Implementation of the continuous wavelet transform for digital time series analysis

The wavelet transform has emerged as an important tool for the analysis of intermittent and nonstationary signals. This article addresses implementation issues of a digital continuous wavelet transform that is sufficiently general that any continuous wavelet can be used. Working equations are derived for wavelet sampling, aliasing, and scale population by using the band-pass filter interpretation of wavelet functions. The implementation procedure is applied to the Morlet wavelet in detail as an example. Finally, the Morlet wavelet is applied to velocity fluctuations measured in a subsonic wake undergoing transition to turbulence.