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Analysis and Control of Linear Systems - Chapter 5

Chapter 5 Signals: Deterministic and Statistical Models 5.1. Giới thiệu Chương này là dành riêng cho tín hiệu mô hình thủ tục và đặc biệt là các tín hiệu văn phòng phẩm ngẫu nhiên. Sau khi thảo luận về các đặc tính quang phổ của tín hiệu xác định, với sự giúp đỡ của biến đổi Fourier và mật độ năng lượng quang phổ, chúng tôi sẽ xác định mật độ năng lượng quang phổ của tín hiệu văn phòng phẩm ngẫu nhiên. Chúng tôi sẽ cho thấy rằng một mô hình đơn giản bởi bộ lọc máy ép tuyến tính kích. | Chapter 5 Signals Deterministic and Statistical Models 5.1. Introduction This chapter is dedicated to signal modeling procedures and in particular to stationary random signals. After having discussed the spectral characterization of deterministic signals with the help of the Fourier transform and energy spectral density we will now define the power spectral density of stationary random signals. We will show that a simple modeling by linear shaper filter excited by a white noise makes it possible to approach a spectral density with the help of a reduced number of parameters and we will present a few standard structures of shaper filters. Next we will extend this modeling to the case of linear processes with deterministic input in which the noises and disturbances can be considered as additional stationary noises. Further on we will present the representation in the state space of such a modeling and the relation with the Markovian processes. 5.2. Signals and spectral analysis A continuous-time deterministic signal y t t G K is by definition a function of K in C y K C 11 y t where variable t designates time. In short we speak of a continuous signal even if the signal considered is not continuous in the usual mathematical sense. Chapter written by Eric Le Carpentier. 142 Analysis and Control of Linear Systems A discrete-time deterministic signal y k k e Z is by definition a sequence of complex numbers y MkEZ In short we often speak of a discrete signal. In general the signals considered be they continuous-time or discrete-time have real values but the generalization to complex signals done here does not entail any theoretical problem. The spectral analysis of deterministic signals consists of decomposing them into simpler signals for example sine curves in the same way as a point in space is located by its three coordinates. The most famous technique is the Fourier transform from the French mathematician J.B. Fourier 1768-1830 which consists of using cisoid functions