A Generalized Wavelet Transformation Technique for High Selectivity over a Wide Frequency Range

The wavelet transform is a powerful time-frequency analysis tool for the analysis of non-stationary signals. The choice of best time signal specific wavelet is very important for accounting different frequencies present in a signal. The vanishing moment of the mother wavelet defines that more the order of vanishing moment, the higher is the frequency function of the mother wavelet, and the Wavelet transform is more sensitive to process the high frequency component. In this work, we have proposed a modified wavelet transformation technique where a general wavelet which consists of a weighted sum of several wavelet components i.e. a mother wavelet and its higher order derivatives is used. Parameters such as correction factor and squeezing effect have been introduced in the higher order derivatives to serve our purpose. A predefined membership function influences a particular wavelet component to boost up a certain frequency range. This leads to better selectivity and covers a wider frequency range. By proposing this generalized solution the problem of choosing the best time signal specific wavelet can be countered effectively. The transformation technique has been implemented upon a stationary and a non-stationary signal.