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Special Topics in Computer Science: Wavelets and Filter Banks in Image Processing
Signal processing has become an essential part of contemporary scientific and technological activity. Dramatic changes have already been made in a broad range of fields such as communications, imaging, radar & sonar, and music reproduction, to name just a few. Each of these areas has developed its own algorithms, mathematics, and specialized techniques. Describing signals in terms of frequency and using the Fourier Transform for analysis has been essential in all of these fields. Like the Fourier transform (FT), a wavelet transform (WT) represents a signal in another domain, a timefrequency domain. However, wavelet transforms are more general than the Fourier transform. Unlike the Fourier transform, wavelet transforms may describe localized signals more efficiently. For example, a wavelet transform may describe a function into different frequency components, and then study each component with a resolution matched to its scale. Although the first wavelet transform was discovered in 1910 by Alfred Haar, wavelet transforms have only recently been used. They are gaining widespread acceptance in many fields and already dominates some technologies such as signal compression. Knowledge of wavelet transforms is essential for any current work in processing signals.
The basis functions of the WT, scaling functions and wavelets, are
often more complicated than the basis functions of the FT, sines and
cosines. Unlike the FT the basis functions in the WT are localized in
both the input and wavelet domain. Furthermore, like the FT, the WT is
a linear operation that is invertible and can be made orthogonal. The
general idea behind the wavelet transform is to represent any arbitrary
function as a superposition of wavelets. Based on a mother wavelet,
scaled and shifted versions of the mother wavelet can be summed to
represent an arbitrary function. Like the FT, scaled and shifted versions
of sine and cosine functions can be summed to represent an arbitrary function. LecturerDr. Ildiko LASZLOEötvös Lorand University Budapest (ELTE) ildiko@inf.elte.hu Dates
Contents
Downloadsnot yet available ExamStudents will do a project that will be marked. Literature
Software: Matlab, only the signal processing toolbox is needed. 