## WWZ

The WWZ Weighted Wavelet Z-Transform method1 is a time-frequency analysis method, exploring both the frequency domain and the time domain. While a regular period analysis method produces a plot of some response (e.g., power) as a function of either time or frequency, WWZ produces output for a range of frequencies and time. Hence, WWZ plots the response as a function of two variables, and therefore results in a 3D plot, where the X axis represents time, the Y axis represents frequency, and a color (Z axis) is used to plot the WWZ response. The WWZ method performs a wavelet transform using a wavelet function, which includes both a periodic, sinusoidal test function and a Gaussian window function. The width of the window is defined by the so called Decay constant (see below) and by the Time divisions (see below). This method then fits a sinusoidal wavelet to the observations. As it does so, it weights the observations by applying the sliding window function to the observations. Observations near the center of the window have the heighest weights in the fit. The window slides along the observations, producing a representation of the spectral content of the signal at times corresponding to the center of that window. The WWZ dialog box is similar to the Lomb-Scargle dialog box, but allows to enter two additional parameters in the Additional parameters section: - Decay constant: it defines the width of the wavelet "window". Said differently, it defines the number of cycles of a given frequency f expected within the wavelet window. Smaller values will produce wider windows. Reasonable values are between 0.001 and 0.0125. Note that using small values will result in improved frequency resolution of variations, but will smear out temporal variations. Conversely, large values will improve the temporal resolution, but will generate larger uncertainties in peak frequency.
- Time divisions: defines the wavelet window width together with the Decay constant. We recommend to use the default value of 50.
(1) Foster G., Wavelets for period analysis of unevenly sampled time series, AJ 112 (1996), p.1709-1729 |