwenden Sie die Wavelet-Transformationsfunktionen, um Daten zu komprimieren.

1. Definieren Sie ein einzelnes Rechteckwellensignal. Dabei gilt:

2. Werten Sie das Array n aus, und plotten Sie das Signal S:

Im Bereich von 0...255 hat das Signal S eine Amplitude von 1 für alle Werte von n (96...160) und ansonsten eine Amplitude von null.

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3. Verwenden Sie die Funktion wave, um die Wavelet-Transformation des Signals S zu berechnen:

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4. Berechnen Sie die in dieser Transformation enthaltene Anzahl von Ebenen:

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5. Verwenden Sie die Funktionen submatrix und floor, um ein Gespür für die relative Wichtigkeit jeder Ebene zu entwickeln:

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6. Plotten Sie mehrere Ebenen von Koeffizienten gleichzeitig:

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7. Stellen Sie das Signal mit weniger Daten dar, indem Sie zwei Schritte ausführen:

a. Setzen Sie die Koeffizienten höherer Ebene gleich null.

b. Berechnen Sie die inverse Wavelet-Transformation der neuen Koeffizientenvektoren.

Erste Ebene, auf der die Koeffizienten auf null eingestellt werden (L < 7 kann variiert werden).

8. Verwenden Sie die Funktion iwave, um das ursprüngliche Signal wiederherzustellen:

9. Plotten und vergleichen Sie das ursprüngliche Signal mit dem transformierten Signal:

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Auf diese Weise kann die für die Signaldarstellung erforderliche Datenmenge reduziert werden.

Zugehörige Themen

Wavelet-Transformation

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