1Lecture 2: Discrete-Time Systems and z-Transform•Discrete-time signals v.s. continuous-time signals•Discrete-time systems v.s. continuous-time systems•z-Transform •Inverse z-Transform•z-Transform for solving linear difference equationsContinuous-Time Signals•A signal that changes continuously in time:•Defined at all times t(no gap)•Signal can take arbitrary values• Example: temperature, position, velocity,…e(t);¡1< t <1;ort¸0e(t)t
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2•A signal (sequence, or series) whose values are defined only at discrete times:•Signal defined only at integer times k•Signal can still take arbitrary valuesDiscrete-Time Signals4¢¢¢¡1k013¢¢¢e(k)2e(k);k=:::;¡1;0;1;:::ork= 0;1;2;:::Origin of Discrete-Time Signals•Some come naturally–Population of a species in different generations–Annual growth percentage of GDP–Results of a numerical algorithm in different rounds of iteration•Some arise by sampling continuous-time signals at regular time intervals, say, every Tsecondse(t)te(kT)0T2T3T4T¡T¢¢¢¢¢¢e(t);¡1< t <1)e(kT);k=:::;¡1;0;1;:::)e(k);k=¢ ¢ ¢;¡1;0;1;:::;(ifTis known from the context)