ABSTRACT
Wavelet theory is the outcome of a multidisciplinary endeavor that brought together mathematicians, physicists and engineers. This interaction created a flow of ideas that goes well beyond the construction of new bases and transforms. In fact, wavelet theory is a refinement and extension of Joseph Fourier analysis. Short-comings of Fourier analysis were realized as early as 1946. To remove these deficiencies, Nobel Laureate of Physics, Dennis Gabor, introduced the windowed Fourier transform. This transform suffered from some algorithmic difficulties and to eliminate them wavelet theory was introduced. During the 1980's, French geophysicist Morlet developed a new approach the wavelet transform, while studying problems in oil and gas exploration. The chapter presents an overview of wavelet methods and their applications to several areas of engineering and technology, namely biometrics, computed axial tomography, seismic tomography, medical imaging and power systems. The chapter provides a concept called multi-resolution analysis that provides a method to construct wavelets.
