电子通信专业英语之信号线性系统篇.ppt

Signals, Linear Systems, and Convolution 课文讲解 Instead, we must find some way of making a finite number of measurements?that allow us to infer how the system will respond to other inputs that we have not yet measured [译文]因此，必须找到一些方法，通过一定数量的测试就能可以推断出系统对那些没有测试过的输入会有怎样的响应。 The type of signal which depends on one independent variable, namely, time is called the one-dimensional signal. It can be represented by x(t). [译文]一维信号是指取决于某一独立变量，即时间t的一类信号，可用x(t)来表示 。 Representing signals with impulses（用脉冲函数表示信号）. Any signal can be expressed as a sum of scaled and shifted unit impulses（任何信号都可以表述为许多经过缩放、位移的脉冲函数的总和）. We begin with the pulse or “staircase”（阶梯） approximation to a continuous signal, as illustrated in Figure4.1. Conceptually, this is trivial（简单的）: for each discrete sample of the original signal, we make a pulse signal. Then we add up all these pulse signals to make up the approximate signal. Each of these pulse signals can in turn （依次） be represented as a standard pulse scaled（缩放） by the appropriate value and shifted（位移） to the appropriate place. In mathematical notation（符号）: 用脉冲函数表示信号：任何信号都可以表述为许多经过缩放、位移的脉冲函数的总和。连续信号x(t) 可以用脉冲或阶梯函数来近似，如图4.1。从概念上来讲这很简单：原始信号的每一个离散采样都可以用一个脉冲函数来表示，然后将所有采样累加起来近似原始信号。每一个冲激信号依次可以表示为将一个标准脉冲进行适当的缩放和位移后得到。用数学公式表示如下： In other words, we can represent any signal as an infinite sum of shifted and scaled unit impulses. A digital compact disc, for example, stores whole complex pieces of music as lots of simple numbers representing（表示） very short impulses, and then the CD player adds all the impulses back together one after another to recreate（重构） the complex musical waveform. 也就是说，任何信号均可以由无限多个经过缩放、位移的单位冲激函数的和来表示。例如，数字CD机即是利用许多小的脉冲来储存完整而复杂的音乐，而这些冲激函数在CD机中是由大量简单的数字来表示。播放时，CD机依次将这些脉冲迭加起来重构复杂的音乐波形。 Systems come in a wide variety of types. One important class is known as linear systems. To see whether a system is linear, we need to test whether it obeys certain rules that all linear systems obey. The two basic tests（特性） of linearity（线性）