奥本海姆信号与系统期末复习PPT.pdf

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Signals & Systems Final Review Email:penghe@cqu.edu.cn Tel:+86-23-65111163 Lab of Optoelectronic Measurement and Imaging, Department of Optoelectronics Engineering, Chongqing University

CHAPTER 1 Signals & Systems

Chapter 1: Signals & Systems 1. Continuous-time and Discrete-time signals Signals: functions of one or more independent variables Continuous-time signal: signals are defined for a continuum of values of the independent variable; 2. Energy & Power Energy over t1 t  t2: Average power: ♠ 2018/6/5 2121)()(2ttttdttxdttp2121)(1)(121212ttttdttxttdttptt

Chapter 1: Signals & Systems Total Energy: (when t1→∞, t2→∞) Average Power: ♠ Finite Energy Signal : Finite Power Signal : 2018/6/5 ( P  0 ) ( E   ) dttxdttxETTT22)()(limTTTdttxTP2)(21limdttxE2)(TTTdttxTP2)(21lim

Chapter 1: Signals & Systems 3. Examples of Transformations A. Time Shift Replace the independent variable t in the signal x(t) by t-t0 t0>0 t0<0 x(t)  x(t-t0) Right Shift Left Shift Delayed Advanced B. Time Reversal x(t)  x(t) C. Time Scaling x(t)  x(at) 2018/6/5

Chapter 1: Signals & Systems Replace t by at+b (a&b are real constants) x(t) x(at+b) |a|>1: Time Compressed |a|<1: Time Stretched ♠ a<0: Time Reversal b≠0: Time Shift (b>0, left shift; b<0, right shift) (b>0, advanced; b<0, delayed) First Shift Then Scaling Finally Reversal Example 1.1~1.3(Illustration) 2018/6/5

Chapter 1: Signals & Systems 4 Periodic Signals: There is a positive value of T which : x(t)=x(t+T) , for all t x(t) is periodic with period T . The smallest T  Fundamental Period T0 x1(t) = Acos(3t)+ Bsin(2t) ♠ It is the sum of two periodic signals with T1= 2/ 3, T2= . x1(t) is periodic. T0  The smallest multiples of T1 and T2 in common, T0 = 2. x2(t) = Acos(t)+ Bsin(2t) It is the sum of two periodic signals with T1= 2, T2= . 2018/6/5 x2(t) is aperiodic.

Chapter 1: Signals & Systems Inversely proportional Frequency(Hz) Euler’s Relation: ♠ and

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