The continuous wavelet transform and variable resolution time-frequency analysis

Wavelet transforms have recently emerged as a mathematical tool for multiresolution decomposition of signals. They have potential applications in many areas of signal processing that require variable time-frequency localization. The continuous wavelet transform is presented here, and its frequency resolution is derived analytically and shown to depend exclusively on one parameter that should be carefully selected in constructing a variable resolution time-frequency distribution for a given signal, Several, examples of application to synthetic and real data are shown.