Lately I have read a number of articles that use multiscale analysis (wavelets) to decompose the signal into different frequency bands. On each of the scales, invariant measures such as correlation dimension and largest Lyapunov exponents are estimated (via Takens delay embedding theorem). My questions are: Since linear filters are generally not recommended as a preprocessing step before calculating nonlinear invariants (such filtering removes important dynamics), what will happen to the dynamics when applying wavelets to the data before the nonlinear analysis? Aren't wavelets just a bunch of linear filter? How come this recent interest in combining wavelets and nonlinear time series analysis tools?

# Nonlinear time series analysis and wavelets

Started by ●December 17, 2007

Reply by ●December 18, 20072007-12-18

On Dec 17, 8:40 am, "Chris111" <ch...@imt.liu.se> wrote:> Lately I have read a number of articles that use multiscale analysis > (wavelets) to decompose the signal into different frequency bands. On each > of the scales, invariant measures such as correlation dimension and largest > Lyapunov exponents are estimated (via Takens delay embedding theorem). My > questions are: Since linear filters are generally not recommended as a > preprocessing step before calculating nonlinear invariants (such filtering > removes important dynamics), what will happen to the dynamics when applying > wavelets to the data before the nonlinear analysis? Aren't wavelets just a > bunch of linear filter? How come this recent interest in combining > wavelets and nonlinear time series analysis tools?Maybe if you cited a few of these papers, people would be in a better position to comment. IMHO your question is overly broad.

Reply by ●December 18, 20072007-12-18

On Dec 17, 7:40 am, "Chris111" <ch...@imt.liu.se> wrote:> Lately I have read a number of articles that use multiscale analysis > (wavelets) to decompose the signal into different frequency bands. On each > of the scales, invariant measures such as correlation dimension and largest > Lyapunov exponents are estimated (via Takens delay embedding theorem). My > questions are: Since linear filters are generally not recommended as a > preprocessing step before calculating nonlinear invariants (such filtering > removes important dynamics), what will happen to the dynamics when applying > wavelets to the data before the nonlinear analysis? Aren't wavelets just a > bunch of linear filter? How come this recent interest in combining > wavelets and nonlinear time series analysis tools?I'm not really up on strange attractors and chaotic dynamical systems, however, my comments may start a different thought area. Wavelets (at least some wavelets) are basis functions. The data is being transformed into a different basis set. Is it possible the basis set (wavelet) being used acts as a kernal for the dynamic system you're examining? Maurice Givens