数字信号处理与滤波器设计基础

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"《数字信号处理和滤波器设计》是由B.A. Shenoi撰写的一本专业书籍，由John Wiley & Sons, Inc. 出版。本书深入介绍了数字信号处理和滤波器设计的核心概念和技术，是电子工程、通信工程以及相关领域的经典教材。" 在数字信号处理领域，这本书可能会涵盖以下重要知识点： 1. **数字信号基础**：书中可能首先解释了数字信号的基本概念，包括离散时间信号和离散频谱分析，以及它们与模拟信号的区别。 2. **采样理论**：讲解奈奎斯特定理和香农采样定理，讨论如何从连续信号中正确地采样得到数字信号，避免信息损失。 3. **数字信号运算**：包括加法、乘法、卷积、傅里叶变换等基本运算，以及z变换和离散时间傅里叶变换（DTFT）在数字信号处理中的应用。 4. **滤波器设计**：滤波器是数字信号处理的关键部分，书可能详细讨论了各种类型的滤波器，如IIR（无限 impulse response）滤波器和FIR（有限 impulse response）滤波器的设计方法，包括巴特沃斯、切比雪夫、椭圆函数滤波器等。 5. **数字信号的频率响应**：如何分析和设计滤波器以实现特定的频率响应特性，例如低通、高通、带通和带阻滤波器。 6. **滤波器稳定性**：讨论滤波器的稳定性和振铃效应，以及如何通过改进结构和参数选择来避免这些问题。 7. **窗函数**：窗函数在滤波器设计中的作用，以及不同窗函数对滤波器性能的影响。 8. **数字信号处理的应用**：可能涉及信号增强、降噪、谱分析、调制解调、图像处理等方面的实际应用。 9. **MATLAB或Simulink工具**：可能介绍了使用这些软件工具进行数字信号处理和滤波器设计的方法。 10. **优化和实时处理**：讨论如何优化算法以适应实时系统，包括硬件实现和算法复杂度的考虑。这本教材不仅适合初学者理解基本概念，也为高级读者提供了深入的技术细节，有助于他们在实际项目中应用数字信号处理和滤波器设计的知识。同时，书中可能包含丰富的例题和实践练习，帮助读者巩固理论并提升技能。

PREFACE xv

of the optimization technique in the Remez exchange algorithm. However, I have

included many examples using the MATLAB functions to explain the subject

matter.

Solutions to the problems given at the end of chapters can be obtained by the in-

structors from the Website

http://www.wiley.com/WileyCDA/WileyTitle/

productCd-0471464821.html

. They have to access the solutions by clicking

“Download the software solutions manual link” displayed on the Webpage. The

author plans to add more problems and their solutions, posting them on the Website

frequently after the book is published.

As mentioned at the beginning of this preface, the book is written from my

own experience in teaching a junior-level course on digital signal processing.

I wish to thank Dr. M. D. Srinath, Southern Methodist University, Dallas, for

making a thorough review and constructive suggestions to improve the material

of this book. I also wish to thank my colleague Dr. A. K. Shaw, Wright State

University, Dayton. And I am most grateful to my wife Suman, who has spent

hundreds of lonely hours while I was writing this book. Without her patience

and support, I would not have even started on this project, let alone complete it.

So I dedicate this book to her and also to our family.

B. A. Shenoi

May 2005

2 INTRODUCTION

mobile phones, besides voice, music, and other audio signals—all of which are

classiﬁed as multimedia—because of limited hardware in the mobile phones and

not the software that has already been developed. However, the computers can

be used to carry out the same functions more efﬁciently with greater memory and

large bandwidth. We see a seamless integration of wireless telephones and com-

puters already developing in the marke t at present. The new technologies being

used in the abovementioned applications are known by such terms as CDMA,

TDMA,

spread spectrum, echo cancellation, channel coding, adaptive equaliza-

tion, ADPCM coding, and data encryption and decryption, some of which are

used in the software to be introduced in the third-generation (G3) mobile phones.

2. Speech Processing. The quality of speech transmission in real time over

telecommunications networks from wired (landline) telephones or wireless (cel-

lular) telephones is very high. Speech recognition, speech synthesis, speaker

veriﬁcation, speech enhancement, text-to-speech translation, and speech-to-text

dictation are some of the other applications of speech processing.

3. Consumer Electronics. We have already mentioned cellular or mobile

phones. Then we have HDTV, digital cameras, digital phones, answering

machines, fax and modems, music synthesizers, recording and mixing of music

signals to produce CD and DVDs. Surround-sound entertainment systems includ-

ing CD and DVD players, laser printers, copying machines, and scanners are

found in many homes. But the TV set, PC, telephones, CD-DVD players, and

scanners are present in our homes as separate systems. However, the TV set can

be used to read email and access the Internet just like the PC; the PC can be

used to tune and view TV channels, and record and play music as well as data

on CD-DVD in addition to their use to make telephone calls on VoIP. This trend

toward the development of fewer systems with multiple applications is expected

to accelerate in the near future.

4. Biomedical Systems. The variety of machines used in hospitals and biomed-

ical applications is staggering. Included are X-ray machines, MRI, PET scanning,

bone scanning, CT scanning, ultrasound imaging, fetal monitoring, patient moni-

toring, and ECG and EEC mapping. Another example of advanced digital signal

processing is found in hearing aids and cardiac pacemakers.

5. Image Processing. Image enhancement, image restoration, image under-

standing, computer vision, radar and sonar processing, geophysical and seismic

data processing, remote sensing, and weather monitoring are some of the applica-

tions of image processing. Reconstruction of two-dimensional (2D) images from

several pictures taken at different angles and three-dimensional (3D) images from

several contiguous slices has been used in many applications.

6. Military Electronics. The applications of digital signal processing in mili-

tary and defense electronics systems use very advanced techniques. Some of the

applications are GPS and navigation, radar and sonar image processing, detection

Code- and time-division multiple access. In the following sections we will mention several technical

terms and well-known acronyms without any explanation or deﬁnition. A few of them will be

described in detail in the remaining part of this book.

DISCRETE-TIME SIGNALS 3

and tracking of targets, missile guidance, secure communications, jamming and

countermeasures, remote control of surveillance aircraft, and electronic warfare.

7. Aerospace and Automotive Electronics. Applications include control of air-

craft and automotive engines, monitoring and control of ﬂying performance of

aircraft, navigation and communications, vibration analysis and antiskid control

of cars, control of brakes in aircrafts, control of suspension, and riding comfort

of cars.

8. Industrial Applications. Numerical control, robotics, control of engines and

motors, manufacturing automation, security access, and videoconferencing are a

few of the industrial applications.

Obviously there is some overlap among these applications in different devices

and systems. It is also true that a few basic operations are common in all the

applications and systems, and these basic operations will be discussed in the

following chapters. The list of applications given above is not exhaustive. A few

applications are described in further detail in [1]. Needless to say, the number of

new applications and improvements to the existing applications will continue to

grow at a very rapid rate in the near future.

1.3 DISCRETE-TIME SIGNALS

A signal deﬁnes the variation of some physical quantity as a function of one

or more independent variables, and this variation contains information that is of

interest to us. For example, a c ontinuous-time signal that is periodic contains the

values of its fundamental frequency and the harmonics contained in it, as well

as the amplitudes and phase angles of the individual harmonics. The purpose of

signal processing is to modify the given signal such that the quality of information

is improved in some well-deﬁned meaning. For example, in mixing consoles for

recording music, the frequency responses of different ﬁlters are adjusted so that

the overall quality of the audio signal (music) offers as high ﬁdelity as possible.

Note that the contents of a telephone directory or the encyclopedia downloaded

from an Internet site contains a lot of useful information but the contents do

not constitute a signal according to the deﬁnition above. It is the functional

relationship between the function and the independent variable that allows us to

derive methods for modeling the signals and ﬁnd the output of the systems when

they are excited by the input signals. This also leads us to develop methods for

designing these systems such that the information contained in the input signals

is improved.

We deﬁne a continuous-time signal as a function of an independent variable

that is continuous. A one-dimensional continuous-time signal f(t) is expressed

as a function of time that varies continuously from −∞ to ∞.Butitmaybe

a function of other variables such as temperature, pressure, or elevation; yet we

will denote them as continuous-time signals, in which time is continuous but the

signal may have discontinuities at some values of time. The signal may be a

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