研究生复试《信号与系统 》英语翻译

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 reception 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 u[n] in the context of a discrete-time system.

3.A graphical description of the impulse δ[n] for discrete time is straightforward,as shown in Fig.1.38. In contrast,visualization of the unit impulse δ[t] for continuous time requires more detailed attention.One way to visualize δ[t] is to view it as the limiting form of a rectangular pulse of unit area,as illustrated 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 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 function 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 produce 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 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 discrete-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 description 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 completely 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 time-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 superposition is termed the convolution sun for discrete-time systems