"奧本海姆近年力作；本書立足的由基本原理和概念所構架的信號、繫統、概率的研究和應用非常豐富，支持的領域非常廣泛，有著豐富的歷史重要性，因此內容非常豐富；本書將信號與繫統狀態、模態結合起來，將觀測器與濾波理論結合起來，無論是在狀態估計還是信號檢測上，構成的推理具有數學上的基礎和普適性的應用；本書在信號與繫統的基礎上，融合並擴展了信號與繫統時頻域分析的基本素材和概率論知識；書中所提出的“推理”（Inference）是結合先驗知識和可用的信號量測來歸納不確定性的存在性的，從而領引信號與等

●Prologue
開場白23
第1章Signals and Systems
信號與繫統31
1.1Signals, Systems, Models, and Properties
信號、繫統、模型及性質31
1.1.1System Properties
繫統的性質33
1.2Linear,Time-Invariant Systems
線性時不變繫統35
1.2.1Impulse-Response Representation of LTI Systems
LTI繫統的衝激響應表示35
1.2.2Eigenfunction and Transform Representation of LTI Systems
LTI繫統的特征函數和變換表示36
1.2.3Fourier Transforms
傅裡葉變換40
1.3Deterministic Signals and Their Fourier Transforms
確定性信號及其傅裡葉變換41
1.3.1Signal Classes and Their Fourier Transforms
信號種類及其傅裡葉變換41
1.3.2Parseval’s Identity, Energy Spectral Density, and Deterministic Autocorrelation
Parseval恆等式、能量譜密度以及確定性自相關44
1.4Bilateral Laplace and z-Transforms
雙邊z變換和雙邊拉普拉斯變換46
1.4.1The Bilateral z-Transform
雙邊z變換46
1.4.2The Bilateral Laplace Transform
雙邊拉普拉斯變換50
1.5Discrete-Time Processing of Continuous-Time Signals
連續時間信號的離散時間處理51
1.5.1Basic Structure for DT Processing of CT Signals
連續時間信號的離散時間處理過程的基本結構52
1.5.2DT Filtering and Overall CT Response
離散時間濾波以及全局連續時間響應54
1.5.3Nonideal D/C Converters
非理想的D/C轉換器56
1.6Further Reading
延伸閱讀58
Problems
習題59
第2章Amplitude, Phase, and Group Delay
幅度、相位和群延遲92
2.1Fourier Transform Magnitude and Phase
傅裡葉變換的幅度和相位92
2.2Group Delay and the Effect of Nonlinear Phase
群延遲和非線性相位的影響96
2.2.1Narrowband Input Signals
窄帶輸入信號96
2.2.2Broadband Input Signals
寬帶輸入信號98
2.3All-Pass and Minimum-Phase Systems
全通繫統與最小相位繫統103
2.3.1All-Pass Systems
全通繫統103
2.3.2Minimum-Phase Systems
最小相位繫統105
2.4Spectral Factorization
譜因式分解108
2.5Further Reading
延伸閱讀110
Problems
習題110
第3章Pulse Amplitude Modulation
脈衝幅度調制132
3.1Baseband Pulse Amplitude Modulation
基帶脈衝幅度調制133
3.1.1The Transmitted Signal
發送信號133
3.1.2The Received Signal
接收信號135
3.1.3Frequency-Domain Characterizations
頻域特性135
3.1.4Intersymbol Interference at the Receiver
接收機處的碼間干擾138
3.2Nyquist Pulses
奈奎斯特脈衝140
3.3Passband Pulse Amplitude Modulation
通帶脈衝幅度調制143
3.3.1Frequency-Shift Keying (FSK)
頻移鍵控144
3.3.2Phase-Shift Keying (PSK)
相移鍵控144
3.3.3Quadrature Amplitude Modulation (QAM)
正交幅度調制146
3.4Further Reading
延伸閱讀148
Problems
習題149
第4章State-Space Models
狀態空間模型163
4.1System Memory
繫統記憶性163
4.2Illustrative Examples
舉例說明164
4.3State-Space Models
狀態空間模型176
4.3.1DT State-Space Models
離散時間狀態空間模型176
4.3.2CT State-Space Models
連續時間狀態空間模型179
4.3.3Defining Properties of State-Space Models
狀態空間模型的典型性質181
4.4State-Space Models from LTI Input-Output Models
基於LTI輸入輸出模型的狀態空間模型183
4.5Equilibria and Linearization of Nonlinear State-Space Models
非線性狀態空間模型的平衡狀態和線性化188
4.5.1Equilibrium
平衡狀態188
4.5.2Linearization
線性化191
4.6Further Reading
延伸閱讀194
Problems
習題195
第5章LTI State-Space Models
LTI狀態空間模型204
5.1Continuous-Time and Discrete-Time LTI Models
連續時間和離散時間LTI模型204
5.2Zero-Input Response and Modal Representation
零輸入響應和模態表示207
5.2.1Undriven CT Systems
未驅動的連續時間繫統207
5.2.2Undriven DT Systems
未驅動的離散時間繫統215
5.2.3Asymptotic Stability of LTI Systems
LTI繫統的漸進穩定性217
5.3General Response in Modal Coordinates
模態坐標下的通用響應221
5.3.1Driven CT Systems
被驅動的連續時間繫統221
5.3.2Driven DT Systems
被驅動的離散時間繫統224
5.3.3Similarity Transformations and Diagonalization
相似變換和對角化226
5.4Transfer Functions, Hidden Modes, Reachability, and Observability
傳輸函數、隱藏模式、可達性和可觀測性232
5.4.1Input-State-Output Structure of CT Systems
連續時間繫統的輸入狀態輸出結構232
5.4.2Input-State-Output Structure of DT Systems
離散時間繫統的輸入狀態輸出結構240
5.5Further Reading
延伸閱讀249
Problems
習題250
第6章State Observers and State Feedback
狀態觀測器和狀態反饋266
6.1Plant and Model
設備和模型267
6.2State Estimation and Observers
狀態估計和觀測器269
6.2.1Real-Time Simulation
實時仿真269
6.2.2The State Observer
狀態觀測器271
6.2.3Observer Design
觀測器設計273
6.3State Feedback Control
狀態反饋控制282
6.3.1Open-Loop Control
開環控制282
6.3.2Closed-Loop Control via LTI State Feedback
經由LTI狀態反饋的閉環控制283
6.3.3LTI State Feedback Design
LTI狀態反饋設計284
6.4Observer-Based Feedback Control
基於觀測器的反饋控制292
6.5Further Reading
延伸閱讀297
Problems
習題297
第7章Probabilistic Models
概率模型309
7.1The Basic Probability Model
基本概率模型309
7.2Conditional Probability, Bayes’ Rule, and Independence
條件概率、貝葉斯法則和事件的獨立性310
7.3Random Variables
隨機變量313
7.4Probability Distributions
概率分布313
7.5Jointly Distributed Random Variables
聯合分布的隨機變量315
7.6Expectations, Moments, and Variance
期望、矩和方差317
7.7Correlation and Covariance for Bivariate Random Variables
7.8A Vector-Space Interpretation of Correlation Properties
向量空間中的相關性質324
7.9Further Reading
延伸閱讀326
Problems
習題327
第8章Estimation
估計算法336
8.1Estimation of a Continuous Random Variable
單個連續隨機變量的估計337
8.2From Estimates to the Estimator
從估計到估計器342
8.2.1Orthogonality
正交性347
8.3Linear Minimum Mean Square Error Estimation
線性最小均方誤差估計348
8.3.1Linear Estimation of One Random Variable from a Single Measurement of Another
從一個隨機變量的單次量測中線性估計另一個隨機變量348
8.3.2 ltiple Measurements
多重量測353
8.4Further Reading
延伸閱讀357
Problems
習題358
第9章Hypothesis Testing
假設檢驗373
9.1Binary Pulse-Amplitude Modulation in Noise
噪聲中的二進制脈衝幅度調制373
9.2Hypothesis Testing with Minimum Error Probability
最小差錯概率下的假設檢驗375
9.2.1Deciding with Minimum Conditional Probability of Error
最小條件差錯概率的判決376
9.2.2MAP Decision Rule for Minimum Overall Probability of Error
最小化總體差錯概率的MAP判決準則377
9.2.3Hypothesis Testing in Coded Digital Communication
編碼數字通信中的假設檢驗380
9.3Binary Hypothesis Testing
9.3.1False Alarm, Miss, and Detection
虛警、漏警和檢測384
9.3.2The Likelihood Ratio Test
似然比檢驗386
9.3.3Neyman-Pearson Decision Rule and Receiver Operating Characteristic
紐曼-皮爾遜判決準則和接收者操作特性387
9.4Minimum Risk Decisions
最小風險判決391
9.5Further Reading
延伸閱讀393
Problems
習題393
第10章Random Processes
隨機過程410
10.1Definition and Examples of a Random Process
隨機過程的定義和舉例410
10.2First-and Second-Moment Characterization of Random Processes
隨機過程的一階矩和二階矩特性415
10.3Stationarity
平穩性416
10.3.1Strict-Sense Stationarity
嚴格平穩性416
10.3.2Wide-Sense Stationarity
廣義平穩性416
10.3.3Some Properties of WSS Correlation and Covariance Functions
WSS相關函數和協方差函數的性質418
10.4Ergodicity
各態歷經性421
10.5Linear Estimation of Random Processes
隨機過程的線性估計422
10.5.1Linear Prediction
線性預測422
10.5.2Linear FIR Filtering
線性FIR濾波424
10.6LTI Filtering of WSS Processes
WSS過程的LTI濾波425
10.7Further Reading
延伸閱讀431
Problems
習題431
第11章Power Spectral Density
功率譜密度451
11.1Spectral Distribution of Expected Instantaneous Power
瞬時功率期望的頻譜分布452
11.1.1Power Spectral Density
功率譜密度452
11.1.2Fluctuation Spectral Density
波動譜密度456
11.1.3Cross-Spectral Density
互譜密度461
11.2Expected Time-Averaged Power Spectrum and the Einstein-Wiener-Khinchin Theorem
時間平均的功率譜期望和愛因斯坦-維納-辛欽理論462
11.3Applications
應用467
11.3.1Revealing Cyclic Components
揭示循環分量467
11.3.2Modeling Filters
模型濾波器469
11.3.3Whitening Filters
白化濾波器473
11.3.4Sampling Bandlimited Random Processes
帶限隨機過程的采樣474
11.4Further Reading
延伸閱讀474
Problems
習題475
第12章Signal Estimation
信號估計494
12.1LMMSE Estimation for Random Variables
隨機變量的LMMSE估計495
12.2FIR Wiener Filters
FIR維納濾波器497
12.3The Unconstrained DT Wiener Filter
無約束的離散時間維納濾波器502
12.4Causal DT Wiener Filtering
離散時間的因果維納濾波510
12.5Optimal Observers and Kalman Filtering
很好觀測器和卡爾曼濾波517
12.5.1Causal Wiener Filtering of a Signal Corrupted by Additive Noise
受加性噪聲干擾的信號的因果維納濾波517
12.5.2Observer Implementation of the Wiener Filter
維納濾波器的觀測器實現519
12.5.3Optimal State Estimates and Kalman Filtering
很好狀態估計和卡爾曼濾波521
12.6Estimation of CT Signals
連續時間信號的估計522
12.7Further Reading
延伸閱讀523
Problems
習題523
第13章Signal Detection
信號檢測541
13.1Hypothesis Testing with ltiple Measurements
基於多重量測的假設檢驗542
13.2Detecting a Known Signal in I.I.D. Gaussian Noise
獨立同分布高斯噪聲中已知信號的檢測544
13.2.1The Optimal Solution
很好檢測方案545
13.2.2Characterizing Performance
性能描述547
13.2.3Matched Filtering
匹配濾波549
13.3Extensions of Matched-Filter Detection
匹配濾波器檢測的推廣552
13.3.1Infinite-Duration, Finite-Energy Signals
無限長度的有限能量信號552
13.3.2Maximizing SNR for Signal Detection in White Noise
白噪聲中信號檢測的SNR優選化552
13.3.3Detection in Colored Noise
有色噪聲中的檢測555
13.3.4Continuous-Time Matched Filters
連續時間匹配濾波器558
13.3.5Matched Filtering and Nyquist Pulse Design
匹配濾波和奈奎斯特脈衝設計559
13.3.6Unknown Arrival Time and Pulse Compression
未知的到達時間和脈衝壓縮560
13.4Signal Discrimination in I.I.D. Gaussian Noise
獨立同分布高斯噪聲中的信號識別562
13.5Further Reading
延伸閱讀568
Problems
習題568
Bibliography
參考文獻585
Index
索引

本書是美國麻省理工學院（MIT）知名教授奧本海姆的近年力作，是其在MIT開展了二十餘年的Signals,Systems and Inference課程所涉及知識體繫的拓展和延伸。本書詳細闡述了確定性信號與繫統的性質和表示形式，包括群延遲和狀態空間模型的結構與行為；引入了相關函數和功率譜密度來描述和處理隨機信號。本書涉及的應用實例包括脈衝幅度調制，基於觀測器的反饋控制，最小均方誤差估計下的很好線性濾波器，以及匹配濾波器；強調了基於模型的推理方法，特別是針對狀態估計、信號估計和信號檢測的應用。本書融合並擴展了信號與繫統時頻域分析的基本素材和概率論知識，這些都是信號處理、控制、通信、金融工程、生物醫學工程等工程和應用科學領域的基本分析方法。