研究生复试《信号与系统》英语翻译

1、1.For example,in speech communication,a sound source or signal excites the vocal tract,which represents a system.The processing of speech signals usually relies on the use of our ears and auditory pathways in the brain.In the situation described here,the systems responsible for the production and re

2、ception of signals are biological in nature.2.As a test signal,it is useful because the output of a system due to a step input reveals a great deal about how quickly the system responds to an abrupt change in the input signal.A similar remark applies to un in the context of a discrete-time system.3.

3、A graphical description of the impulse n for discrete time is straightforward,as shown in Fig.1.38. In contrast,visualization of the unit impulse t for continuous time requires more detailed attention.One way to visualize t is to view it as the limiting form of a rectangular pulse of unit area,as il

4、lustrated in Fig.1.39(a).4.Having defined what a unit impulse is and described its properties,there is one more question that needs to be addressed:What is the practical use of a unit impulse?We cannot generate a physical impulse function,since that would correspond to a signal of infinite amplitude

5、 at t=0 and that is zero elsewhere.5.In mechanical terms,a ramp function may be visualized as follows.If the input variable is represented as the angular displacement of a shaft,then the constant-speed rotation of the shaft provides a representation of the ramp function.As a test signal,the ramp fun

6、ction enables us to evaluate how a continuous-time system would respond to a signal that increases linearly with time.6.Form an engineering perspective,it is important that a system of interest remains stable under all possible operating conditions.It is only then that the system is guaranteed to pr

7、oduce a bounded output for a bounded input.Unstable systems are usually to be avoided,unless some mechanism can be found to stabilize them.7.In general,the problem of finding the inverse of a given system is a difficult one.In any event,a system is not invertible(可逆矩阵) unless distinct inputs applied

8、 to the system produce distinct outputs.That is,there must be a one-to-one mapping between input and output signals for a system to be invertible.8.A continuous-time system is described by an operator that changes a continuous-time input signal into a continuous-time output signal.In contrast,a disc

9、rete-time system is described by an operator that changes a discrete-time input signal into a discrete-time output signal.9.In this chapter we consider several methods for describing the relationship between the input an output of linear time-invariant(LTI) systems.The focus here is on system descri

10、ption that relate the output signal to the input signal when both signals are represented as functions of time,hence the terminology “time domain” in the chapter title.10.The impulse response is the output of a LTI system due to an impulse input applied at time t=0 or n=0.The impulse response comple

11、tely characterizes the behavior of any LTI system.This may seem surprising,but it is a basic property of all LTI systems.11.If the input to a linear system is expressed as a weighted superposition of time-shifted impulses,then the output is a weighted superposition of the system response to each tim

12、e-shifted impulse.If the system is also time invariant,then the system response to a time-shifted impulse is a time-shifted version of the system response to an impulse.12.Hence the output of a LTI system is given by a weighted superposition of time-shifted impulse responses.This weighted superposit

13、ion is termed the convolution sun for discrete-time systems and the convolution integral for continuous-time systems.13.We begin by considering the discrete-time case.First an arbitrary signal is expressed as a weighted superposition of time-shifted impulses.The convolution sum is then obtained by a

14、pplying a signal represented in this manner to a LTI system.A similar procedure is used to obtain the convolution integral for continuous-time systems later in this section.14.In general,the output of any discrete-time system with a finite-duration impulse response is given by a weighted sum of the

15、input signal values.Such weighted sums can easily be implemented in a computer to process discrete-time signals.The effect of the system on the signal depends on the weights or values of the system impulse response.15.The output of a continuous-time LTI system may also be determined solely form know

16、ledge of the input and the systems impulse response.The approach and result are analogous to the discrete-time case.We first express an arbitrary input signal sa a weighted superposition of time-shifted impulses.16.Note that the identify system is represented for a=0 since in this case the output is

17、 equal to the input.When a0,the system time shifts the input.If a is positive the input is delayed,and if a is negative the input is advanced.Hence the location of the impulse response relative to the time origin determines the amount of delay introduced by the system.17.The impulse response complet

18、ely characterizes the input-output behavior of a LTI system. Hence properties of a system,such as memory, causality, and stability, are related to its impulse response.Also, the impulse response of an interconnection of LTI systems is related to the impulse response of the constituent systems.18.In

19、this section,we examine the impulse response of interconnected systems and relate the impulse response to system properties.These relationships tell us how the impulse response characterizes system behavior.The results for continuous and discrete-time systems are obtained using nearly identical appr

20、oaches.19.A system can be viewed as any process that results in the transformation of signals.Thus, a system has an input signal and an output signal which is related to the input through the system transformation.20.To illustrate the procedure for checking whether a system is time-invariant or not

21、and at the same time to gain some insight into this property, let us consider the continuous-time system defined by To check if this system is time-invariant or time-varying,we proceed as follows.Let be any input to this system,and let Be the corresponding output.Then consider a second input obtaine

22、d by shifting :The output corresponding to this input is 21. Mathematically,let y1(t) be the response of a continuous-time system to x1(t) and let y2(t) be the output corresponding to the input x2(t).Then the system is linear if: 1. The response to x1(t)+x2(t) is y1(t)+y2(t). 2. The response to ax1(

23、t) is ay1(t),where a is any complex constant.22. 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.Such a system is often referred to as being nonanticipative, as the system output does not anticipate future values of the input.23. D

24、iscrete-time systems and convolution have identical properties to their continuous-time counterparts.The impulse response of a cascade connection of LTI systems is given by the convolution of the individual impulse response and the output of a cascade combination of LTI systems is independent of the

25、 order in which the systems are connected.24. Interconnection of systems occur naturally in analysis.Often it is easier to break a complex system into simpler subsystems,analyze each subsystem,and then study the entire system as an interconnection of subsystems than it is to analyze the overall system directly.25. This is an example of the “divide-and-conquer” approach to problem solving and is possible due to the assumptions of linearity and time invariance.Interconnections of systems are also