Chapter 2 Chapter 2A Part A-Discrete-Time Signals Part A ●●● Part B--Discrete-Time Systems ●●● ●●●● Discrete-Time Signals and Part C--Time-Domain Characterization of Discrete-Time Signals Systems in the Time-Domain LTI Discrete-Time Systems Part A:Discrete-Time Signals 1.Time-Domain Representation 1.Time-Domain Representation Signals represented as sequences of numbers, Discrete-time signal may also be written as a Time-Domain Representation called samples(采样、样本) sequence of numbers inside braces: Operations on Sequences Sample value of a typical signal or sequence denoted as x(n)with n being an integer in the {(m}={.,-0.2.22,1.10.2,-3,7,2.9} Classification of Sequences range-∞≤m≤∞ In the above,x(-1=-0.2,x0=2.2,x3=-3 ·Typical Sequences .x(n)defined only for integer values of n and etc. ·The Sample Process undefined for non-integer values of n The arrow is placed under the sample at time Discrete-time signal represented by {x (n) indexn=0 4 6Chapter 2A Discrete-Time Signals and Systems in the Time-Domain 2 Chapter 2 Part A -- Discrete Discrete-Time Signals Time Signals Part B -- Discrete Discrete-Time Systems Time Systems Part C -- Time-Domain Characterization of Domain Characterization of LTI Discrete LTI Discrete-Time Systems Time Systems Part A Discrete-Time Signals 4 Part A: Discrete-Time Signals Time-Domain Representation Domain Representation Operations on Sequences Operations on Sequences Classification of Sequences Classification of Sequences Typical Sequences Typical Sequences The Sample Process The Sample Process 5 1. Time-Domain Representation Signals represented as sequences of numbers, called samples samples ˄䟷ṧǃṧᵜ˅ Sample value of a typical signal or sequence denoted as x (n) with n being an integer in the range ˉĞİnİĞ x(n) defined only for integer values of n and undefined for non-integer values of n Discrete-time signal represented by {x (n)} 6 Discrete-time signal may also be written as a sequence of numbers inside braces: {x(n)}={…, ˉ0.2, 2.2, 1.1, 0.2, ˉ3, 7, 2.9, …} In the above, x(ˉ1)= ˉ0.2, x(0)=2.2, x(3)=ˉ3 etc. The arrow is placed under the sample at time index n = 0 1. Time-Domain Representation