New and old theses on wavelets (Q1360583)

The paper gives a popularized introduction into the theory of wavelets, their basic ideas and their applications. Wavelets are used for decomposition and reconstruction of signals, they successfully work for noise removal and for data compression. The wavelet transform can be considered as a generalization of the Fourier transform. A wavelet is an oscillating, quadratic integrable, local function. Each signal can be represented as a wavelet series formed by scales and shifts of this wavelet, such that different frequencies can be scanned time-dependently. Compared with Fourier transform, the main advantage of wavelets lies in the better time-frequency localization.