On the applications of orthogonal functions in pattern recognition

Abstract

The properties of the hybrid functions which consists of block-pulse functions plus Chebyshev polynomials are presented. By using these hybrid functions, the differential and integral expressions which arise in the radiative transfer equation are converted into some linear systems of differential equations which can be solved for the unknown coefficient. A numerical example is included to demonstrate the validity and applicability of the technique and a comparison is made with existing results. Introduction.In the applications of remote sensing at optical wavelengths to different surfaces from satellite borne and high-resolution instruments, an understanding of the various physical mechanisms that contribute to the measured data is important. Accordingly, the solution of radiative transfer equation (RTE) has been utilized in

Explicit construction of W-system over triangular domain

“…, , , h h h h to represent its row vectors and (1) ij h to represent its element at ith row and jth column, matrix 1 H can be rewritten as …”

“…belong. The third class is the set of sine-cosine functions in the Fourier series [1]. Orthogonal polynomials in the second class along with sine-cosine functions in the third class are continuous, whereas piecewise constant basis functions in the first class have discontinuities or jumps.…”