On the analysis of fluctuating velocity signals through methods based on the wavelet and Hilbert transforms

In the present paper we describe signal processing procedures based on the wavelet and Hilbert transforms, which may be used to characterize the time variation of the amplitude and frequency modulations that are present in the fluctuating components of experimental velocity signals. The classical Hilbert demodulation technique is described together with the wavelet-ridge extraction procedure, and a new joint wavelet-Hilbert technique is presented. Methods to obtain the instantaneous contribution to the correlation between the components present in two signals through the wavelet and Hilbert transforms are also described. The procedures are then applied to the analysis of the velocity fluctuations in the wake of a bluff body, and it is shown that they allow a physical interpretation to be given of the connection between different fluctuating components present in the velocity signals and the dynamics of the vorticity structures in the wake.