Wavelet Analysis Applied to the Real Dat ...

Wavelet Analysis Applied to the Real Dataset in a Quick and Easy Way

May 02, 2021

A wavelet series represents a real or complex-valued function by a certain orthonormal series generated by a wavelet.

Since in geosciences, we work mostly with dynamical systems, most of the signals are non-stationary in nature. In such cases, the Wavelet Transform is a much better approach.

The Wavelet Transform retains high resolution in both time and frequency domains (Torrence & Compo 1998; Chao et al. 2014). It tells us both the details of the frequency present in the signal along with its location in time. This is achieved by analyzing the signal at different scales. Unlike the Fourier Transform that uses a series of sine waves with different frequencies, the Wavelet Transform uses a series of functions called wavelets, each with different scales to analyze a signal. The advantage of using a wavelet is that wavelets are localized in time unlike their counterparts in the Fourier Transform. This property of time localization of wavelets can be exploited by multiplying the signal with wavelets at different locations in time, starting from the beginning and slowly moving towards the end of the signal. This procedure is known as convolution. We can iterate the whole process by increasing the scale of the wavelet at each iteration. This will give us the wavelet spectrogram (or scaleogram).

I apply the Wavelet analysis concept on the quarterly dataset for El Niño–Southern Oscillation (ENSO) sea surface temperature in degree Celsius (1871-1997) and Indian monsoon rainfall in mm (1871-1995) (Torrence & Webster 1999). 

For codes and details, please visit my original blog post:

https://www.earthinversion.com/geophysics/Wavelet-analysis-applied-to-the-real-dataset-in-a-quick-and-easy-way/

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