Non-MSF Wavelets - Aparna Vyas - Bog

The notion of wavelets came into being because the Fourier analysis which depends on oscillating building blocks is poorly suited to signals that change suddenly. A wavelet is crudely a function which together with its dilates and their translates determine all functions of our need. The Haar wavelet (1910) is the oldest wavelet which has limited application as it is not continuous. To suit for approximating data with sharp discontinuities, wavelets that could automatically adapt to different components of a signal were targeted for investigation in early 1980's. It was 1989, when Stephane G. Mallat discovered the underlying concept for obtaining orthonormal wavelets now popularly known as the multiresolution analysis (MRA). A wavelet arose through an MRA is known as an MRA wavelet. The Haar wavelet, the Shannon wavelet and Daubechies wavelets are some amongst MRA wavelets. The Journe wavelet is a non-MRA wavelet. The Fourier transform of the Shannon wavelet possesses the minimal support and also that of the Journne wavelet has the minimal support. An orthonormal wavelet whose Fourier transform has minimal support is known to be the minimally supported frequency (MSF) wavelet.