MATLAB实现的数字滤波器原理与应用深度解析

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《Digital Filters Principles and Applications with MATLAB》是一本专门针对数字滤波器的深入研究著作，它并非一般意义上的数字信号处理(DSP)教程，而是聚焦于滤波器设计、理论与应用的全面探讨。该书以系统性的方式组织内容，首先从滤波器的目的出发，逐步展开各个主题和子话题，强调它们在核心概念中的地位，以及理论框架的建立。作者在讲解中紧密结合实际，通过MATLAB平台的活动和实例，帮助读者理解滤波器的工作原理和设计过程。书中内容涵盖了滤波器设计的各个方面，包括但不限于滤波器类型（如低通、高通、带通和带阻）、频率响应、稳定性分析、滤波器设计方法（如巴特沃斯、切比雪夫和椭圆滤波器）以及数字滤波器在无线通信、图像处理、音频信号处理等领域的具体应用。每章最后都会提供一个综合的设计案例研究，让读者能够将理论知识转化为实践操作能力。作者John B. Anderson以其深厚的专业背景，结合MATLAB工具，确保了读者不仅能够掌握理论知识，还能通过实例掌握实际编程技巧。这使得本书成为电子工程、通信工程、信号处理等相关专业学生和研究人员的理想学习资料，也可供从事数字信号处理工作的工程师参考和应用。通过阅读这本书，读者可以期待深入理解数字滤波器的构造、工作原理、优化策略，以及如何利用MATLAB进行滤波器设计与仿真。无论是初学者还是经验丰富的专业人士，都能从中收获宝贵的理论基础和实践经验，提升在数字化时代的信号处理能力。

SIGNAL TAXONOMY 7

ted to a receiver where it was demodulated, returning all the samples to their original

sign. This gave rise to a technology called sampled - data control, which had a strong

following in the 1950s and 1960s.

The most enduring technology emerging from this era is found in telephony.

It was discovered that a number of distinct discrete - time time series could be inter-

laced (i.e., time - division multiplexed) onto a common channel, thereby increasing

the channel ’ s capacity in terms of the number of subscribers per line per unit time.

The result was that the telephone company could bill multiple clients for using a

single copper line. Claude Shannon developed the mathematical framework by

which these signals can be time multiplexed, transmitted along a common line, and

reconstructed at each individual receiver. Shannon ’ s innovation, known as Shannon ’ s

sampling theorem, has been a driving force behind most DSP techniques and

methodologies.

Digital Signals

Digital signals are discrete - time signals that are also quantized along the dependent

axis (amplitude). Digital signals can be produced by a digital computer using ﬁ nite

precision arithmetic or by passing an analog signal x ( t ) through an ADC or A/D,

also producing a ﬁ nite precision approximation of a discrete - time signal. In either

case, quantizing the amplitude of the original signal introduces an uncertainty called

quantization error. Controlling and managing such errors is often critical to the suc-

cessful design of a DSP solution.

A general signal taxonomy is presented in Figure 1.4 . Contemporary signal

processing systems typically contain a mix of analog, discrete, and digital signals

and systems. A signal ’ s original point of origin is often the continuous - time or analog

domain. Digital signals, however, are becoming increasingly dominant in this mix.

Applications that were once considered to be exclusively analog, such as sound

Figure 1.4 Signal hierarchy consisting of an analog, discrete - time or sampled signal, and

digital or quantized signal process.

0 50

3.00

3.01

3.02

3.03

3.00

3.01

3.02

3.03

050

Continuous

Time

Discrete

Time

050

3000

3010

3020

3030

Digital

8 CHAPTER 1 INTRODUCTION TO DIGITAL SIGNAL PROCESSING

recording and reproduction, have become digital. The wireless communications

industry are replacing analog components in radios, as well as back - end audio and

signal decoding sections, with digital devices. Images and video signals are now

routinely coded and decoded as digital signals. Discrete - time systems, as deﬁ ned,

are rarely found in use today except as part of the sampling subsystems (samplers)

found in ADCs. The reason for this paradigm shift from analog signal processing to

DSP is primarily due to two breakthroughs. The ﬁ rst is the sampling theorem and

the second is the product of the fruitful digital semiconductor industry. Once this

bridge was crossed, it became logical to replace everything possible with digital

technology.

DSP : A DISCIPLINE

Signal processing is a gift of the sampling theorem and formidable armada of com-

panion theories, methodologies, and tools, such as the celebrated FFT. Initially DSP

was envisioned simply as an analog replacement technology. It is now clearly appar-

ent to many that DSP will move into new areas and become the dominant signal

processing technology in the 21st century. DSP has matured to the point where it

can claim to be an academic discipline replete with a rich infrastructure industry.

DSP continues to gain semiconductor market share mainly because it can deliver

solutions. The DSP advantage is summarized below.

Digital Advantages

The attributes of a digital solution are as follows:

• Both analog and digital systems can generally be fabricated as highly

integrated semiconductor systems. Compared with analog circuitry, digital

devices can take full advantage of submicron technologies and are generally

more electronically dense, resulting in both economic and performance

advantages.

• As semiconductor technologies shrink (deep submicron) and signal voltages

continue to decline (1.25 V and lower), the intrinsic signal - to - noise ratio found

at the transistor level decreases. Digital systems are far more tolerant of such

internal noise. These devices, however, are essentially useless as an analog

system (e.g., equivalent 3 - bit precision per transistor).

• Digital systems can operate at extremely low frequencies, which would require

unrealistically large capacitor and resistor values if implemented as an analog

solution.

• Digital systems can be designed with increased precision with only an incre-

mental increase in cost, whereas the precision of an analog system precision

is physically limited (10 bits ∼ 60 - dB dynamic range typical).

• Digital systems can be easily programmed to change their function whereas

reprogramming analog systems is extremely difﬁ cult.

DSP: A DISCIPLINE 9

• Digital signals can be easily delayed and/or compressed, an effect which is

difﬁ cult to achieve with analog signals.

• Digital systems require no external alignment, while analog systems need

periodic adjustment (due to temperature drift, aging, etc.).

• Digital systems do not have impedance - matching requirements, while analog

systems do.

• Digital systems, compared with analog devices, are less sensitive to additive

noise as a general rule.

Analog Advantages

There are, however, a few analog attributes that resist the digital challenge. They

are as follows:

• Analog systems can operate at extremely high frequencies (e.g., microwave

and optical frequencies) that exceed the maximum clock rate of a digital device

or ADC.

• Analog solutions are sometimes more cost effective (e.g., ﬁ rst - order resistor -

capacitor [RC] ﬁ lter) compared with solutions fashioned with digital compo-

nents (e.g., ADC, digital ﬁ lter, plus DAC).

Driven by advancements in semiconductors, software, and algorithms, DSP will be

a principal enabling and facilitating technology in the following areas:

Audio

Audio - video

receivers

Computing

Digital radio

Home audio

Flat panel displays

Internet audio

Pro audio

Speech

Toys

Transportation

Chassis sensors

Power train

Driver displays

Security systems

Safety systems

Broadband

Wireless local area network

(LAN)

Cable

Digital subscriber line (DSL)

Voice - over Internet protocol (VoIP)

Control

Digital power supplies

Embedded sensors

Industrial drives

Motors

Instrumentation

Medical

Automated external deﬁ brillators

Monitoring

Hearing aids

Imaging

Prosthetics

Military

Avionics

Countermeasures

Imaging

Munitions

Navigation

Radar/sonar

Wireless

Handsets

Infrastructure

Radiofrequency

tagging

Security

Biometrics

Smart sensors

Telecom

High - frequency

radios

Infrastructure

CHAPTER 2

SAMPLING THEOREM

INTRODUCTION

One of the most important scientiﬁ c advancements of the ﬁ rst half of the 20th

century is attributable to Claude Shannon of Bell Laboratories. Many of Shannon ’ s

inventions remain with us today. One of his more amusing creations was a black

box that, when activated with a switch, would extend a green hand outward and turn

the switch off. Of greater value is his celebrated and enduring sampling theorem.

Shannon ’ s interest in sampling can be attributed to the fact that he worked for the

telephone company. He was therefore interested in maximizing the number of bill-

able subscribers that could simultaneously use a copper telephone line, the technol-

ogy of the day. Shannon ’ s innovation was to sample the individual subscriber ’ s

conversations, interlace the samples with samples from other subscribers, place them

all on a common telephone wire, and ﬁ nally reconstruct the original message at the

receiver after de - interlacing the samples. Today, we refer to this process as time -

division multiplexing ( TDM ). Shannon established the rules that govern the sam-

pling and signal reconstruction procedure. Without a reconstruction rule, however,

Shannon ’ s labors would have held no value to the telephone company. The outcome

was the sampling theorem, which has become the core to understand the theory and

practice of digital signal processing (DSP). The theorem both enables and constrains

the performance of the typical DSP system suggested in Figure 2.1 . The diagrammed

system consists of an analog - to - digital converter (ADC), digital - to - analog converter

(DAC), digital or DSP processor, plus analog signal conditioning ﬁ lters (i.e., anti -

aliasing and interpolation ﬁ lter). The sampling theorem also motivates the need for

these signal conditioning ﬁ lters.

SHANNON ’ S SAMPLING THEOREM (AN ENABLING

TECHNOLOGY)

The sampling theorem states that if a band - limited signal x ( t ), whose highest fre-

quency component is bounded from above by some f

max

, is periodically sampled at

some rate f

, where

Digital Filters: Principles and Applications with MATLAB, First Edition. Fred J. Taylor.

Published 2012 by John Wiley & Sons, Inc.

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