Consistent physical frequencies in time-frequency analysis

Abstract

Wavelet transforms have been studied extensively for a wide variety of applications such as signal compression and signal denoising. Wavelet transforms have also been examined for the detection of transient signals. However, wavelet levels (and corresponding pseudo-frequencies) are inherently dependent on the sampling rate of the analyzed data. The work presented herein examines how wavelet analysis can produce inconsistent data representations for the same analytical signal digitized at different sampling rates. Results are compared to time-octave and other time-frequency representations to identify methodologies which produce consistent characterization of physical frequencies. Similarities and difference between approaches are discussed.