Implementation of time-scale transformation based on continuous wavelet theory

The basic objective of time-scale transformation is to compress or expand the signal in time field while keeping the same spectral properties. This paper presents two methods to derive time-scale transformation formula based on continuous wavelet transform. For an arbitrary given square-integrable function f(t), g(t) = f(t/λ) is derived by continuous wavelet transform and its inverse transform. The result shows t at time-scale transformation may be obtained through the modification of the time-scale of wavelet function filter using equivalent substitution. The paper demonstrates the result by theoretic derivations and experimental simulation.