Scaling and filtering of a sampled signal by the continuous wavelet transform

Scaling of a discrete time sequence is necessary in some applications. An example is in estimating the time delay and Doppler stretch between two waveforms received at spatially separated sensors, when there is relative motions between the signal source and the sensors. The scaling task is non-trivial because the signal to be scaled does not have an analytical form. This paper considers the use of continuous wavelet transform (CWT) to perform scaling of a discrete time signal. The method involves wavelet transforming the discrete sequence, thresholding coefficients for noise reduction and forming the scaled samples using the CWT reconstruction formula. Simulations are presented to evaluate the performance of the method