MATLAB实用教程：工程师必备的信号处理与分析应用手册

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"《实用Matlab工程应用手册》是一本针对工程师编写的实践指南，由Misza Kalechman教授撰写，他是纽约城市科技学院电气与电信工程技术系的教授，隶属于纽约市立大学城市大学系统。该书是CRC Press出版于2009年的作品，版权属于Taylor & Francis Group。书中深入探讨了Matlab在工程领域的实际应用，包括时间域信号表示、直流和暂态分析、交流电流分析、傅里叶和拉普拉斯变换、离散傅里叶变换（DFT）、快速傅里叶变换（FFT）以及模拟与数字滤波器的设计等内容。第1章介绍了时间域信号的连续和离散表示，包括介绍、目标、背景知识，并通过大量实例帮助读者理解概念。随后的章节分别聚焦于直流和暂态分析、交流电流分析，以及频域分析工具如傅里叶变换和拉普拉斯变换。此外，还详细讲解了离散时间傅立叶变换（DTFT）、离散傅立叶变换（DFT）、z变换和快速傅立叶变换（FFT）在工程中的应用，这些都是信号处理和系统分析的核心技术。在第六章，作者讨论了模拟和数字滤波器的设计，这是电子工程中至关重要的部分，能够用于信号滤波、信号调理等任务。每个章节都包含应用问题，旨在让读者通过解决实际问题来巩固所学知识，并鼓励他们将Matlab技能应用于工程项目中。值得注意的是，书中使用了Matlab这一商标，但明确指出The MathWorks公司并未对本书的内容或示例提供官方保证，其使用仅出于许可，且不构成对特定教学方法或软件使用的支持或赞助。本书先前由Pearson Education出版，现由CRC Press发行，强调了美国政府作品的声明，并表明书籍是在美国使用环保纸张印刷的。《实用Matlab工程应用手册》是一本实用的教材，适合工程师在工程设计、数据分析和信号处理等领域提升Matlab技能，解决实际工程问题。"

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Time Domain Representation of Continuous and Discrete Signals 5

R.1.3 Analytically, the sampling process is accomplished by multiplying f(t) by a se-

quence of impulses. The concept of the unit impulse δ(t), also known as the Dirac

function, is introduced and discussed next.

R.1.4 The unit impulse, denoted by δ(t), also known as the Dirac or the Delta function, is

de ned by the following relation:

()tdt



∞

∞

∫

meaning that the area under [δ(t)] = 1,

where

(t) = 0, for t ≠ 0

(t) = 1, for t = 0

δ(t) is an even function, that is, δ(t) = δ(−t).

The impulse function δ(t) is not a true function in the traditional mathematical

sense. However, it can be de ned by the following limiting process:

by taking the limit of a rectangular function with an amplitude 1/τ and width τ,

when τ approaches zero, as illustrated in Figure 1.2.

The impulse function δ(t), as de ned, has been accepted and widely used by engi-

neers and scientists, and rigorously justi ed by an extensive literature referred as

the generalized functions, which was  rst proposed by Kirchhoff as far back as

1882. A more modern approach is found in the work of K.O. Friedrichs published

in 1939. The present form, widely accepted by engineers and used in this chapter is

attributed to the works of S.L. Sobolov and L. Swartz who labeled those functions

with the generic name of distribution functions.

Teams of scientists developed the general theory of generalized (or distribu-

tion) functions apparently independent from each other in the 1940s and 1950s,

respectively.

R.1.5 Observe that the impulse function δ(t) as de ned in R.1.4 has zero duration, unde-

 ned amplitude at t = 0, and a constant area of one. Obviously, this type of func-

tion presents some interesting properties when analyzed at one point in time, that

is, at t = 0.

lim

{

FIGURE 1.2

The impulse function δ(t).

CRC_47760_CH001.indd 5CRC_47760_CH001.indd 5 7/25/2008 4:16:10 PM7/25/2008 4:16:10 PM

Time Domain Representation of Continuous and Discrete Signals 9

In general, the set of samples given by f(−n), f(−n + 1), …, f(0), f(1), …, f(n − 1), f(n),

can be real or complex. f(n) is called a real sequence if all its samples are real and a

complex sequence if at least one sample is complex.

Observe that any (discrete) sequence f(n) can be expressed by the equation

fn fk n k

() ()( )



 





∑

Examples of analog signals are often encountered in nature such as sound, tem-

peratures, pressure, growth, and precipitations waves.

Discrete time signals or events are usually man-made functions such as weekly

pay, monthly payment of a loan or mortgage, or the (U.S.) presidential election

every 4 years.

Discrete signals are often confused with digital signals and binary signals. A

digital signal f(nT) or in short f(n) is a discrete time signal whose values are one of

a prede ned  nite set of values.

A binary signal is a discrete signal whose values consist of either zeros or ones.

An analog or continuous time function or signal can be transformed into a digital

signal using an A/D. Conversely, a digital signal can be converted into an analog

signal by means of a digital to analog converter (D/A).

Digital signals are frequently encoded using binary codes such as ASCII* into

strings of ones and zeros because in this format they can be stored and processed

by digital devices such as computers, and are in general more immune to noise and

interference.

R.1.16 The discrete impulse sequence δ(n) also called the Kronecker delta sequence (named

after the German mathematician Leopold Kronecker [1823–1891]) is de ned ana-

lytically as follows and illustrated in Figure 1.7.

()n



10

for

for 







Note that the discrete impulse is similar to the analog version δ(t).

R.1.17 A discrete shifted impulse δ(n − m) is illustrated in Figure 1.8.

The ASCII code is de ned in Chapter 3 of Practical MATLAB

Basics for Engineers.

−2 −1

1230

FIGURE 1.7

Plot of the discrete impulse δ(n).

FIGURE 1.8

Plot of δ(n − m).

m − 1 m m + 1

(n − m)

CRC_47760_CH001.indd 9CRC_47760_CH001.indd 9 7/25/2008 4:16:11 PM7/25/2008 4:16:11 PM

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