信号与系统技术分析.pptx

Signals and Systems----Lecture 3 Y. C. Zeng Sep. 12th, 2014 2 天下事有难易乎?为之，则难者亦易矣；不为，则易者亦难矣。人之为学有难易乎?学之，则难者亦易矣；不学，则易者亦难矣。 …… --------[清]彭端淑 3 2) The second typical continuous-time signal Unit impulse(delta signal / Dirac function) （1）definition 4 (2)the properties of Delta function ① Delta multiplied by a continuous-time function 5 Problems 6 t0 How to express the sampled by using x(t), Delta ？ How to express x(t) by using Delta function？ ②the sampled signal value of a continuous-time signal 7 Sampling implementation multiplier integrator 用什么样的电路来实现采样呢？ 8 3) The third typical continuous-time signal The general form of complex exponential signal Is it a/an ①continuous or discrete？ ②analog or digital？ ③real or complex？ ④deterministic or stochastic？ ⑤odd or even？⑥periodic or non-periodic？ ⑦energy or power？ 9 10 Let T is the period 11 4) The fourth typical continuous-time signal Real exponential signal 12 5) The fifth typical continuous-time signal The sine signal 13 The Unit step sequence, defined as Note: n=0, u[0] is defined 6) The first typical discrete-time signal 14 u[n+1] u[n-2] 15 Unit impulse sequence It is defined as following 7) The second typical discrete-time signal remark: It is completely different from u(t) 16 (1) Time shift 17 (2) Unit impulse sequence multiplied by the other sequence： 18 (3)the relations between unit impulse sequence and unit step sequence 19 Now what is the formula for the discrete? For the continuous 20 .complex exponential sequence 8) The third typical discrete-time signal It is ①continuous or discrete？ ②analog or digital？ ③real or complex？ ④deterministic or stochastic？ ⑤odd or even？⑥periodic or non-periodic？ ⑦energy or power？ 21 Due to Euler formula , we have 22 For instance: 23 24 25 Deriving the periodic condition 26 is periodic for the variable 27 Real exponential sequence 9) The fourth typical discrete-time signal 28 29 initial phase Is x[n] a periodic signal？ 10) T