A Few Signal Questions

In this paper,we will discuss a few signal questions and this paper consists of 3 chapters.In the first part,the present situation of two kinds-of signal question is stated . One is the frequency analysis problem and the other is about the stability of a iterat-ion method on signal equation.In the second part ,we investigate the frequency analysis problem .The freque-ncy analysis problem is to determine the unknown frequency wj when values of x(m) (observations) are known.We give a trigonometric signal XN (m) which in the discrete form iswhere are the amplitudes and wj are the unknown frequencies,N denotes the number of observed values ,m is discrete time .From the observations,we construct an absolutely continuous measure defined by discussing its weak star convengence and moments' properties. Furthermore,themeasure gives rise to an inner product and hence to a sequence of monic orthogonal polynomials -the Szego polynomials ,Its zeros can approximate critical frequency point is a unknown frequency). We also get the bound of Szego polynomials .In the third part ,we study stability of Ishikawa iteration procedure.Let (E) be a normed linear space ,Ta selfmap of E satisfyingLet P be a fixed point of T, x0 E and define where andsatisfy a few stable conditions .We shall prove that theIshikawa iteration procedure (1) is also T-stable and give its convergence rate .