Beispiel: Lineares Detrending

Funktionen > Signalverarbeitung > Zeitreihenanalyse > Beispiel: Lineares Detrending

Verwenden Sie die Funktion detrend, um einen linearen Trend mithilfe einer Kleinste-Quadrate-Mittelwertgeraden zu approximieren und aus Daten zu entfernen.

1. Definieren Sie ein Exponentialsignal.

2. Plotten Sie das exponentielle Signal.

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3. Verwenden Sie die Funktion whiten, um dem Signal weißes Rauschen hinzuzufügen.

4. Plotten Sie das ursprüngliche Signal und das Signal mit dem Rauschen.

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5. Wenden Sie die Funktion detrend auf das Signal mit dem Rauschen an.

6. Plotten Sie die ursprüngliche Funktion und die trendbereinigte Funktion.

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Der Wegfall des linearen Trends lässt sich weiter veranschaulichen, indem man die Kleinste-Quadrate-Gerade vor und nach der Entfernung des Trends betrachtet.

7. Verwenden Sie die Funktionen slope und intercept, um die Steigung und den Schnittpunkt vor und nach der Trendeliminierung zu berechnen.

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Das ist immer der Fall. Die Ausgabe von detrend ist ein Vektor, dessen Kleinste-Quadrate-Gerade eine durch den Ursprung verlaufende horizontalen Linie ist, d.h. Steigung und Achsenabschnitt sind beide sehr nahe an 0.

Ein Effekt von detrend besteht darin, dass der Mittelwert aus den Eingabedaten entfernt wurde. Dies wird deutlich, wenn man den DC-Term vor und nach der Trendeliminierung betrachtet.

8. Verwenden Sie die Funktion dft, um den (ersten) DC-Term vor und nach der Trendeliminierung zu berechnen.

Die Funktion detrend führt eine einfache Vorverarbeitungsaufgabe aus, die dem Glätten häufig vorausgeht. Wie oben erwähnt, ist die Trendbereinigung häufig ein hilfreicher erster Schritt bei der Spektralschätzung.

Zugehörige Themen

Lineares Detrending

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