《信号与系统》课件 ch1.ppt

* SUMMARY 1. The concepts of signals and systems ; 2. The graphical and mathematical representations of signals ; 3. The classifications of signals ; 4. Transformations of the independent variable of signals ; 5. The periodicity of signals ; 6. Several basic signals ; 7. Interconnection of systems ; 8. Block diagram of systems ; 9. Properties of systems . * 作业： 1.21(d)(e)(f) 1.22(b)(d)(f) 1.25(c)(e)(f) 1.26 (b)(c)(d) 1.27(a)(b)(f) 1.28(c)(e)(g) 1.31 * A. For discrete-time complex exponential signals, we need to consider a frequency interval of 2?.(在考虑离散时间复指数时，仅需要在某一个2?间隔内选择即可） Thus, ej?0 n and ej(?0 + 2 ?) n are the same signals. ej?0 n不具备随?0在数值上的增加而不断增加其振荡速率的特性！ 当?0从０开始增加，其振荡速率愈来愈快，直到?0= ?,达到最大，若继续增加?0 ，其振荡速率就下降，直到?0= 2?时,又得到与?0=0时同样的效果(常数序列). * Lowest oscillation rate: Highest oscillation rate: * Continuous-time: e j?0t , T=2?/?0 Discrete-time: e j?0n , N=? Calculate period: By definition: e j?0n = e j?0(n+N) thus e j?0N = 1 or ?0N = 2? m So N = 2?m/?0 with interger N Condition of periodicity: 2?/?0 is rational. B. Periodicity of e j?0n 若2?/?0为一有理数， e j?0n就是周期的，否则就不是周期的． * C. Finite number of distinct harmonics For a periodic signal with fundamental period of N, There are only N distinct periodic exponentials for discrete-time signals. In the Continuous-time case,all of the harmonically related complex exponentials are distinct. * Unit Sample (Impulse): Unit Step Function: (4) The Discrete-Time Unit Impulse and Unit Step Sequences * Relationship between unit sample and unit step sequence the unit sample is the first difference of the unit step sequence the unit step sequence is the running sum of the unit sample or here * write any discrete-time signal in terms of delayed unit sample as Sampling Property of Unit Sample * Unit Step Function: Unit Impulse Function: (5) The Continuous-Time Unit Step and Unit Impulse Functions * Relation Between Unit Impulse and Unit Step *