信号分析基础The Fundamentals of Signal Analysis

The Fundamentals of Signal Analysis

Application Note 243

Table of Contents

Chapter 1Introduction4 Chapter 2The Time, Frequency and Modal Domains:5

Chapter 3Understanding Dynamic Signal Analysis25

Chapter 4Using Dynamic Signal Analyzers49

Appendix A The Fourier Transform: A Mathematical Background63 Appendix B Bibliography66 Index67

Chapter 1 Introduction

The analysis of electrical signals is a fundamental problem for many engineers and scientists. Even if the immediate problem

is not electrical, the basic param-eters of interest are often changed into electrical signals by means of transducers. Common transducers include accelerometers and load cells in mechanical work, EEG electrodes and blood pressure probes in biology and medicine, and pH and conductivity probes in chemistry. The rewards for trans-forming physical parameters to electrical signals are great, as many instruments are available for the analysis of electrical sig-nals in the time, frequency and modal domains. The powerful measurement and analysis capa-bilities of these instruments can lead to rapid understanding of the system under study.

This note is a primer for those who are unfamiliar with the advantages of analysis in the frequency and modal domains and with the class of analyzers we call Dynamic Signal Analyzers. In Chapter 2 we develop the con-cepts of the time, frequency and modal domains and show why these different ways of looking

at a problem often lend their own unique insights. We then intro-duce classes of instrumentation available for analysis in these domains.

Because of the tutorial nature of

this note, we will not attempt to

show detailed solutions for the

multitude of measurement prob-

lems which can be solved by

Dynamic Signal Analysis. Instead,

we will concentrate on the fea-

tures of Dynamic Signal Analysis,

how these features are used in a

wide range of applications and

the benefits to be gained from

using Dynamic Signal Analysis.

Those who desire more details

on specific applications should

look to Appendix B. It contains

abstracts of Hewlett-Packard

Application Notes on a wide

range of related subjects. These

can be obtained free of charge

from your local HP field engineer

or representative.

In Chapter 3 we develop the

properties of one of these classes

of analyzers, Dynamic Signal

Analyzers. These instruments are

particularly appropriate for the

analysis of signals in the range

of a few millihertz to about a

hundred kilohertz.

Chapter 4 shows the benefits of

Dynamic Signal Analysis in a wide

range of measurement situations.

The powerful analysis tools of

Dynamic Signal Analysis are

introduced as needed in each

measurement situation.

This note avoids the use of rigor-

ous mathematics and instead

depends on heuristic arguments.

We have found in over a decade

of teaching this material that such

arguments lead to a better under-

standing of the basic processes

involved in the various domains

and in Dynamic Signal Analysis.

Equally important, this heuristic

instruction leads to better instru-

ment operators who can intelli-

gently use these analyzers to

solve complicated measurement

problems with accuracy and

ease*.

*A more rigorous mathematical justification

for the arguments developed in the main

text can be found in Appendix A.

Chapter 2

The Time, Frequency and Modal Domains:Section 1:

The Time Domain

The traditional way of observing signals is to view them in the time domain. The time domain is a record of what happened to a parameter of the system versus time. For instance, Figure 2.1shows a simple spring-mass system where we have attached a pen to the mass and pulled a piece of paper past the pen at a constant rate. The resulting graph is a record of the displacement of the mass versus time, a time do-main view of displacement.Such direct recording schemes are sometimes used, but it usually is much more practical to convert the parameter of interest to an electrical signal using a trans-ducer. Transducers are commonly available to change a wide variety of parameters to electrical sig-nals. Microphones, accelerom-eters, load cells, conductivity and pressure probes are just a few examples.

This electrical signal, which represents a parameter of the

system, can be recorded on a strip chart recorder as in Figure 2.2. We can adjust the gain of the system to calibrate our measurement.Then we can reproduce exactly the results of our simple direct recording system in Figure 2.1.Why should we use this indirect approach? One reason is that we are not always measuring dis-placement. We then must convert the desired parameter to the

displacement of the recorder https://www.sodocs.net/doc/2215160057.html,ually, the easiest way to do this is through the intermediary of electronics. However, even when measuring displacement we would normally use an indirect approach. Why? Primarily be-cause the system in Figure 2.1 is hopelessly ideal. The mass must be large enough and the spring stiff enough so that the pen s mass and drag on the paper will

A matter of Perspective

In this chapter we introduce the concepts of the time, frequency and modal domains. These three ways of looking at a problem are interchangeable; that is, no infor-mation is lost in changing from one domain to another. The advantage in introducing these three domains is that of a change of perspective . By changing per-spective from the time domain,the solution to difficult problems can often become quite clear in the frequency or modal domains.After developing the concepts of each domain, we will introduce the types of instrumentation avail-able. The merits of each generic instrument type are discussed to give the reader an appreciation of the advantages and disadvantages

of each approach.

Figure 2.2

Indirect recording of displacement.

Figure 2.1Direct record-ing of displace-ment - a time

domain view.

not affect the results appreciably. Also the deflection of the mass must be large enough to give a usable result, otherwise a me-chanical lever system to amplify the motion would have to be added with its attendant mass and friction.

With the indirect system a trans-ducer can usually be selected which will not significantly affect the measurement. This can go to the extreme of commercially available displacement transduc-ers which do not even contact the mass. The pen deflection can be easily set to any desired value

by controlling the gain of the electronic amplifiers.

This indirect system works well until our measured parameter be-gins to change rapidly. Because of the mass of the pen and recorder mechanism and the power limita-tions of its drive, the pen can only move at finite velocity. If the mea-sured parameter changes faster, the output of the recorder will be in error. A common way to reduce this problem is to eliminate the pen and record on a photosensi-Figure 2.3

Simplified

oscillograph

operation.

Figure 2.4

Simplified

oscilloscope

operation

(Horizontal

deflection

circuits

omitted for

clarity).

tive paper by deflecting a light

beam. Such a device is called

an oscillograph. Since it is only

necessary to move a small,

light-weight mirror through a

very small angle, the oscillograph

can respond much faster than a

strip chart recorder.

Another common device for dis-

playing signals in the time domain

is the oscilloscope. Here an

electron beam is moved using

electric fields. The electron beam

is made visible by a screen of

phosphorescent material. It is

capable of accurately displaying

signals that vary even more rap-

idly than the oscillograph can

handle. This is because it is only

necessary to move an electron

beam, not a mirror.

The strip chart, oscillograph and

oscilloscope all show displace-

ment versus time. We say that

changes in this displacement rep-

resent the variation of some pa-

rameter versus time. We will now

look at another way of represent-

ing the variation of a parameter.

Section 2: The Frequency Domain

It was shown over one hundred years ago by Baron Jean Baptiste Fourier that any waveform that exists in the real world can be generated by adding up sine waves. We have illustrated this in Figure 2.5 for a simple waveform composed of two sine waves. By

picking the amplitudes, frequen-cies and phases of these sine waves correctly, we can generate a waveform identical to our desired signal.

Conversely, we can break down our real world signal into these same sine waves. It can be shown that this combination of sine waves is unique; any real world signal can be represented by only one combination of sine waves. Figure 2.6a is a three dimensional graph of this addition of sine waves. Two of the axes are time and amplitude, familiar from the time domain. The third axis is frequency which allows us to visually separate the sine waves which add to give us our complex waveform. If we view this three dimensional graph along the frequency axis we get the view

in Figure 2.6b. This is the time domain view of the sine waves. Adding them together at each instant of time gives the original waveform.Figure 2.6

The relationship

between the time

and frequency

domains.

a) Three

dimensional

coordinates

showing time,

frequency and

amplitude

b) Time

domain view

c) Frequency

domain view

Figure 2.5

Any real

waveform

can be

produced

by adding

sine waves

together.

However, if we view our graph

along the time axis as in Figure

2.6c, we get a totally different

picture. Here we have axes of

amplitude versus frequency, what

is commonly called the frequency

domain. Every sine wave we

separated from the input appears

as a vertical line. Its height repre-

sents its amplitude and its posi-

tion represents its frequency.

Since we know that each line

represents a sine wave, we have

uniquely characterized our input

signal in the frequency domain*.

This frequency domain represen-

tation of our signal is called the

spectrum of the signal. Each sine

wave line of the spectrum is

called a component of the

total signal.

*Actually, we have lost the phase

information of the sine waves. How

we get this will be discussed in Chapter 3.

The Need for Decibels

Since one of the major uses of the frequency domain is to resolve small signals in the

presence of large ones, let us now address the problem of how we can see both large and small signals on our display simultaneously.

Suppose we wish to measure a distortion component that is 0.1% of the signal. If we set the fundamental to full scale on a four inch (10 cm) screen, the harmonic would be only four thousandths of an inch. (.1mm) tall. Obviously, we could barely see such a signal, much less measure it accurately. Yet many analyzers are available with the ability to measure signals even smaller than this.

Since we want to be able to see all the components easily at the same time, the only answer is to change our amplitude scale. A logarithmic scale would compress our large signal amplitude and expand the small ones, allowing all components to be displayed at the same time.

Alexander Graham Bell discovered that the human ear responded logarithmically to power difference and invented a unit, the Bel, to help him measure the ability of people to hear. One tenth of a Bel, the deciBel (dB) is the most common unit used in the frequency domain today. A table of the relationship between volts, power and dB is given in Figure 2.8. From the table we can see that our 0.1% distortion component example is 60 dB below the fundamental. If we had an 80 dB display as in Figure 2.9, the distortion component would occupy 1/4 of the screen, not 1/1000 as in a linear display.Figure 2.8

The relation-ship between decibels, power and voltage.

Figure 2.9

Small signals

can be measured with a logarithmic

amplitude scale.

Figure 2.7Small signals are not hidden in the frequency

domain.

a) Time Domain - small signal not visible

b) Frequency Domain - small signal easily resolved

It is very important to understand that we have neither gained nor lost information, we are just representing it differently. We are looking at the same three-dimensional graph from different angles. This different perspective can be very useful.

Why the Frequency Domain?Suppose we wish to measure the level of distortion in an audio os-cillator. Or we might be trying to detect the first sounds of a bear-ing failing on a noisy machine. In each case, we are trying to detect a small sine wave in the presence of large signals. Figure 2.7a shows a time domain waveform which seems to be a single sine wave. But Figure 2.7b shows in the frequency domain that the same signal is composed of a large sine wave and significant other sine wave components (distortion components). When these components are separated in the frequency domain, the

small components are easy to see because they are not masked by larger ones.

The frequency domain s useful-ness is not restricted to electron-ics or mechanics. All fields of science and engineering have measurements like these where large signals mask others in the time domain. The frequency domain provides a useful tool in analyzing these small but important effects.

The Frequency Domain:A Natural Domain

At first the frequency domain may seem strange and unfamiliar, yet it is an important part of everyday life. Your ear-brain combination is an excellent frequency domain analyzer. The ear-brain splits the audio spectrum into many narrow bands and determines the power present in each band. It can easily pick small sounds out of loud background noise thanks in part

to its frequency domain capabil-ity. A doctor listens to your heart and breathing for any unusual sounds. He is listening for

frequencies which will tell him something is wrong. An experi-enced mechanic can do the same thing with a machine. Using a screwdriver as a stethoscope,he can hear when a bearing is failing because of the frequencies it produces.

So we see that the frequency domain is not at all uncommon. We are just not used to seeing it in graphical form. But this graphi-cal presentation is really not any stranger than saying that the temperature changed with time like the displacement of a line

on a graph.

Spectrum Examples

Let us now look at a few common signals in both the time and fre-quency domains. In Figure 2.10a, we see that the spectrum of a sine wave is just a single line. We expect this from the way we con-structed the frequency domain. The square wave in Figure 2.10b is made up of an infinite number of sine waves, all harmonically related. The lowest frequency present is the reciprocal of the square wave period. These two examples illustrate a property of the frequency transform: a signal which is periodic and exists for all time has a discrete frequency spectrum. This is in contrast to the transient signal in Figure

2.10c which has a continuous Figure 2.10

Frequency

spectrum ex-

amples.

fore, require infinite energy to

generate a true impulse. Never-

theless, it is possible to generate

an approximation to an impulse

which has a fairly flat spectrum

over the desired frequency range

of interest. We will find signals

with a flat spectrum useful in our

next subject, network analysis. spectrum. This means that the

sine waves that make up this

signal are spaced infinitesimally

close together.

Another signal of interest is the

impulse shown in Figure 2.10d.

The frequency spectrum of an

impulse is flat, i.e., there is energy

at all frequencies. It would, there-

Network Analysis

If the frequency domain were restricted to the analysis of signal spectrums, it would certainly not be such a common engineering tool. However, the frequency domain is also widely used in analyzing the behavior of net-works (network analysis) and

in design work.

Network analysis is the general engineering problem of determin-ing how a network will respond to an input*. For instance, we might wish to determine how a structure will behave in high winds. Or we might want to know how effective a sound absorbing wall we are planning on purchas-ing would be in reducing machin-ery noise. Or perhaps we are interested in the effects of a tube of saline solution on the transmis-sion of blood pressure waveforms from an artery to a monitor.

All of these problems and many more are examples of network analysis. As you can see a net-work can be any system at all. One-port network analysis is the variation of one parameter with respect to another, both measured at the same point (port) of the network. The impedance or compliance of the electronic or mechanical networks shown in Figure 2.11 are typical examples of one-port network analysis.Figure 2.11 One-port network analysis

examples.

*Network Analysis is sometimes called Stimulus/Response Testing. The input is then known as the stimulus or excitation and the output is called the response.

Two-port analysis gives the re-sponse at a second port due to an input at the first port. We are gen-erally interested in the transmis-sion and rejection of signals and in insuring the integrity of signal transmission. The concept of two-port analysis can be extended to any number of inputs and outputs. This is called N-port analysis, a subject we will use in modal analysis later in this chapter.

We have deliberately defined net-work analysis in a very general way. It applies to all networks with no limitations. If we place one condition on our network, linearity, we find that network analysis becomes a very powerful tool.Figure 2.12

Two-port

network

analysis.

1

Figure 2.14

Non-linear

system

example.

Figure 2.15

Examples of

non-linearities.

Figure 2.13

Linear network.

When we say a network is linear, we mean it behaves like the net-work in Figure 2.13. Suppose one input causes an output A and a second input applied at the same port causes an output B. If we apply both inputs at the same time to a linear network, the output will be the sum of the individual outputs, A + B.

At first glance it might seem that all networks would behave in this fashion. A counter example, a non-linear network, is shown

in Figure 2.14. Suppose that the first input is a force that varies in a sinusoidal manner. We pick its amplitude to ensure that the displacement is small enough so that the oscillating mass does not quite hit the stops. If we add a second identical input, the mass would now hit the stops. Instead of a sine wave with twice the amplitude, the output is clipped as shown in Figure 2.14b.

This spring-mass system with stops illustrates an important principal: no real system is completely linear. A system may be approximately linear over a wide range of signals, but eventu-ally the assumption of linearity breaks down. Our spring-mass system is linear before it hits the stops. Likewise a linear electronic amplifier clips when the output voltage approaches the internal supply voltage. A spring may com-press linearly until the coils start pressing against each other.Figure 2.16

A positioning

system.

Other forms of non-linearities are

also often present. Hysteresis (or

backlash) is usually present in

gear trains, loosely riveted joints

and in magnetic devices. Some-

times the non-linearities are less

abrupt and are smooth, but non-

linear, curves. The torque versus

rpm of an engine or the operating

curves of a transistor are two

examples that can be considered

linear over only small portions of

their operating regions.

The important point is not that all

systems are nonlinear; it is that

most systems can be approxi-

mated as linear systems. Often

a large engineering effort is spent

in making the system as linear as

practical. This is done for two

reasons. First, it is often a design

goal for the output of a network

to be a scaled, linear version of

the input. A strip chart recorder

is a good example. The electronic

amplifier and pen motor must

both be designed to ensure that

the deflection across the paper

is linear with the applied voltage.

The second reason why systems

are linearized is to reduce the

problem of nonlinear instability.

One example would be the posi-

tioning system shown in Figure

2.16. The actual position is com-

pared to the desired position and

the error is integrated and applied

to the motor. If the gear train

has no backlash, it is a straight

forward problem to design this

system to the desired specifica-

tions of positioning accuracy and

response time.

However, if the gear train has ex-

cessive backlash, the motor will

hunt causing the positioning

system to oscillate around the

desired position. The solution

is either to reduce the loop gain

and therefore reduce the overall

performance of the system, or to

reduce the backlash in the gear

train. Often, reducing the back-

lash is the only way to meet the

performance specifications.

Analysis of Linear Networks

As we have seen, many systems are designed to be reasonably lin-ear to meet design specifications. This has a fortuitous side benefit when attempting to analyze networks*.

Recall that an real signal can

be considered to be a sum of sine waves. Also, recall that the response of a linear network is the sum of the responses to each component of the input. There-fore, if we knew the response of the network to each of the sine wave components of the input spectrum, we could predict the output.

It is easy to show that the steady-state response of a linear network to a sine wave input is a sine wave of the same frequency. As shown in Figure 2.17, the ampli-tude of the output sine wave is proportional to the input ampli-tude. Its phase is shifted by an amount which depends only on the frequency of the sine wave. As we vary the frequency of the sine wave input, the amplitude propor-tionality factor (gain) changes as does the phase of the output.

If we divide the output of the

*We will discuss the analysis of networks which have not been linearized in Chapter 3, Section 6.Figure 2.17 Linear network response to a

sine wave input.

Figure 2.18 The frequency response of a

network.

network by the input, we get a normalized result called the fre-quency response of the network. As shown in Figure 2.18, the fre-quency response is the gain (or loss) and phase shift of the net-work as a function of frequency. Because the network is linear, the frequency response is indepen-dent of the input amplitude; the frequency response is a property of a linear network, not depen-dent on the stimulus.

The frequency response of a net-work will generally fall into one of three categories; low pass, high pass, bandpass or a combination of these. As the names suggest, their frequency responses have relatively high gain in a band of frequencies, allowing these fre-quencies to pass through the network. Other frequencies suffer a relatively high loss and are rejected by the network. To see what this means in terms of the response of a filter to an input, let us look at the bandpass

filter case.Figure 2.19 Three classes of frequency

response.

In Figure 2.20, we put a square wave into a bandpass filter. We recall from Figure 2.10 that a square wave is composed of harmonically related sine waves. The frequency response of our example network is shown in Figure 2.20b. Because the filter is narrow, it will pass only one com-ponent of the square wave. There-fore, the steady-state response of this bandpass filter is a sine wave.

Notice how easy it is to predict the output of any network from its frequency response. The spectrum of the input signal is multiplied by the frequency re-sponse of the network to deter-mine the components that appear in the output spectrum. This fre-quency domain output can then be transformed back to the time domain.

In contrast, it is very difficult to compute in the time domain the output of any but the simplest networks. A complicated integral must be evaluated which often can only be done numerically on a digital computer*. If we computed the network response by both evaluating the time domain inte-gral and by transforming to the frequency domain and back, we would get the same results. How-ever, it is usually easier to com-pute the output by transforming to the frequency domain. Transient Response

Up to this point we have only discussed the steady-state re-sponse to a signal. By steady-state we mean the output after any transient responses caused by applying the input have died out. However, the frequency response of a network also contains all the Figure 2.20 Bandpass filter response to a square wave

input.

Figure 2.21 Time response of bandpass

filters.

* This operation is called convolution.

information necessary to predict the transient response of the net-work to any signal.

Let us look qualitatively at the transient response of a bandpass filter. If a resonance is narrow compared to its frequency, then it is said to be a high Q reso-nance*. Figure 2.21a shows a high Q filter frequency response. It has a transient response which dies out very slowly. A time re-sponse which decays slowly is said to be lightly damped. Figure 2.21b shows a low Q resonance. It has a transient response which dies out quickly. This illustrates a general principle: signals which are broad in one domain are narrow in the other. Narrow, selective filters have very long response times, a fact we will find important in the next section. Section 3: Instrumentation for the Frequency Domain

Just as the time domain can

be measured with strip chart recorders, oscillographs or oscilloscopes, the frequency domain is usually measured with spectrum and network analyzers. Spectrum analyzers are instru-ments which are optimized to characterize signals. They intro-duce very little distortion and few spurious signals. This insures that the signals on the display are truly part of the input signal spectrum, not signals introduced by the analyzer.Figure 2.22

Parallel filter

analyzer.

Network analyzers are optimized

to give accurate amplitude and

phase measurements over a

wide range of network gains and

losses. This design difference

means that these two traditional

instrument families are not

interchangeable.** A spectrum

analyzer can not be used as a

network analyzer because it does

not measure amplitude accurately

and cannot measure phase. A net-

work analyzer would make a very

poor spectrum analyzer because

spurious responses limit its

dynamic range.

In this section we will develop the

properties of several types of

analyzers in these two categories.

The Parallel-Filter

Spectrum Analyzer

As we developed in Section 2 of

this chapter, electronic filters can

be built which pass a narrow band

of frequencies. If we were to add

a meter to the output of such a

bandpass filter, we could measure

the power in the portion of the

spectrum passed by the filter. In

Figure 2.22a we have done this

for a bank of filters, each tuned to

a different frequency. If the center

frequencies of these filters are

chosen so that the filters overlap

properly, the spectrum covered

by the filters can be completely

characterized as in Figure 2.22b.

*Q is usually defined as:

Q =

Center Frequency of Resonance

**Dynamic Signal Analyzers are an exception to this rule, they can act as both network and spectrum analyzers.

How many filters should we use to cover the desired spectrum? Here we have a trade-off. We would like to be able to see closely spaced spectral lines, so we should have a large number

of filters. However, each filter is expensive and becomes more ex-pensive as it becomes narrower, so the cost of the analyzer goes up as we improve its resolution. Typical audio parallel-filter ana-lyzers balance these demands with 32 filters, each covering

1/3 of an octave.

Swept Spectrum Analyzer One way to avoid the need for such a large number of expensive filters is to use only one filter and sweep it slowly through the fre-quency range of interest. If, as in Figure 2.23, we display the output of the filter versus the frequency to which it is tuned, we have the spectrum of the input signal. This swept analysis technique is com-monly used in rf and microwave spectrum analysis.

We have, however, assumed the input signal hasn t changed in the time it takes to complete a sweep of our analyzer. If energy appears at some frequency at a moment when our filter is not tuned to that frequency, then we will not measure it.

One way to reduce this problem would be to speed up the sweep time of our analyzer. We could still miss an event, but the time in which this could happen would be shorter. Unfortunately though, we cannot make the sweep arbitrarily fast because of the response time of our filter.

To understand this problem, recall from Section 2 that a filter takes a finite time to respond to

*More information on the performance of

swept spectrum analyzers can be found in

Hewlett-Packard Application Note Series

150.

Figure 2.24

Amplitude

error form

sweeping

too fast.

Figure 2.23

Simplified

swept spectrum

analyzer.

changes in its input. The narrower

the filter, the longer it takes to

respond. If we sweep the filter

past a signal too quickly, the filter

output will not have a chance to

respond fully to the signal. As we

show in Figure 2.24, the spectrum

display will then be in error; our

estimate of the signal level will be

too low.

In a parallel-filter spectrum ana-

lyzer we do not have this prob-

lem. All the filters are connected

to the input signal all the time.

Once we have waited the initial

settling time of a single filter, all

the filters will be settled and the

spectrum will be valid and not

miss any transient events.

So there is a basic trade-off

between parallel-filter and swept

spectrum analyzers. The parallel-

filter analyzer is fast, but has

limited resolution and is expen-

sive. The swept analyzer can be

cheaper and have higher resolu-

tion but the measurement takes

longer (especially at high resolu-

tion) and it can not analyze

transient events*.

Dynamic Signal Analyzer

In recent years another kind of

analyzer has been developed

which offers the best features

of the parallel-filter and swept

spectrum analyzers. Dynamic Sig-

nal Analyzers are based on a high

speed calculation routine which

acts like a parallel filter analyzer

with hundreds of filters and yet

are cost competitive with swept

Figure 2.26Tuned net-work analyzer

operation.

Figure 2.25Gain-phase meter

operation.

spectrum analyzers. In addition,two channel Dynamic Signal

Analyzers are in many ways better network analyzers than the ones we will introduce https://www.sodocs.net/doc/2215160057.html,work Analyzers

Since in network analysis it is required to measure both the in-put and output, network analyzers are generally two channel devices with the capability of measuring the amplitude ratio (gain or loss)and phase difference between the channels. All of the analyzers dis-cussed here measure frequency response by using a sinusoidal input to the network and slowly changing its frequency. Dynamic Signal Analyzers use a different,much faster technique for net-work analysis which we discuss in the next chapter.

Gain-phase meters are broadband devices which measure the ampli-tude and phase of the input and output sine waves of the network.A sinusoidal source must be

supplied to stimulate the network when using a gain-phase meter as in Figure 2.25. The source can be tuned manually and the gain-phase plots done by hand or a sweeping source and an x-y plotter can be used for automatic frequency response plots.The primary attraction of gain-phase meters is their low price. If a sinusoidal source and a plotter are already available, frequency response measurements can be made for a very low investment.However, because gain-phase meters are broadband, they mea-sure all the noise of the network as well as the desired sine wave.As the network attenuates the input, this noise eventually becomes a floor below which the meter cannot measure. This

typically becomes a problem with attenuations of about 60 dB (1,000:1).

Tuned network analyzers mini-mize the noise floor problems of gain-phase meters by including a bandpass filter which tracks the source frequency. Figure 2.26shows how this tracking filter

virtually eliminates the noise and any harmonics to allow measurements of attenuation to 100 dB (100,000:1).

By minimizing the noise, it is also possible for tuned network ana-lyzers to make more accurate measurements of amplitude and phase. These improvements do

not come without their price, however, as tracking filters and a dedicated source must be added to the simpler and less costly gain-phase meter.

Tuned analyzers are available

in the frequency range of a

few Hertz to many Gigahertz (109 Hertz). If lower frequency analysis is desired, a frequency response analyzer is often used. To the operator, it behaves exactly like a tuned network analyzer. However, it is quite different inside. It integrates the signals in the time domain to effectively filter the signals at very low frequencies where it is not practical to make filters by more conventional techniques. Frequency response analyzers are generally limited to from

1 mHz to about 10 kHz. Section 4:

The Modal Domain

In the preceding sections we have developed the properties of the time and frequency domains and the instrumentation used in these domains. In this section we will develop the properties of another domain, the modal domain. This change in perspective to a new domain is particularly useful if we are interested in analyzing the behavior of mechanical structures.

To understand the modal domain let us begin by analyzing a simple mechanical structure, a tuning fork. If we strike a tuning fork, we easily conclude from its tone that it is primarily vibrating at a single frequency. We see that we have excited a network (tuning fork) with a force impulse (hitting

the fork). The time domain

view of the sound caused by

the deformation of the fork is a Figure 2.27

The vibration

of a tuning fork.

Figure 2.28

Example

vibration modes

of a tuning fork.

lightly damped sine wave shown

in Figure 2.27b.

In Figure 2.27c, we see in the fre-

quency domain that the frequency

response of the tuning fork has a

major peak that is very lightly

damped, which is the tone we

hear. There are also several

smaller peaks.

安捷伦矢量信号分析基础(中文版)

安捷伦矢量信号分析基础应用指南

目录矢量信号分析 (3) VSA 测量优势 (4) VSA 测量概念和操作理论 (6) 数据窗口—泄漏和分辨率带宽 (12) 快速傅立叶变换 (FFT) 分析 (14) 时域显示 (16) 总结 (17) 矢量调制分析 (18) 简介 (18) 矢量调制和数字调制概况 (19) 数字射频通信系统概念 (23) VSA 数字调制分析概念和操作理论 (26) 灵活定制的或用户定义的解调 (27) 解调分析 (31) 测量概念 (32) 模拟调制分析 (36) 总结 (38) 其他资源 (39) 下载 89600B 软件并免费试用 14 天，与您的分析硬件结合使 用 ; 或通过选择软件工具栏上的File> Recall> Recall Demo> QPSK>，使用我们记录的演示信号进行测量。立即申请您的 免费试用许可: https://www.sodocs.net/doc/2215160057.html,/?nd/89600B_trial

矢量信号分析本应用指南是关于矢量信号分析(Vector Signal Aanlysis) 的入门读物。本 节将讨论 VSA 的测量概念和操作理论 ; 下一节将讨论矢量调制分析，特别是 数字调制分析。 模拟扫描调谐式频谱分析仪使用超外差技术覆盖广泛的频率范围 ; 从音 频、微波直到毫米波频率。快速傅立叶变换 (FFT) 分析仪使用数字信号处理 (DSP) 提供高分辨率的频谱和网络分析。如今宽带的矢量调制 ( 又称为复调制 或数字调制 ) 的时变信号从 FFT 分析和其他 D SP 技术上受益匪浅。VSA 提供快 速高分辨率的频谱测量、解调以及高级时域分析功能，特别适用于表征复杂 信号，如通信、视频、广播、雷达和软件无线电应用中的脉冲、瞬时或调制 信号。 图 1 显示了一个简化的 VSA 方框图。VSA 采用了与传统扫描分析截然不 同的测量方法 ; 融入 FFT 和数字信号处理算法的数字中频部分替代了模拟中频 部分。传统的扫描调谐式频谱分析是一个模拟系统 ; 而 VSA 基本上是一个使 用数字数据和数学算法来进行数据分析的数字系统。VSA 软件可以接收并分 析来自许多测量前端的数字化数据，使您的故障诊断可以贯穿整个系统框图。 图 1. 矢量信号分析过程要求输入信号是一个被数字化的模拟信号，然后使用 D SP 技术处理 并提供数据输出 ; FFT 算法计算出频域结果，解调算法计算出调制和码域结果。

信号与系统基础知识

第1章 信号与系统的基本概念 1.1 引言 系统是一个广泛使用的概念，指由多个元件组成的相互作用、相互依存的整体。我们学习过“电路分析原理”的课程，电路是典型的系统，由电阻、电容、电感和电源等元件组成。我们还熟悉汽车在路面运动的过程，汽车、路面、空气组成一个力学系统。更为复杂一些的系统如电力系统，它包括若干发电厂、变电站、输电网和电力用户等，大的电网可以跨越数千公里。 我们在观察、分析和描述一个系统时，总要借助于对系统中一些元件状态的观测和分析。例如，在分析一个电路时，会计算或测量电路中一些位置的电压和电流随时间的变化；在分析一个汽车的运动时，会计算或观测驱动力、阻力、位置、速度和加速度等状态变量随时间的变化。系统状态变量随时间变化的关系称为信号，包含了系统变化的信息。 很多实际系统的状态变量是非电的，我们经常使用各种各样的传感器，把非电的状态变量转换为电的变量，得到便于测量的电信号。 隐去不同信号所代表的具体物理意义，信号就可以抽象为函数，即变量随时间变化的关系。信号用函数表示，可以是数学表达式，或是波形，或是数据列表。在本课程中，信号和函数的表述经常不加区分。 信号和系统分析的最基本的任务是获得信号的特点和系统的特性。系统的分析和描述借助于建立系统输入信号和输出信号之间关系，因此信号分析和系统分析是密切相关的。 系统的特性千变万化，其中最重要的区别是线性和非线性、时不变和时变。这些区别导致分析方法的重要差别。本课程的内容限于线性时不变系统。 我们最熟悉的信号和系统分析方法是时域分析，即分析信号随时间变化的波形。例如，对于一个电压测量系统，要判断测量的准确度，可以直接分析比较被测的电压波形)(in t v （测量系统输入信号）和测量得到的波形)(out t v （测量系统输出信号），观察它们之间的相似程度。为了充分地和规范地描述测量系统的特性，经常给系统输入一个阶跃电压信号，得到系统的阶跃响应，图1-1是典型的波形，通过阶跃响应的电压上升时间（电压从10％上升至90％的时间）和过冲（百分比）等特征量，表述测量系统的特性，上升时间和过冲越小，系统特性越好。其中电压上升时间反映了系统的响应速度，小的上升时间对应快的响应速度。如果被测电压快速变化，而测量系统的响应特性相对较慢，则必然产生较大的测量误差。 信号与系统分析的另一种方法是频域分析。信号频域分析的基本原理是把信号分解为不同频率三角信号的叠加，观察信号所包含的各频率分量的幅值和相位，得到信号的频谱特性。图1-2是从时域和频域观察一个周期矩形波信号的示意图，由此可以看到信号频域和时域的关系。系统的频域分析是观察系统对不同频率激励信号的响应，得到系统的频率响应特性。频域分析的重要优点包括：（1）对信号变化的快慢和系统的响应速度给出定量的描述。例如，当我们要用一个示波器观察一个信号时，需要了解信号的频谱特性和示波器的模拟带宽，当示波器的模拟带宽能够覆盖被测信号的频率范围时，可以保证测量的准确。（2）

《信号与系统分析基础》第3章习题解答

第三章习题解答 3.2 求下列方波形的傅里叶变换。 (a) 解： 110 2 ()()11()2 t j t t j t t j t t j t j a F j f t e dt e e dt j e t tS e j ωωωωωωω ωω-----=-=?= -==?? (b) 解： 20 00 2 2 ()1 1 1()[]1 (1) 1 (1) t j t t j t t t j t j t t t j t j t j t j t j t j t t F e dt e e dt tde j j j te e dt j e e e j e ωωωωωωωωωωωτ ω τωτω ω τω ωττω----------=-=?= =??-=-=+-= +-???? (c) 解： 1 31 1 2 2 11()()2 211 1 ()()22 1 1 ()cos 2 1 ()2 1()211 12() 2() 2 2 j t j t j t j t j t j t j t j t F t e dt e e e dt e e dt e e j j ωπ π ωππ ωωπ π ωωπ ωππ ωω-------+---+--=?=+?=+=- -+?? ? ()()()()22221 111 [][]2222 j j j j e e e e j j ππππ ωωωωππωω----++=?--?--+

2222sin()sin()cos ()cos () cos 2222()()2222 ππππ ωωωωωωπωππππωωωω-+?++?-?=+== -+-- (d)解： 242 22()()22 22()()2 2 ()()()()2 2 2 2 ()sin 1()21()2112()2() sin[(22() 2() T j t T T j t j t j t T T j t j t T T T j t j t T T T T T T j j j j F t e dt e e e dt j e e dt j e e T e e e e j j j j ωωωωωωωωωωωωωωω--Ω-Ω--Ω--Ω+-Ω--Ω+--Ω--Ω-Ω+-Ω+=Ω?=-= --=-Ω-Ω+Ω---= + =?Ω-?Ω+???)]sin[()] 2()() T j j ωωωωΩ++Ω-Ω+ 3.3依据上题中a,b 的结果，利用傅里叶变换的性质，求题图3.3所示各信号的傅里叶变换. (a) 解：11111()()()f t f t f t =-- 11()f t 就是3.2中(a)的1()f t 如果1()()f t F ω?，则1()()f t F ω-?- 11111111122 2 ()()()()()sin()42 ( )[]sin( )sin ()2 2 2 2 j j a f t f t f t F F t S e e j j τ τ ω ω ωωωτ ωτ τωτ ωττωτ ω-∴=--?--=??-= ? = (b) 解：2()()()f t g t g t στ=+,而()( )2 a g t S τωτ τ? 2()(3)2()a a F S S ωσωω∴=+ 如利用3.2中(a)的结论来解，有： 211'()(3)(1)f t f t f t ττ=+++，其中,'2τστ==. 3211'()()()(3)2()j j a a F e F e F S S ωωττωωωσωω∴=?+?=+ (如()()f t F ω?，则0 0()()j t f t t e F ωω±?) 2()f t

于博士信号完整性分析入门-初稿

于博士信号完整性分析入门 于争博士 https://www.sodocs.net/doc/2215160057.html, 整理:runnphoenix

什么是信号完整性? 如果你发现，以前低速时代积累的设计经验现在似乎都不灵了，同样的设计，以前没问题，可是现在却无法工作，那么恭喜你，你碰到了硬件设计中最核心的问题：信号完整性。早一天遇到，对你来说是好事。 在过去的低速时代，电平跳变时信号上升时间较长，通常几个ns。器件间的互连线不至于影响电路的功能，没必要关心信号完整性问题。但在今天的高速时代，随着IC输出开关速度的提高，很多都在皮秒级，不管信号周期如何，几乎所有设计都遇到了信号完整性问题。另外，对低功耗追求使得内核电压越来越低，1.2v内核电压已经很常见了。因此系统能容忍的噪声余量越来越小，这也使得信号完整性问题更加突出。 广义上讲，信号完整性是指在电路设计中互连线引起的所有问题，它主要研究互连线的电气特性参数与数字信号的电压电流波形相互作用后，如何影响到产品性能的问题。主要表现在对时序的影响、信号振铃、信号反射、近端串扰、远端串扰、开关噪声、非单调性、地弹、电源反弹、衰减、容性负载、电磁辐射、电磁干扰等。 信号完整性问题的根源在于信号上升时间的减小。即使布线拓扑结构没有变化，如果采用了信号上升时间很小的IC芯片，现有设计也将处于临界状态或者停止工作。 下面谈谈几种常见的信号完整性问题。 反射： 图1显示了信号反射引起的波形畸变。看起来就像振铃，拿出你制作的电路板，测一测各种信号，比如时钟输出或是高速数据线输出，看看是不是存在这种波形。如果有，那么你该对信号完整性问题有个感性的认识了，对，这就是一种信号完整性问题。 很多硬件工程师都会在时钟输出信号上串接一个小电阻，至于为什么，他们中很多人都说不清楚，他们会说，很多成熟设计上都有，照着做的。或许你知道，可是确实很多人说不清这个小小电阻的作用，包括很多有了三四年经验的硬件工程师，很惊讶么?可这确实是事实，我碰到过很多。其实这个小电阻的作用就是为了解决信号反射问题。而且随着电阻的加大，振铃会消失，但你会发现信号上升沿不再那么陡峭了。这个解决方法叫阻抗匹配，奥，对了，一定要注意阻抗匹配，阻抗在信号完整性问题中占据着极其重要的

第三章 信号分析基础

第三章 信号分析基础 3.1 信号空间 3.1.1 信号范数与赋范线性空间 信号)(t x （或)(n x ）的范数定义为： })(max{)(∞<<∞-=∞t t x t x ， （或 })(max{)(∞<<∞-=∞n n x n x ，） (3-1) dt t x t x ? ∞ ∞ -=)()(1 （或 ∑∞ -∞ == n n x n x )()(1） (3-2) 2 12 2 )() (?? ????=?∞ ∞-dt t x t x （或 2 122 )() (?? ? ???=∑∞ -∞=n n x n x ） (3-3) 以下简写为：p x 。 信号范数具有如下性质（其中，p=1,2,∞）： 1）0≥p x ；0=p x ，当且仅当x 恒为零； (3-4) 2）p p x x ?=?λλ，λ为实数； (3-5) 3）p p p y x y x +≤+ (3-6) 【 证明 ：略】 在时间域（+∞∞-,）范围，最大幅度有界的全体信号所构成的信号空间记为 }:{∞<=∞∞x x L (3-7) 绝对可积（或绝对可和）的全体信号所构成的信号空间记为 }:{11∞<=x x L (3-8) 平方可积（或平方可和）的全体信号所构成的信号空间记为 }:{22∞<=x x L (3-9) 根据泛函理论可知，L ∞、L 2和L 1都是赋范线性空间。 3.1.2 信号内积与内积空间 在赋范线性空间2L （或2l ）中，定义二信号的内积 ?∞ ∞ -=dt t y t x t y t x )()()(),(（2L 空间） (3-10) 或 ∑∞ -∞ == n n y n x n y n x )()()(),(（2 l 空间） (3-11) 以下简写为：y x ,。 通过简单验证，可知内积y x ,满足： 1） y x y x ,,αα= (3-12) 2）z y z x z y x ,,,+=+ (3-13) 3）x y y x ,,= (3-14) 4）0,≥x x ，并且0,=x x 的充要条件是θ=x 。 (3-15) 因此，2L （2l ）称为内积空间，并且具有完备性、可分性，是希尔伯特—Hilbert 空间。 特例，当y x =时，有 2 2,x x x = (3-16)

信号分析与处理答案第二版完整版

信号分析与处理答案第 二版 HEN system office room 【HEN16H-HENS2AHENS8Q8-HENH1688】

第二章习题参考解答 求下列系统的阶跃响应和冲激响应。 (1) 解当激励为时，响应为，即： 由于方程简单，可利用迭代法求解： ，， …， 由此可归纳出的表达式： 利用阶跃响应和冲激响应的关系，可以求得阶跃响应： (2) 解 (a)求冲激响应 ，当时，。 特征方程，解得特征根为。所以： …(2.1.2.1) 通过原方程迭代知，，，代入式(2.1.2.1)中得：解得，代入式(2.1.2.1)： …(2.1.2.2) 可验证满足式(2.1.2.2)，所以： (b)求阶跃响应 通解为 特解形式为，，代入原方程有，即 完全解为 通过原方程迭代之，，由此可得 解得，。所以阶跃响应为： (3)

解 (4) 解 当t>0时，原方程变为：。 …(2.1.3.1) …(2.1.3.2) 将(2.1.3.1)、式代入原方程，比较两边的系数得： 阶跃响应： 求下列离散序列的卷积和。 (1) 解用表 格法求 解 (2) 解用表 格法求 解 (3) 和 如题图2.2.3所示 解用表 格法求 解

(4) 解 (5) 解 (6) 解参见右图。 当时： 当时： 当时： 当时： 当时： (7) ， 解参见右图： 当时： 当时： 当时： 当时： 当时： (8) ，解参见右图

当时： 当时： 当时： 当时： (9) ， 解 (10) ， 解 或写作：

求下列连续信号的卷积。 (1) ， 解参见右图： 当时： 当时： 当时： 当时： 当时： 当时： (2) 和如图2.3.2所示 解当时： 当时： 当时： 当时： 当时： (3) ， 解 (4) ， 解 (5) ， 解参见右图。当时：当时： 当时：

信号与系统基础知识

第1章 信号与系统的基本概念 1.1 引言 系统是一个广泛使用的概念，指由多个元件组成的相互作用、相互依存的整体。我们学习过“电路分析原理”的课程，电路是典型的系统，由电阻、电容、电感和电源等元件组成。我们还熟悉汽车在路面运动的过程，汽车、路面、空气组成一个力学系统。更为复杂一些的系统如电力系统，它包括若干发电厂、变电站、输电网和电力用户等，大的电网可以跨越数千公里。 我们在观察、分析和描述一个系统时，总要借助于对系统中一些元件状态的观测和分析。例如，在分析一个电路时，会计算或测量电路中一些位置的电压和电流随时间的变化；在分析一个汽车的运动时，会计算或观测驱动力、阻力、位置、速度和加速度等状态变量随时间的变化。系统状态变量随时间变化的关系称为信号，包含了系统变化的信息。 很多实际系统的状态变量是非电的，我们经常使用各种各样的传感器，把非电的状态变量转换为电的变量，得到便于测量的电信号。 隐去不同信号所代表的具体物理意义，信号就可以抽象为函数，即变量随时间变化的关系。信号用函数表示，可以是数学表达式，或是波形，或是数据列表。在本课程中，信号和函数的表述经常不加区分。 信号和系统分析的最基本的任务是获得信号的特点和系统的特性。系统的分析和描述借助于建立系统输入信号和输出信号之间关系，因此信号分析和系统分析是密切相关的。 系统的特性千变万化，其中最重要的区别是线性和非线性、时不变和时变。这些区别导致分析方法的重要差别。本课程的内容限于线性时不变系统。 我们最熟悉的信号和系统分析方法是时域分析，即分析信号随时间变化的波形。例如，对于一个电压测量系统，要判断测量的准确度，可以直接分析比较被测的电压波形)(in t v （测量系统输入信号）和测量得到的波形)(out t v （测量系统输出信号），观察它们之间的相似程度。为了充分地和规范地描述测量系统的特性，经常给系统输入一个阶跃电压信号，得到系统的阶跃响应，图1-1是典型的波形，通过阶跃响应的电压上升时间（电压从10％上升至90％的时间）和过冲（百分比）等特征量，表述测量系统的特性，上升时间和过冲越小，系统特性越好。其中电压上升时间反映了系统的响应速度，小的上升时间对应快的响应速度。如果被测电压快速变化，而测量系统的响应特性相对较慢，则必然产生较大的测量误差。 信号与系统分析的另一种方法是频域分析。信号频域分析的基本原理是把信号分解为不

信号完整性分析基础系列之一——眼图测量

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信号分析基础The Fundamentals of Signal Analysis

The Fundamentals of Signal Analysis Application Note 243

Table of Contents Chapter 1Introduction4 Chapter 2The Time, Frequency and Modal Domains:5 Chapter 3Understanding Dynamic Signal Analysis25 Chapter 4Using Dynamic Signal Analyzers49 Appendix A The Fourier Transform: A Mathematical Background63 Appendix B Bibliography66 Index67

Chapter 1 Introduction The analysis of electrical signals is a fundamental problem for many engineers and scientists. Even if the immediate problem is not electrical, the basic param-eters of interest are often changed into electrical signals by means of transducers. Common transducers include accelerometers and load cells in mechanical work, EEG electrodes and blood pressure probes in biology and medicine, and pH and conductivity probes in chemistry. The rewards for trans-forming physical parameters to electrical signals are great, as many instruments are available for the analysis of electrical sig-nals in the time, frequency and modal domains. The powerful measurement and analysis capa-bilities of these instruments can lead to rapid understanding of the system under study. This note is a primer for those who are unfamiliar with the advantages of analysis in the frequency and modal domains and with the class of analyzers we call Dynamic Signal Analyzers. In Chapter 2 we develop the con-cepts of the time, frequency and modal domains and show why these different ways of looking at a problem often lend their own unique insights. We then intro-duce classes of instrumentation available for analysis in these domains. Because of the tutorial nature of this note, we will not attempt to show detailed solutions for the multitude of measurement prob- lems which can be solved by Dynamic Signal Analysis. Instead, we will concentrate on the fea- tures of Dynamic Signal Analysis, how these features are used in a wide range of applications and the benefits to be gained from using Dynamic Signal Analysis. Those who desire more details on specific applications should look to Appendix B. It contains abstracts of Hewlett-Packard Application Notes on a wide range of related subjects. These can be obtained free of charge from your local HP field engineer or representative. In Chapter 3 we develop the properties of one of these classes of analyzers, Dynamic Signal Analyzers. These instruments are particularly appropriate for the analysis of signals in the range of a few millihertz to about a hundred kilohertz. Chapter 4 shows the benefits of Dynamic Signal Analysis in a wide range of measurement situations. The powerful analysis tools of Dynamic Signal Analysis are introduced as needed in each measurement situation. This note avoids the use of rigor- ous mathematics and instead depends on heuristic arguments. We have found in over a decade of teaching this material that such arguments lead to a better under- standing of the basic processes involved in the various domains and in Dynamic Signal Analysis. Equally important, this heuristic instruction leads to better instru- ment operators who can intelli- gently use these analyzers to solve complicated measurement problems with accuracy and ease*. *A more rigorous mathematical justification for the arguments developed in the main text can be found in Appendix A.

信号完整性分析基础之八——抖动的频域分析

在上两篇文章中，我们分别介绍了直方图（统计域分析）和抖动追踪（时域分析）在抖动分析中的应用。从抖动的直方图和抖动追踪波形上我们可以得到抖动的主要构成成分以及抖动参数的变化趋势。如需对抖动的构成做进一步的分析，还需要从频域角度去进一步分析抖动的跟踪波形。 抖动的频谱即是对抖动追踪（jitter track）波形做FFT运算。如下图1所示 为一个时钟周期测量参数的追踪、频谱分析步骤及效果，在抖动频谱图上可以清楚的看出某两个频率值点抖动比较大： 图1 抖动频谱 黄色为实际采集到的时钟波形（C1通道） P1测量C1通道时钟信号的时钟周期 F7函数对P1测量参数进行跟踪 F6对F7进行FFT分析 下图2所示为一典型的串行信号抖动追踪频谱图，从图中可看出各种抖动成分；DDj和Pj为窄带频谱（三角形谱或者谱线）但是DDj和Pj的区别是由于DDj是和码型相关的，其频率fDDJ一般会是数据位率的整数倍，如果Pj的频率fPJ正好等于fDDJ，那么从抖动的频谱图里面是很难将DDj和Pj精确的分开的，所以通常在抖动分解的过程中一般通过时域平均的方法来分解DDj；BUj主要由于串扰等因素引起的，一般分为两种，一种是窄带，但幅度较高，很显然这类BUJ也是很难和PJ区分开的，除非我们知道引起BUJ的源头，知道其频率，所以说我们在抖动测试时得到的PJ一般会包含这类BUJ(所以通常情况下对这类BUJ不加区分，直接算做PJ，而将BUJ分类为PJ和OBUJ，在之前的抖动分类文章中有提及)；另外一类是宽带的BUJ（很多时候也叫OBUJ，other bounded uncorrelated jitter），幅度很小，基本会埋没到RJ中去，这类抖动很容易被误算作RJ，目前使用在示波器上的抖动分解软件只有Lecroy最近推出的SDAII（基于NQ-SCALE抖动分解理论）能够较好的将这类抖动从Rj中剥离出来；RJ是 宽带频谱，幅度很小。

信号完整性分析

信号完整性背景 信号完整性问题引起人们的注意，最早起源于一次奇怪的设计失败现象。当时，美国硅谷一家著名的影像探测系统制造商早在7 年前就已经成功设计、制造并上市的产品，却在最近从生产线下线的产品中出现了问题，新产品无法正常运行，这是个20MHz 的系统设计，似乎无须考虑高速设计方面的问题，更为让产品设计工程师们困惑的是新产品没有任何设计上的修改，甚至采用的元器件型号也与原始设计的要求一致，唯一的区别是 IC 制造技术的进步，新采购的电子元器件实现了小型化、快速化。新的器件工艺技术使得新生产的每一个芯片都成为高速器件，也正是这些高速器件应用中的信号完整性问题导致了系统的失败。随着集成电路(IC)开关速度的提高，信号的上升和下降时间迅速缩减，不管信号频率如何，系统都将成为高速系统并且会出现各种各样的信号完整性问题。在高速PCB 系统设计方面信号完整性问题主要体现为：工作频率的提高和信号上升/下降时间的缩短，会使系统的时序余量减小甚至出现时序方面的问题；传输线效应导致信号在传输过程中的噪声容限、单调性甚至逻辑错误；信号间的串扰随着信号沿的时间减少而加剧；以及当信号沿的时间接近0.5ns 及以下时，电源系统的稳定性下降和出现电磁干扰问题。

信号完整性含义 信号完整性(Signal Integrity)简称SI，指信号从驱动端沿传输线到达接收端后波形的完整程度。即信号在电路中以正确的时序和电压作出响应的能力。如果电路中信号能够以要求的时序、持续时间和电压幅度到达IC，则该电路具有较好的信号完整性。反之，当信号不能正常响应时，就出现了信号完整性问题。从广义上讲，信号完整性问题指的是在高速产品中由互连线引起的所有问题，主要表现为五个方面:

(完整版)信号与系统的理解与认识

1.《信号与系统》这门课程主要讲述什么内容？ 《信号与系统》是一门重要的专业基础课程。它的任务是研究信号和线性非时变系统的基本理论和基本分析方法，要求掌握最基本的信号变换理论，并掌握线性非时变系统的分析方法，为学习后续课程，以及从事相关领域的工程技术和科学研究工作奠定坚实的理论基础。 2. 这门在我们的知识架构中占有什么地位？ 是一门承上启下的重要的专业基础课程。其基本概念和方法对所有的 工科专业都很重要。信号与系统的分析方法的应用范围一直不断的在扩大。信号与系统不仅仅是工科教育中一门最基本的课程，而且能够成为工科类学生最有益处而又引人入胜又最有用处的一门课程。 《信号与系统》是将我们从电路分析的知识领域引入信号处理与传输领域的关键性课程。 3.学习这门课程有什么用处？

学习这门课程有什么用处呢？百度告诉我：通过本课程的学习，学生将理解信号的 函数表示与系统分析方法，掌握连续时间系和离散时间系统的时域分析和频域分析， 连续时间系统的S域分析和散时间系统的Z分析，以及状态方程与状态变量分析法等 相关内容。通过上机实验，使学生掌握利用计算机进行信号与系统分析的基本方法加 深对信号与线性非时变系统的基本理论的理解，训练学生的实验技能和科学实验方法，提高分析和解决实际问题的能力。 在百度上和道客巴巴还有知乎上都是很多这样看起来很高大上的解释，但是作为学 生的我还是不能很清楚的了解到学习这门课程有什么用处，后面我发现了这样一个个 例子，觉得对信号与系统的用处有了一定的了解。 如图这样一个轮子是怎么设计的呢？ （打印有可能打印不出来，就是很神奇的一个轮子，交通工具） 没学过信号与系统的小明想到了反馈与系统，在轮子上放一个传感器，轮子正不正 系统就知道了，所以设计这个轮子其实就是设计一个系统。 好，现在我们有了一个传感器，要是机器朝左边偏一度，他就会输出一个信号。这个信号接下来就会传给处理器进行处理。处理器再控制电机，让他驱动轮子产生向左 的加速度，加速度就相当于给予系统向右的力，来修正向左的偏移。 小明就按照这一思想设计了一个小车车。踏上踏板，一上电，尼玛，他和他的车车就变成了一个节拍器。左边摔一下，右边摔一下。幸亏小明戴了头盔。小明觉得被骗了。找了一本反馈理论来看，原来有些反馈系统是不稳定的。 想要这个系统稳定地立着，我该怎么办？小明眼神呆滞，望着天空。 天边传来一个声音：你要分析环路稳定性呀。 怎么分析呢？ 你要从信号传输入手，分析信号的传输函数。

信号完整性分析基础系列之一__关于眼图测量(全)

信号完整性分析基础系列之一_——关于眼图测量(全) 您知道吗？眼图的历史可以追溯到大约47年前。在力科于2002年发明基于连续比特位的方法来测量眼图之前，1962年-2002的40年间，眼图的测量是基于采样示波器的传统方法。 您相信吗？在长期的培训和技术支持工作中，我们发现很少有工程师能完整地准确地理解眼图的测量原理。很多工程师们往往满足于各种标准权威机构提供的测量向导，Step by Step，满足于用“万能”的Sigtest软件测量出来的眼图给出的Pass or Fail结论。这种对于Sigtest 的迷恋甚至使有些工程师忘记了眼图是可以作为一项重要的调试工具的。 在我2004年来力科面试前，我也从来没有听说过眼图。那天面试时，老板反复强调力科在眼图测量方面的优势，但我不知所云。之后我Google“眼图”，看到网络上有限的几篇文章，但仍不知所云。刚刚我再次Google“眼图”，仍然没有找到哪怕一篇文章讲透了眼图测量。 网络上搜到的关于眼图的文字，出现频率最多的如下，表达得似乎非常地专业，但却在拒绝我们的阅读兴趣。 “在实际数字互连系统中，完全消除码间串扰是十分困难的，而码间串扰对误码率的影响目前尚无法找到数学上便于处理的统计规律，还不能进行准确计算。为了衡量基带传输系统的性能优劣，在实验室中，通常用示波器观察接收信号波形的方法来分析码间串扰和噪声对系统性能的影响，这就是眼图分析法。 如果将输入波形输入示波器的Y轴，并且当示波器的水平扫描周期和码元定时同步时，适当调整相位，使波形的中心对准取样时刻，在示波器上显示的图形很象人的眼睛，因此被称为眼图（Eye Map）。 二进制信号传输时的眼图只有一只“眼睛”，当传输三元码时，会显示两只“眼睛”。眼图是由各段码元波形叠加而成的，眼图中央的垂直线表示最佳抽样时刻，位于两峰值中间的水平线是判决门限电平。 在无码间串扰和噪声的理想情况下，波形无失真，每个码元将重叠在一起，最终在示波器上看到的是迹线又细又清晰的“眼睛”，“眼”开启得最大。当有码间串扰时，波形失真，码元不完全重合，眼图的迹线就会不清晰，引起“眼”部分闭合。若再加上噪声的影响，则使眼图的线条变得模糊，“眼”开启得小了，因此，“眼”张开的大小表示了失真的程度，反映了码间串扰的强弱。由此可知，眼图能直观地表明码间串扰和噪声的影响，可评价一个基带传输系统性能的优劣。另外也可以用此图形对接收滤波器的特性加以调整，以减小码间串扰和改善系统的传输性能。通常眼图可以用下图所示的图形来描述，由此图可以看出：（1）眼图张开的宽度决定了接收波形可以不受串扰影响而抽样再生的时间间隔。显然，最佳抽样时刻应选在眼睛张开最大的时刻。 （2）眼图斜边的斜率，表示系统对定时抖动（或误差）的灵敏度，斜率越大，系统对定时抖动越敏感。