《数字信号处理》：科学家与工程师的权威指南

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"Digital Signal Processing——科学家与工程师的数字信号处理指南" 本书《Digital Signal Processing: The Scientist and Engineer's Guide to Digital Signal Processing》是作者Steven W. Smith博士专门为那些对数字信号处理感兴趣的科学家和工程师编写的。Smith博士在医学、安全和工业应用领域有丰富的经验，尤其擅长开发创新成像系统。他的主要项目包括SECURE1000安全系统和SentryScope超高清监控摄像头。SECURE1000系统用于检测隐藏在衣物下的武器、爆炸物和毒品，而SentryScope则是一款具有超过2000万像素的高分辨率监控相机。在医学领域，Smith博士设计了用于检测心脏动脉阻塞（动脉硬化）和骨质疏松症的X射线系统。此外，他在无损检测领域的研究也促成了检查罐装和瓶装产品填充水平和泄漏，以及印刷电路板缺陷焊点的产品。这本书涵盖了数字信号处理的广泛主题，适合从初学者到专业人士的不同层次读者。标签中的"DSP"代表数字信号处理，它是电子工程和通信领域的一个关键部分，涉及将模拟信号转换为数字形式以便进行分析和处理。"adc-dac"指的是模数转换器（ADC）和数模转换器（DAC），它们在数字信号处理中起着桥梁作用，使得数字系统能够与现实世界的模拟信号交互。"dft"和"fft"分别代表离散傅立叶变换（DFT）和快速傅立叶变换（FFT），它们是分析周期性和非周期性信号的基础工具，广泛应用于滤波、频谱分析等场景。"filter"则涉及滤波器设计，是数字信号处理中的核心概念，用于去除噪声、提取特定频率成分或改变信号特性。书中详细讨论了这些基本概念，并通过实例来阐述其应用，使读者能够理解并掌握数字信号处理的原理和实践。无论你是想提升学术研究能力，还是希望在工业界应用这些技术，这本书都将为你提供宝贵的资源和指导。

The Scientist and Engineer's Guide to Digital Signal Processing8

Sonar

Sonar is an acronym for SOund NAvigation and Ranging. It is divided into

two categories, active and passive. In active sonar, sound pulses between

2 kHz and 40 kHz are transmitted into the water, and the resulting echoes

detected and analyzed. Uses of active sonar include: detection &

localization of undersea bodies, navigation, communication, and mapping

the sea floor. A maximum operating range of 10 to 100 kilometers is

typical. In comparison, passive sonar simply listens to underwater sounds,

which includes: natural turbulence, marine life, and mechanical sounds from

submarines and surface vessels. Since passive sonar emits no energy, it is

ideal for covert operations. You want to detect the other guy, without him

detecting you. The most important application of passive sonar is in

military surveillance systems that detect and track submarines. Passive

sonar typically uses lower frequencies than active sonar because they

propagate through the water with less absorption. Detection ranges can be

thousands of kilometers.

DSP has revolutionized sonar in many of the same areas as radar: pulse

generation, pulse compression, and filtering of detected signals. In one

view, sonar is simpler than radar because of the lower frequencies involved.

In another view, sonar is more difficult than radar because the environment

is much less uniform and stable. Sonar systems usually employ extensive

arrays of transmitting and receiving elements, rather than just a single

channel. By properly controlling and mixing the signals in these many

elements, the sonar system can steer the emitted pulse to the desired

location and determine the direction that echoes are received from. To

handle these multiple channels, sonar systems require the same massive

DSP computing power as radar.

Reflection seismology

As early as the 1920s, geophysicists discovered that the structure of the earth's

crust could be probed with sound. Prospectors could set off an explosion and

record the echoes from boundary layers more than ten kilometers below the

surface. These echo seismograms were interpreted by the raw eye to map the

subsurface structure. The reflection seismic method rapidly became the

primary method for locating petroleum and mineral deposits, and remains so

today.

In the ideal case, a sound pulse sent into the ground produces a single echo for

each boundary layer the pulse passes through. Unfortunately, the situation is

not usually this simple. Each echo returning to the surface must pass through

all the other boundary layers above where it originated. This can result in the

echo bouncing between layers, giving rise to echoes of echoes being detected

at the surface. These secondary echoes can make the detected signal very

complicated and difficult to interpret. Digital Signal Processing has been

widely used since the 1960s to isolate the primary from the secondary echoes

in reflection seismograms. How did the early geophysicists manage without

DSP? The answer is simple: they looked in easy places, where multiple

reflections were minimized. DSP allows oil to be found in difficult locations,

such as under the ocean.

Chapter 1- The Breadth and Depth of DSP 9

Image Processing

Images are signals with special characteristics. First, they are a measure of a

parameter over space (distance), while most signals are a measure of a

parameter over time. Second, they contain a great deal of information. For

example, more than 10 megabytes can be required to store one second of

television video. This is more than a thousand times greater than for a similar

length voice signal. Third, the final judge of quality is often a subjective

human evaluation, rather than an objective criterion. These special

characteristics have made image processing a distinct subgroup within DSP.

Medical

In 1895, Wilhelm Conrad Röntgen discovered that x-rays could pass through

substantial amounts of matter. Medicine was revolutionized by the ability to

look inside the living human body. Medical x-ray systems spread throughout

the world in only a few years. In spite of its obvious success, medical x-ray

imaging was limited by four problems until DSP and related techniques came

along in the 1970s. First, overlapping structures in the body can hide behind

each other. For example, portions of the heart might not be visible behind the

ribs. Second, it is not always possible to distinguish between similar tissues.

For example, it may be able to separate bone from soft tissue, but not

distinguish a tumor from the liver. Third, x-ray images show anatomy, the

body's structure, and not physiology, the body's operation. The x-ray image of

a living person looks exactly like the x-ray image of a dead one! Fourth, x-ray

exposure can cause cancer, requiring it to be used sparingly and only with

proper justification.

The problem of overlapping structures was solved in 1971 with the introduction

of the first computed tomography scanner (formerly called computed axial

tomography, or CAT scanner). Computed tomography (CT) is a classic

example of Digital Signal Processing. X-rays from many directions are passed

through the section of the patient's body being examined. Instead of simply

forming images with the detected x-rays, the signals are converted into digital

data and stored in a computer. The information is then used to calculate

images that appear to be slices through the body. These images show much

greater detail than conventional techniques, allowing significantly better

diagnosis and treatment. The impact of CT was nearly as large as the original

introduction of x-ray imaging itself. Within only a few years, every major

hospital in the world had access to a CT scanner. In 1979, two of CT's

principle contributors, Godfrey N. Hounsfield and Allan M. Cormack, shared

the Nobel Prize in Medicine. That's good DSP!

The last three x-ray problems have been solved by using penetrating energy

other than x-rays, such as radio and sound waves. DSP plays a key role in all

these techniques. For example, Magnetic Resonance Imaging (MRI) uses

magnetic fields in conjunction with radio waves to probe the interior of the

human body. Properly adjusting the strength and frequency of the fields cause

the atomic nuclei in a localized region of the body to resonate between quantum

energy states. This resonance results in the emission of a secondary radio

The Scientist and Engineer's Guide to Digital Signal Processing10

wave, detected with an antenna placed near the body. The strength and other

characteristics of this detected signal provide information about the localized

region in resonance. Adjustment of the magnetic field allows the resonance

region to be scanned throughout the body, mapping the internal structure. This

information is usually presented as images, just as in computed tomography.

Besides providing excellent discrimination between different types of soft

tissue, MRI can provide information about physiology, such as blood flow

through arteries. MRI relies totally on Digital Signal Processing techniques,

and could not be implemented without them.

Space

Sometimes, you just have to make the most out of a bad picture. This is

frequently the case with images taken from unmanned satellites and space

exploration vehicles. No one is going to send a repairman to Mars just to

tweak the knobs on a camera! DSP can improve the quality of images taken

under extremely unfavorable conditions in several ways: brightness and

contrast adjustment, edge detection, noise reduction, focus adjustment, motion

blur reduction, etc. Images that have spatial distortion, such as encountered

when a flat image is taken of a spherical planet, can also be warped into a

correct representation. Many individual images can also be combined into a

single database, allowing the information to be displayed in unique ways. For

example, a video sequence simulating an aerial flight over the surface of a

distant planet.

Commercial Imaging Products

The large information content in images is a problem for systems sold in mass

quantity to the general public. Commercial systems must be cheap, and this

doesn't mesh well with large memories and high data transfer rates. One

answer to this dilemma is image compression. Just as with voice signals,

images contain a tremendous amount of redundant information, and can be run

through algorithms that reduce the number of bits needed to represent them.

Television and other moving pictures are especially suitable for compression,

since most of the image remain the same from frame-to-frame. Commercial

imaging products that take advantage of this technology include: video

telephones, computer programs that display moving pictures, and digital

television.

CHAPTER

Statistics, Probability and Noise

Statistics and probability are used in Digital Signal Processing to characterize signals and the

processes that generate them. For example, a primary use of DSP is to reduce interference, noise,

and other undesirable components in acquired data. These may be an inherent part of the signal

being measured, arise from imperfections in the data acquisition system, or be introduced as an

unavoidable byproduct of some DSP operation. Statistics and probability allow these disruptive

features to be measured and classified, the first step in developing strategies to remove the

offending components. This chapter introduces the most important concepts in statistics and

probability, with emphasis on how they apply to acquired signals.

Signal and Graph Terminology

A signal is a description of how one parameter is related to another parameter.

For example, the most common type of signal in analog electronics is a voltage

that varies with time. Since both parameters can assume a continuous range

of values, we will call this a continuous signal. In comparison, passing this

signal through an analog-to-digital converter forces each of the two parameters

to be quantized. For instance, imagine the conversion being done with 12 bits

at a sampling rate of 1000 samples per second. The voltage is curtailed to 4096

) possible binary levels, and the time is only defined at one millisecond

increments. Signals formed from parameters that are quantized in this manner

are said to be discrete signals or digitized signals. For the most part,

continuous signals exist in nature, while discrete signals exist inside computers

(although you can find exceptions to both cases). It is also possible to have

signals where one parameter is continuous and the other is discrete. Since

these mixed signals are quite uncommon, they do not have special names given

to them, and the nature of the two parameters must be explicitly stated.

Figure 2-1 shows two discrete signals, such as might be acquired with a

digital data acquisition system. The vertical axis may represent voltage, light

The Scientist and Engineer's Guide to Digital Signal Processing12

intensity, sound pressure, or an infinite number of other parameters. Since we

don't know what it represents in this particular case, we will give it the generic

label: amplitude. This parameter is also called several other names: the y-

axis, the dependent variable, the range, and the ordinate.

The horizontal axis represents the other parameter of the signal, going by

such names as: the x-axis, the independent variable, the domain, and the

abscissa. Time is the most common parameter to appear on the horizontal axis

of acquired signals; however, other parameters are used in specific applications.

For example, a geophysicist might acquire measurements of rock density at

equally spaced distances along the surface of the earth. To keep things

general, we will simply label the horizontal axis: sample number. If this

were a continuous signal, another label would have to be used, such as: time,

distance, x, etc.

The two parameters that form a signal are generally not interchangeable. The

parameter on the y-axis (the dependent variable) is said to be a function of the

parameter on the x-axis (the independent variable). In other words, the

independent variable describes how or when each sample is taken, while the

dependent variable is the actual measurement. Given a specific value on the

x-axis, we can always find the corresponding value on the y-axis, but usually

not the other way around.

Pay particular attention to the word: domain, a very widely used term in DSP.

For instance, a signal that uses time as the independent variable (i.e., the

parameter on the horizontal axis), is said to be in the time domain. Another

common signal in DSP uses frequency as the independent variable, resulting in

the term, frequency domain. Likewise, signals that use distance as the

independent parameter are said to be in the spatial domain (distance is a

measure of space). The type of parameter on the horizontal axis is the domain

of the signal; it's that simple. What if the x-axis is labeled with something

very generic, such as sample number? Authors commonly refer to these signals

as being in the time domain. This is because sampling at equal intervals of

time is the most common way of obtaining signals, and they don't have anything

more specific to call it.

Although the signals in Fig. 2-1 are discrete, they are displayed in this figure

as continuous lines. This is because there are too many samples to be

distinguishable if they were displayed as individual markers. In graphs that

portray shorter signals, say less than 100 samples, the individual markers are

usually shown. Continuous lines may or may not be drawn to connect the

markers, depending on how the author wants you to view the data. For

instance, a continuous line could imply what is happening between samples, or

simply be an aid to help the reader's eye follow a trend in noisy data. The

point is, examine the labeling of the horizontal axis to find if you are working

with a discrete or continuous signal. Don't rely on an illustrator's ability to

draw dots.

The variable, N, is widely used in DSP to represent the total number of

samples in a signal. For example, for the signals in Fig. 2-1. ToN '512

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