ch1第一章-四川大学信号与系统.pptVIP

* Example of Feedback interconnection Figure 1.44 (p43) (a) Simple electrical circuit; (b) block diagram. * 1.6 BASIC SYSTEM PROPERTIES (p44) (基本系统性质) 1.6.1 Systems with and without Memory (p44) (记忆系统与无记忆系统) Memoryless system(无记忆系统): Its output is dependent only on the input at the same time. Features: No capacitor, no conductor, no delayer. Memory system(记忆系统): Its output is dependent not only on the input at times other than the current time. Features: capacitor, conductor, delayer. * Examples of memoryless system: y(t) =Rx(t) (p44, 1.91) or y[n]-0.5y[n-1]=2x[n] Examples of memory system: y[n] =x[n] (p44, 1.92) * 1.6.2 Invertibility and Inverse Systems (p45) (可逆性与可逆系统) Definition: A system is said to be invertible if distinct inputs lead to distinct outputs. If system is invertable (可逆),then an inverse system exists. An inverse system cascaded (级联) with the original system,yields an output equal to the input. y(t)=2x(t) (p45, 1.97) * Figure 1.45 (p46). * 1.6.3 Causality (p46) (因果性) Definition: A system is causal If the output at any time depends only on values of the input at the present time and in the past. For causal system, if x(t)=0 for tt0, there must be y(t)=0 for tt0. ( nonanticipative(不可预测的) ) Memoryless systems are causal. x(t) y(t) t1 t2 * Example 1.12 (p47) Checking the causality of two systems. The first system is defined by It depends on future value, so it is not causal. The second system is defined by It is important to distinguish carefully the effects of the input from those of any other functions used in the definition of the system. It depends on current value, so it is causal. (p47, 1.105) (p47, 1.106) * 1.6.4 Stability (p48) (稳定性) Definition: If the input to a stable system is bounded (i.e., if its magnitude does not grow without bound), then the output must also be bounded. Finite input lead to finite output: if |x(t)|M, then |y(t)|N .