Wavelet transform

Inspection of time series at different scales. Requires one column of ordinal or continuous data with even spacing of points.

The continuous wavelet transform (CWT) is an analysis method where a data set can be inspected at small, intermediate and large scales simultaneously. It can be useful for detecting periodicities at different wavelengths, self-similarity and other features. The vertical axis in the plot is a logarithmic size scale (base 2), with the signal observed at a scale of only two consecutive data points at the top, and at a scale of one fourth of the whole sequence at the bottom. One unit on this axis corresponds to a doubling of the size scale. The top of the figure thus represents a detailed, fine-grained view, while the bottom represents a smoothed overview of longer trends. Signal power (or more correctly squared correlation strength with the scaled mother wavelet) is shown with a grayscale or in colour.

The shape of the mother wavelet can be set to Morlet (wavenumber 6), Paul (4th order) or DOG (Derivative Of Gaussian, 2nd or 6th derivative). The Morlet wavelet usually performs best.

The so-called “cone of influence” can be plotted to show the region where boundary effects are present.

The 'Sample interval' value can be set to a value other than 1. This will only influence the scaling of the labels on the x and y axes.

Significance test: The significance level corresponding to p=0.05 can be plotted as a contour (chi-squared test according to Torrence & Compo 1998). The “Lag” value, as given by the user, specifies the null hypothesis. Lag=0 specifies a white-noise model. Values 0 If the ‘Power’ option is deselected, the program will show only the real part of the scalogram (not squared). This shows the signal in the time domain, filtered at different scales.

In the ‘View numbers’ tab, each row shows one scale, with sample number (position) along the columns.

The ‘Filter’ tab shows the time series at one scale value, as power values if the ‘Power’ option is selected in the main tab, or real parts if not. This, in effect, works as a bandpass filter.

Missing values are treated using linear interpolation before analysis.


Torrence, C. & G.P. Compo. 1998. A practical guide to wavelet analysis. Bulletin of the American Meteorological Society 79:61-78.

Published Aug. 31, 2020 10:06 PM - Last modified Aug. 31, 2020 10:06 PM