tailieunhanh - Phân tích tín hiệu P1

Signals and Signal Spaces The goal of this chapter is to give a brief overview of methods for characterizing signals and for describing their properties. Wewill start with a discussion of signal spaces such as Hilbert spaces, normed and metric spaces. Then, the energy density and correlation function of deterministic signals will be discussed. The remainder of this chapter is dedicated to random signals, which are encountered in almost all areas of signal processing. Here, basic concepts such as stationarity, autocorrelation, and power spectral densitywill be discussed. . | Signal Analysis Wavelets Filter Banks Time-Frequency Transforms and Applications. Alfred Mertins Copyright 1999 John Wiley Sons Ltd Print ISBN 0-471-98626-7 Electronic ISBN 0-470-84183-4 Chapter 1 Signals and Signal Spaces The goal of this chapter is to give a brief overview of methods for characterizing signals and for describing their properties. We will start with a discussion of signal spaces such as Hilbert spaces normed and metric spaces. Then the energy density and correlation function of deterministic signals will be discussed. The remainder of this chapter is dedicated to random signals which are encountered in almost all areas of signal processing. Here basic concepts such as stationarity autocorrelation and power spectral density will be discussed. Signal Spaces Energy and Power Signals Let us consider a deterministic continuous-time signal x t which may be real or complex-valued. If the energy of the signal defined by OO Ex rr i 2 dt J oo 1-1 is finite we call it an energy signal. If the energy is infinite but the mean power 1 rT 2 Px lim -T-voo T J-T 2 rr t 2 dt 1 2 Chapter 1. Signals and Signal Spaces is finite we call a t a power signal. Most signals encountered in technical applications belong to these two classes. A second important classification of signals is their assignment to the signal spaces Lp a 6 where a and b are the interval limits within which the signal is considered. By Lp a 6 with 1 p oo we understand that class of signals x for which the integral b a t p dt to be evaluated in the Lebesgue sense is finite. If the interval limits a and b are expanded to infinity we also write Lp oo or LP 1R . According to this classification energy signals defined on the real axis are elements of the space L2 R . Normed Spaces When considering normed signal spaces we understand signals as vectors that are elements of a linear vector space X. The norm of a vector x can somehow be understood as the length of x. The notation of the .