Discrete-Time Stochastic Processes

Chapter 3 focuses on the theory of discrete-time-stochastic processes, including their mathematical presentation in time and frequency domains. Typical discrete processes, including the Gaussian process, white noise and binary and harmonic processes, are presented. A comprehensive analysis of discrete-time stationary and ergodic processes and linear-time-invariant (LTI) systems with discrete stochastic inputs is presented. The processes are analysed in terms of their autocorrelation functions and power spectral densities that are related by the Wiener–Khintchine theorem. This chapter is placed at the beginning of the book because its content is a prerequisite for the chapters that follow, in particular, the chapter related to the theory of discrete communication systems. The unique notation used in this chapter will be used in the rest of the book. For readers of the book, it is highly advisable to read this chapter first and acquire its notation.

Continuous-Time Stochastic Processes

10.1093/oso/9780198860792.003.0019 ◽

2021 ◽

pp. 874-924

Author(s):

Stevan Berber

Keyword(s):

Stochastic Processes ◽

Continuous Time ◽

Communication Systems ◽

Linear Time ◽

Gaussian White Noise ◽

Linear Time Invariant ◽

Ergodic Processes ◽

Power Spectral ◽

Chapter 19 contains the theory of continuous-time stochastic processes, including their mathematical presentation in the time and frequency domains. The typical processes, including Gaussian, white noise, binary, and harmonic processes, are presented. A comprehensive analysis of stationary and ergodic processes and linear-time-invariant systems with stochastic inputs is presented. The processes are analysed in terms of their autocorrelation functions and power spectral densities, which are related via the Wiener–Khintchine theorem. This chapter is important for understanding the theory of digital communication systems. The notation used in this chapter complies with the notation used in other chapters of the book, which makes the book self-sufficient. For readers who are not familiar with continuous-time stochastic processes, it is highly advisable to read this chapter and become familiar with its notation, due to its importance for understanding the content of Chapters 3 to 9.

Deterministic Discrete-Time Signals and Systems

10.1093/oso/9780198860792.003.0014 ◽

2021 ◽

pp. 690-713

Author(s):

Stevan Berber

Keyword(s):

Discrete Time ◽

Communication Systems ◽

Linear Time ◽

Linear Time Invariant ◽

Discrete Signals ◽

Time Signals ◽

Analysis And Synthesis ◽

Definition Of ◽

Due to the importance of the concept of independent discrete variable modification and the definition of discrete linear-time-invariant systems, Chapter 14 presents and discusses basic deterministic discrete-time signals and systems. These discrete signals, which are expressed in the form of functions, including the Kronecker delta function and the discrete rectangular pulse, are used throughout the book for deterministic discrete signal analysis. The chapter also presents the definition of the autocorrelation function and the explanation of the convolution procedure in linear-time-invariant systems for discrete-time signals in detail, due to the importance of these in the analysis and synthesis of discrete communication systems.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

Full-Order Observer for Discrete-Time Linear Time-Invariant Systems with Output Delays

10.1587/transfun.e97.a.1975 ◽

2014 ◽

Vol E97.A (9) ◽

pp. 1975-1978

Author(s):

Joon-Young CHOI

Keyword(s):

Discrete Time ◽

Linear Time ◽

Linear Time Invariant ◽

Time Invariant ◽

Time Linear

Linear Time Invariant Homogeneous Matrix Descriptor (Singular) Discrete-Time Systems with Non Consistent Initial Conditions

2010 Sixth International Conference on Networking and Services ◽

10.1109/icns.2010.60 ◽

2010 ◽

Cited By ~ 1

Author(s):

Athanasios A. Pantelous ◽

Athanasios D. Karageorgos ◽

Grigoris I. Kalogeropoulos

Keyword(s):

Discrete Time ◽

Initial Conditions ◽

Linear Time ◽

Linear Time Invariant ◽

Discrete Time Systems ◽

Homogeneous Matrix ◽

Time Invariant ◽

Time Systems

Simultaneous global external and internal stabilization of linear time-invariant discrete-time systems subject to actuator saturation

Automatica ◽

10.1016/j.automatica.2012.02.004 ◽

2012 ◽

Vol 48 (5) ◽

pp. 699-711 ◽

Cited By ~ 9

Author(s):

Xu Wang ◽

Ali Saberi ◽

Anton A. Stoorvogel ◽

Peddapullaiah Sannuti

Keyword(s):

Discrete Time ◽

Actuator Saturation ◽

Linear Time ◽

Linear Time Invariant ◽

Discrete Time Systems ◽

Internal Stabilization ◽

Time Invariant ◽

Time Systems

Design Methods for Discrete-Time, Linear Time-Invariant Systems

Control System Fundamentals ◽

10.1201/9781315214030-14 ◽

2019 ◽

pp. 283-302

Author(s):

Mohammed S. Santina ◽

Allen R. Stubberud ◽

Gene H. Hostetter

Keyword(s):

Discrete Time ◽

Linear Time ◽

Design Methods ◽

Linear Time Invariant ◽

Time Invariant ◽

Time Linear

FE Analysis of Communications Systems for Drive-Thru Restaurants in a Business Dispute Over Specifications and Design Process

Journal of the National Academy of Forensic Engineers ◽

10.51501/jotnafe.v38i1.106 ◽

2021 ◽

Vol 38 (1) ◽

Author(s):

Robert Peruzzi

Keyword(s):

Communication System ◽

Communication Systems ◽

Linear Time ◽

Forensic Analysis ◽

Time Varying ◽

Audio Quality ◽

Linear Time Invariant ◽

Quick Service ◽

Forensic analysis in this case involves the design of a communication system intended for use in Quick Service Restaurant (QSR) drive-thru lanes. This paper provides an overview of QSR communication system components and operation and introduces communication systems and channels. This paper provides an overview of non-linear, time-varying system design as contrasted with linear, time-invariant systems and discusses best design practices. It also provides the details of how audio quality was defined and compared for two potentially competing systems. Conclusions include that one of the systems was clearly inferior to the other — mainly due to not following design techniques that were available at the time of the project.

Deterministic Continuous-Time Signals and Systems

10.1093/oso/9780198860792.003.0011 ◽

2021 ◽

pp. 562-598

Author(s):

Stevan Berber

Keyword(s):

Discrete Time ◽

Continuous Time ◽

Linear Time ◽

Continuous Variable ◽

Linear Time Invariant ◽

Time Signals ◽

Analysis And Synthesis ◽

Definition Of ◽

Due to the importance of the concept of independent variable modification, the definition of linear-time-invariant system, and their implications for discrete-time signal processing, Chapter 11 presents basic deterministic continuous-time signals and systems. These signals, expressed in the form of functions and functionals such as the Dirac delta function, are used throughout the book for deterministic and stochastic signal analysis, in both the continuous-time and the discrete-time domains. The definition of the autocorrelation function, and an explanation of the convolution procedure in linear-time-invariant systems, are presented in detail, due to their importance in communication systems analysis and synthesis. A linear modification of the independent continuous variable is presented for specific cases, like time shift, time reversal, and time and amplitude scaling.

Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220943071 ◽

2020 ◽

Vol 42 (16) ◽

pp. 3168-3182

Author(s):

Okan Demir ◽

Hitay Özbay

Keyword(s):

Discrete Time ◽

Output Feedback ◽

Linear Time ◽

Feedback Stabilization ◽

Mixed Integer ◽

Static Output Feedback ◽

Linear Time Invariant ◽

Time Invariant ◽

Time Linear ◽

Static Output

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

Modal Control of Linear Time-Invariant Discrete-Time Systems

Measurement and Control ◽

10.1177/002029406900200808 ◽

1969 ◽

Vol 2 (8) ◽

pp. T133-T136 ◽

Cited By ~ 2

Author(s):

B. Porter ◽

T. R. Crossley

Keyword(s):

Discrete Time ◽

Linear Time ◽

Feedback Loops ◽

Modal Control ◽

Discrete Time System ◽

Linear Time Invariant ◽

Modal Theory ◽

Discrete Time Systems ◽

Time Invariant ◽

Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.