About data:

For general illustration of ideas and sample Matlab codes, some simple time-series are provided. It should be noted that the convolution in the continuous wavelet transform implies the use of FFT which is more performant if the data file includes 2^N points; the same applies to the tree of orthogonal coefficients. It is assumed here that all time series are limited to powers-of-2 points. The following can be grabbed by the user (right-click, save into your working directory) for use with the Matlab codes.

• Artificial data: signal.mat , the Matlab code.

In these notes, we assume the data come in form of time series, with a corresponding Fourier representation in the frequency domain, and wavelet space is time-frequency. Changes to spatial distributions, wavenumbers and spatial/spectral decomposition, need no explanation. Most times series are discretized versions of a continuous signal, which imply a filtering of the signal (see Germano’s paper and sources cited there about implicit filters); this operation is so common that it is often taken for granted.  Eventually, a few applications will involve (2- or 3-D) spatial discretization, with corresponding change in terminology. To summarize, we assume time is the 1-D variable (time series), a plane (space) is 2-D default; we will use frequency and wavenumber as their respective spectral counterparts.