ELC 4351: Digital Signal Processing
                                                        Liang Dong
                                          Electrical and Computer Engineering
                                                      Baylor University
                                                   liang dong@baylor.edu
                                                  September 1, 2016
       Liang Dong (Baylor University)           Discrete-Time Signals and Systems                 September 1, 2016       1 / 44
    Discrete-time Signals and Systems
    1    Discrete-time Signals
    2    Discrete-time Systems
    3    Analysis of Discrete-time Linear Time-Invariant Systems
    4    Implementation of Discrete-time Systems
    5    Correlation of Discrete-time Signals
       Liang Dong (Baylor University)           Discrete-Time Signals and Systems                 September 1, 2016       2 / 44
   Elementary Discrete-time Signals
       1   Unit sample sequence
                                              δ(n) =  1, n = 0
                                                             0,    n 6= 0
       2   Unit step signal                              
                                              u(n) =         1,    n ≥ 0
                                                             0,    n < 0
       3   Unit ramp signal                              
                                             u (n) =          n,    n ≥ 0
                                               r              0,    n < 0
       4   Exponential signal
                                                     n          jθ n       n jθn
                                        x(n) = a = (re ) = r e
      Liang Dong (Baylor University)       Discrete-Time Signals and Systems            September 1, 2016   3 / 44
    Classification of Discrete-time Signals
      Energy signals vs. power signals
                          P
    Energy: E =               ∞         |x(n)|2.
                              n=−∞
    If E is finite, 0 < E < ∞, x(n) is energy signal.
                                                P
    Power: P = lim                         1        N         |x(n)|2 = lim                     1    E .
                              N→∞2N+1               n=−N                           N→∞2N+1 N
    E finite ⇒ P = 0.
    If P is finite, 0 < P < ∞, x(n) is power signal.
       Liang Dong (Baylor University)           Discrete-Time Signals and Systems                 September 1, 2016       4 / 44