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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 xnnn2, 0 3, n0 Tabularrepresentation Sequencerepresentation x(n) = {…,0.2, 2.2, 1.1, 0.2, -3.7, 2.9. …} 2011/3/2 Digital Signal Processing 2 1 Discrete-Time Signals Graphical representation 2011/3/2 Digital Signal Processing 3 Discrete-Time Signals Sampling a speech signal xnx()nT,n a 2011/3/2 Digital Signal Processing 4 2 Basic Sequences Unit sample sequence - n 1, n0 0, n0 1, n0 n un k un Unit step sequence - 0, n0 k nk k0 nu nun1 2011/3/2 Digital Signal Processing 5 Basic Sequences Unit ramp signal - unnn,0 r 0, n0 Real exponential signal - n xnA is a real value 0 < 1 >1 -1 0 -1 2011/3/2 Digital Signal Processing 6 3 Basic Sequences Complex exponential signal - n j nj nj 00 x nAAe e e n Ancos jsin n x nxnjxn 00 RI n xnA cos n R 0 n xnA sin n I 0 2011/3/2 Digital Signal Processing 7 Basic Sequences Complex exponential signal - x nxnjxnxnxn RI n x nAnr x nn n 2011/3/2 Digital Signal Processing 8 4
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