Wavelet approximation and analysis

Wavelets are new families of basis functions that practical measurements of real phenomena require time and resources, they provide not all values but only a finite sequence of values called a Sample of the function representing the phenomenon under consideration. Therefore, the first in the analysis of a data with wavelets consists in approximating its function by means of the sample alone. One of the simplest methods of approximation uses a horizontal stair step extended through each sample point. The resulting steps form a new function denoted here by f ̃ and called a simple function or step function, which approximates the sampled function f. Although approximations more accurate than simple step exist, they demand more sophisticated Mathematics, so this paper presents to simple steps. A precise notation will prove useful to indicate the location of such steps. In this paper we have used simple steps, Haar wavelets for approximating the different class of data and analyzed by using wavelets.