数字信号处理基础：科学家与工程师的指南

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"DSP经典之作——《The Scientist and Engineer's Guide to Digital Signal Processing》第二版，作者Steven W. Smith，由California Technical Publishing出版。该书官网为：www.DSPguide.com。" 《The Scientist and Engineer's Guide to Digital Signal Processing》是数字信号处理领域的经典教程，以其深入浅出的方式介绍了这一领域的核心概念。作者Steven W. Smith通过常见的科学和工程问题实例，帮助读者理解和应用数字信号处理的基本原理。这本书面向的读者范围广泛，包括科学家、工程师以及对数字信号处理感兴趣的学者。数字信号处理（DSP）是现代电子工程、通信技术、音频和图像处理等多个领域不可或缺的技术。该书涵盖了以下关键知识点： 1. **基本概念**：书中首先介绍了数字信号与模拟信号的区别，阐述了采样定理，强调了正确采样对于避免信息损失的重要性。 2. **滤波器设计**：包括线性相位滤波器、IIR滤波器和FIR滤波器的设计方法，以及如何根据系统需求选择合适的滤波器类型。 3. **傅里叶变换**：详述了离散傅里叶变换（DFT）和快速傅里叶变换（FFT）的工作原理及其应用，如频谱分析和信号频谱估计。 4. **信号调制与解调**：讲解了模拟信号到数字信号的转换过程，包括脉冲编码调制（PCM）、增量调制（DM）和ΔΣ调制等。 5. **数字信号处理算法**：包括信号的增强、降噪、压缩和恢复技术，以及自适应滤波器和最小均方误差（LMS）算法。 6. **实时处理与硬件实现**：讨论了如何在实际系统中实施数字信号处理，包括专用处理器（如DSP芯片）和FPGA的应用。 7. **安全与警告**：书中明确指出，尽管书中的概念和数据被认为是准确的，但任何实际应用前都需要进行适当的验证，因为错误的处理可能导致人身伤害或财产损失。此书不仅是教学工具，也是科研工作者和工程师的参考手册。然而，作者、出版商和分销商不对其内容的适用性或安全性提供任何明示或暗示的保证，提醒读者在具体问题上应谨慎应用所学知识。《The Scientist and Engineer's Guide to Digital Signal Processing》是一本全面而深入的教程，它以易于理解的方式解释了复杂的数字信号处理理论，并提供了丰富的实际应用案例，有助于读者在实践中提升技能。

The Scientist and Engineer's Guide to Digital Signal Processing2

DSP

Space

Medical

Commercial

Military

Scientific

Industrial

Telephone

-Earthquake recording & analysis

-Data acquisition

-Spectral analysis

-Simulation and modeling

-Oil and mineral prospecting

-Process monitoring & control

-Nondestructive testing

-CAD and design tools

-Radar

-Sonar

-Ordnance guidance

-Secure communication

-Voice and data compression

-Echo reduction

-Signal multiplexing

-Filtering

-Image and sound compression

for multimedia presentation

-Movie special effects

-Video conference calling

-Diagnostic imaging (CT, MRI,

ultrasound, and others)

-Electrocardiogram analysis

-Medical image storage/retrieval

-Space photograph enhancement

-Data compression

-Intelligent sensory analysis by

remote space probes

FIGURE 1-1

DSP has revolutionized many areas in science and engineering. A

few of these diverse applications are shown here.

data are irreplaceable; and medical imaging, where lives could be saved.

The personal computer revolution of the 1980s and 1990s caused DSP to

explode with new applications. Rather than being motivated by military and

government needs, DSP was suddenly driven by the commercial marketplace.

Anyone who thought they could make money in the rapidly expanding field was

suddenly a DSP vender. DSP reached the public in such products as: mobile

telephones, compact disc players, and electronic voice mail. Figure 1-1

illustrates a few of these varied applications.

This technological revolution occurred from the top-down. In the early

1980s, DSP was taught as a graduate level course in electrical engineering.

A decade later, DSP had become a standard part of the undergraduate

curriculum. Today, DSP is a basic skill needed by scientists and engineers

Chapter 1- The Breadth and Depth of DSP 3

Digital

Signal

Processing

Communication

Theory

Analog

Electronics

Digital

Electronics

Probability

and Statistics

Decision

Theory

Analog

Signal

Processing

Numerical

Analysis

FIGURE 1-2

Digital Signal Processing has fuzzy and overlapping borders with many other

areas of science, engineering and mathematics.

in many fields. As an analogy, DSP can be compared to a previous

technological revolution: electronics. While still the realm of electrical

engineering, nearly every scientist and engineer has some background in basic

circuit design. Without it, they would be lost in the technological world. DSP

has the same future.

This recent history is more than a curiosity; it has a tremendous impact on your

ability to learn and use DSP. Suppose you encounter a DSP problem, and turn

to textbooks or other publications to find a solution. What you will typically

find is page after page of equations, obscure mathematical symbols, and

unfamiliar terminology. It's a nightmare! Much of the DSP literature is

baffling even to those experienced in the field. It's not that there is anything

wrong with this material, it is just intended for a very specialized audience.

State-of-the-art researchers need this kind of detailed mathematics to

understand the theoretical implications of the work.

A basic premise of this book is that most practical DSP techniques can be

learned and used without the traditional barriers of detailed mathematics and

theory. The Scientist and Engineer’s Guide to Digital Signal Processing is

written for those who want to use DSP as a tool, not a new career.

The remainder of this chapter illustrates areas where DSP has produced

revolutionary changes. As you go through each application, notice that DSP

is very interdisciplinary, relying on the technical work in many adjacent

fields. As Fig. 1-2 suggests, the borders between DSP and other technical

disciplines are not sharp and well defined, but rather fuzzy and overlapping.

If you want to specialize in DSP, these are the allied areas you will also

need to study.

The Scientist and Engineer's Guide to Digital Signal Processing4

Telecommunications

Telecommunications is about transferring information from one location to

another. This includes many forms of information: telephone conversations,

television signals, computer files, and other types of data. To transfer the

information, you need a channel between the two locations. This may be

a wire pair, radio signal, optical fiber, etc. Telecommunications companies

receive payment for transferring their customer's information, while they

must pay to establish and maintain the channel. The financial bottom line

is simple: the more information they can pass through a single channel, the

more money they make. DSP has revolutionized the telecommunications

industry in many areas: signaling tone generation and detection, frequency

band shifting, filtering to remove power line hum, etc. Three specific

examples from the telephone network will be discussed here: multiplexing,

compression, and echo control.

Multiplexing

There are approximately one billion telephones in the world. At the press of

a few buttons, switching networks allow any one of these to be connected to

any other in only a few seconds. The immensity of this task is mind boggling!

Until the 1960s, a connection between two telephones required passing the

analog voice signals through mechanical switches and amplifiers. One

connection required one pair of wires. In comparison, DSP converts audio

signals into a stream of serial digital data. Since bits can be easily

intertwined and later separated, many telephone conversations can be

transmitted on a single channel. For example, a telephone standard known

as the T-carrier system can simultaneously transmit 24 voice signals. Each

voice signal is sampled 8000 times per second using an 8 bit companded

(logarithmic compressed) analog-to-digital conversion. This results in each

voice signal being represented as 64,000 bits/sec, and all 24 channels being

contained in 1.544 megabits/sec. This signal can be transmitted about 6000

feet using ordinary telephone lines of 22 gauge copper wire, a typical

interconnection distance. The financial advantage of digital transmission

is enormous. Wire and analog switches are expensive; digital logic gates

are cheap.

Compression

When a voice signal is digitized at 8000 samples/sec, most of the digital

information is redundant. That is, the information carried by any one

sample is largely duplicated by the neighboring samples. Dozens of DSP

algorithms have been developed to convert digitized voice signals into data

streams that require fewer bits/sec. These are called data compression

algorithms. Matching uncompression algorithms are used to restore the

signal to its original form. These algorithms vary in the amount of

compression achieved and the resulting sound quality. In general, reducing the

data rate from 64 kilobits/sec to 32 kilobits/sec results in no loss of sound

quality. When compressed to a data rate of 8 kilobits/sec, the sound is

noticeably affected, but still usable for long distance telephone networks.

The highest achievable compression is about 2 kilobits/sec, resulting in

Chapter 1- The Breadth and Depth of DSP 5

sound that is highly distorted, but usable for some applications such as military

and undersea communications.

Echo control

Echoes are a serious problem in long distance telephone connections.

When you speak into a telephone, a signal representing your voice travels

to the connecting receiver, where a portion of it returns as an echo. If the

connection is within a few hundred miles, the elapsed time for receiving the

echo is only a few milliseconds. The human ear is accustomed to hearing

echoes with these small time delays, and the connection sounds quite

normal. As the distance becomes larger, the echo becomes increasingly

noticeable and irritating. The delay can be several hundred milliseconds

for intercontinental communications, and is particularity objectionable.

Digital Signal Processing attacks this type of problem by measuring the

returned signal and generating an appropriate antisignal to cancel the

offending echo. This same technique allows speakerphone users to hear

and speak at the same time without fighting audio feedback (squealing).

It can also be used to reduce environmental noise by canceling it with

digitally generated antinoise.

Audio Processing

The two principal human senses are vision and hearing. Correspondingly,

much of DSP is related to image and audio processing. People listen to

both music and speech. DSP has made revolutionary changes in both

these areas.

Music

The path leading from the musician's microphone to the audiophile's speaker is

remarkably long. Digital data representation is important to prevent the

degradation commonly associated with analog storage and manipulation. This

is very familiar to anyone who has compared the musical quality of cassette

tapes with compact disks. In a typical scenario, a musical piece is recorded in

a sound studio on multiple channels or tracks. In some cases, this even involves

recording individual instruments and singers separately. This is done to give

the sound engineer greater flexibility in creating the final product. The

complex process of combining the individual tracks into a final product is

called mix down. DSP can provide several important functions during mix

down, including: filtering, signal addition and subtraction, signal editing, etc.

One of the most interesting DSP applications in music preparation is

artificial reverberation. If the individual channels are simply added together,

the resulting piece sounds frail and diluted, much as if the musicians were

playing outdoors. This is because listeners are greatly influenced by the echo

or reverberation content of the music, which is usually minimized in the sound

studio. DSP allows artificial echoes and reverberation to be added during

mix down to simulate various ideal listening environments. Echoes with

delays of a few hundred milliseconds give the impression of cathedral like

The Scientist and Engineer's Guide to Digital Signal Processing6

locations. Adding echoes with delays of 10-20 milliseconds provide the

perception of more modest size listening rooms.

Speech generation

Speech generation and recognition are used to communicate between humans

and machines. Rather than using your hands and eyes, you use your mouth and

ears. This is very convenient when your hands and eyes should be doing

something else, such as: driving a car, performing surgery, or (unfortunately)

firing your weapons at the enemy. Two approaches are used for computer

generated speech: digital recording and vocal tract simulation. In digital

recording, the voice of a human speaker is digitized and stored, usually in a

compressed form. During playback, the stored data are uncompressed and

converted back into an analog signal. An entire hour of recorded speech

requires only about three megabytes of storage, well within the capabilities of

even small computer systems. This is the most common method of digital

speech generation used today.

Vocal tract simulators are more complicated, trying to mimic the physical

mechanisms by which humans create speech. The human vocal tract is an

acoustic cavity with resonate frequencies determined by the size and shape of

the chambers. Sound originates in the vocal tract in one of two basic ways,

called voiced and fricative sounds. With voiced sounds, vocal cord vibration

produces near periodic pulses of air into the vocal cavities. In comparison,

fricative sounds originate from the noisy air turbulence at narrow constrictions,

such as the teeth and lips. Vocal tract simulators operate by generating digital

signals that resemble these two types of excitation. The characteristics of the

resonate chamber are simulated by passing the excitation signal through a

digital filter with similar resonances. This approach was used in one of the

very early DSP success stories, the Speak & Spell, a widely sold electronic

learning aid for children.

Speech recognition

The automated recognition of human speech is immensely more difficult

than speech generation. Speech recognition is a classic example of things

that the human brain does well, but digital computers do poorly. Digital

computers can store and recall vast amounts of data, perform mathematical

calculations at blazing speeds, and do repetitive tasks without becoming

bored or inefficient. Unfortunately, present day computers perform very

poorly when faced with raw sensory data. Teaching a computer to send you

a monthly electric bill is easy. Teaching the same computer to understand

your voice is a major undertaking.

Digital Signal Processing generally approaches the problem of voice

recognition in two steps: feature extraction followed by feature matching.

Each word in the incoming audio signal is isolated and then analyzed to

identify the type of excitation and resonate frequencies. These parameters are

then compared with previous examples of spoken words to identify the closest

match. Often, these systems are limited to only a few hundred words; can

only accept speech with distinct pauses between words; and must be retrained

for each individual speaker. While this is adequate for many commercial

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数字信号处理基础：科学家与工程师的指南

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