Date of Award

Spring 2003

Document Type


Degree Name

Doctor of Philosophy (PhD)


Micro and Nanoscale Systems

First Advisor

Louis Roemer


Wavelets are signal-processing tools that have been of interest due to their characteristics and properties. Clear understanding of wavelets and their properties are a key to successful applications. Many theoretical and application-oriented papers have been written. Yet the choice of a right wavelet for a given application is an ongoing quest that has not been satisfactorily answered. This research has successfully identified certain issues, and an effort has been made to provide an understanding of wavelets by studying the wavelet filters in terms of their pole-zero and magnitude-phase characteristics. The magnitude characteristics of these filters have flat responses in both the pass band and stop band. The phase characteristics are almost linear. It is interesting to observe that some wavelets have the exact same magnitude characteristics but their phase responses vary in the linear slopes. An application of wavelets for fast detection of the fault current in a transformer and distinguishing from the inrush current clearly shows the advantages of the lower slope and fewer coefficients—Daubechies wavelet D4 over D20. This research has been published in the IEEE transactions on Power systems and is also proposed as an innovative method for protective relaying techniques.

For detecting the frequency composition of the signal being analyzed, an understanding of the energy distribution in the output wavelet decompositions is presented for different wavelet families. The wavelets with fewer coefficients in their filters have more energy leakage into adjacent bands. The frequency bandwidth characteristics display flatness in the middle of the pass band confirming that the frequency of interest should be in the middle of the frequency band when performing a wavelet transform. Symlets exhibit good flatness with minimum ripple but the transition regions do not have sharper cut off. The number of wavelet levels and their frequency ranges are dependent on the two parameters—number of data points and the sampling frequency—and the selection of these is critical to qualitative analysis of signals.

A wavelet seismic event detection method is presented which has been successfully applied to detect the P phase and the S phase waves of earthquakes. This method uses wavelets to classify the seismic signal to different frequency bands and then a simple threshold trigger method is applied to the rms values calculated on one of the wavelet bands.

Further research on the understanding of wavelets is encouraged through this research to provide qualified and clearly understood wavelet solutions to real world problems. The wavelets are a promising tool that will complement the existing signal processing methods and are open for research and exploration.