Multi Resolution Analysis

Datum konání: 22.04.2022
Přednášející: Vašek Košík
Odpovědná osoba:

In many applications, given a function f ∈ L²(R) we are interested in capturing its frequency content locally. This can be illustrated by a musical score where we read which note to play at a certain time. The Classic Fourier transform describes frequency information in a function, but only globally. Localization can be achieved by “windowing” the function before the transform. Wavelet transform provides a similar time-frequency description. The basic principle is to build an orthonormal basis of L²(R) space defined by extending and shifting a function, so called mother wavelet, which has either a compact support or a reasonably fast decay. The Multiresolution Analysis, introduced in 1988/89 by Stephane Mallat and Yves Meyer, provides a mathematical framework how to construct new examples of such basis. We are going to define Multiresolution analysis, explain its basic principles, see some examples and explain how the coefficients of the transform are practically computed.