Chapter 2
                                       Discrete-Time Signals & 
                                       Systems
                                       清大電機系林嘉文
                                       cwlin@ee.nthu.edu.tw
                                       03-5731152
                             Discrete-Time Signals
                             Signals are represented as sequences of numbers, called 
                              samples
                             Sample value of a typical signal or sequence denoted as x
                              = {x[n]} with − ∞ ≤ n ≤ ∞ 
                             x[n] is defined only for integer values of n and undefined for 
                              non-integer values of n
                             Representation of discrete-time signals:
                                Functional representation   xnnn2,      0
                                                               3,     n0
                                Tabularrepresentation             
                                Sequencerepresentation
                                           x(n) = {…,0.2, 2.2, 1.1, 0.2, -3.7, 2.9. …}
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                         Discrete-Time Signals
                         Graphical representation 
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                         Discrete-Time Signals
                         Sampling a speech signal
                                        xnx()nT,n
                                          a
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                                                           Basic Sequences
                                                            Unit sample sequence -  n 1,                                                       n0
                                                                                                                               0, n0
                                                                                                                                         
                                                                                                                                   1,       n0                                n
                                                                                                                                                                un                  k
                                                                                                                      un                                                            
                                                            Unit step sequence -                                        0, n0                                            
                                                                                                                                                                            k
                                                                                                                                                                              
                                                                                                                                                                                  nk
                                                                                                                                                                              
                                                                                                                                                                             k0
                                                                                                                                                              nu            nun1
                                                                                                                                                                                             
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                                                           Basic Sequences
                                                            Unit ramp signal -                                 unnn,0
                                                                                                                   r  0, n0
                                                                                                                               
                                                            Real exponential signal -
                                                                                                                 n
                                                                                              xnA    is a real value
                                                                                                 
                                                                                          0 <    1                                             >1
                                                                                            -1     0                                       -1
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                                Basic Sequences
                                 Complex exponential signal -
                                                                    n  j nj
                                                         nj            00
                                              x nAAe e              e
                                                
                                                           n
                                                   Ancos           jsin n
                                                                
                                                            
                           x nxnjxn                              00
                                          
                                   RI
                                         n
                               xnA cos n
                                           
                                R              0
                                          n
                               xnA sin n
                                            
                                I               0
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                                Basic Sequences
                                 Complex exponential signal -
                                               x nxnjxnxnxn
                                                                        
                                                       RI
                                                n
                                 x nAnr
                                        
                              x nn       n
                                       
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