Simple and Field Rate-based Relation through Localized Functions and Multi-function Localized Functions

The "Wavelet" or "Ondelettes" was introduced by Jean Morlet, a French geophysicist who was working with an oil company. The main reasons of the discovery of wavelet and wavelet transform is that the Fourier transform analysis cannot analyze the signal in both time and frequency domains. The Fourier analysis is ideal for studying stationary data but is not well suited for studying data with transient events. Wavelets were designed with such disadvantage of Fourier transform in mind. So, the main advantage of the wavelet transform is its possibility to analyze the signal in both time and frequency domains. For the analysis of nonstationary signals, Jean Morlet introduced the idea of wavelets as a family of functions constructed by using the translation and dilation of a single function, called mother wavelet. The concept of wavelet can be viewed as a synthesis of ideas which originated during the last thirty-four years in engineering (sub-band coding), physics (coherent states), and pure mathematics (the study of colderson-zeygmund operators). Wavelet analysis with their characteristic properties has been many new methods for solving difficult problems. Which arising in many diverse fields such as mathematics, engineering, physics, biological signal analysis (EEG, EKG), data compression, denoising, source and channel coding, analysis of seismic activity and prediction of earthquakes, analysis of sounds, multidimensional signal analysis together with data compression often applied to image processing as specific representative, financial data analysis, analysis and attempts to predict the behavior of stock market, the detection of aircraft and submarines, these all things denote the capabilities and applicability of wavelets and wavelet transforms in the future.