A Tutorial on Wavelets from an Electrical Engineering Perspective, Part 2: The Continuous Case

The wavelet transform is described from the perspective of a Fourier transform. The relationships among the Fourier transform, the Gabor transform (windowed Fourier transform), and the wavelet transform are described. The differences are also outlined, to bring out the characteristics of the wavelet transform. The limitations of the wavelets in localizing responses in various domains are also delineated. Finally, an adaptive window is presented that may be optimally tailored to suit one's needs, and hence, possibly, the scaling functions and the wavelets.