信號、系統及推理（英文版）

目??錄 Prologue? 開場白 23 第1章?Signals and Systems 信號與系統 31 1.1?Signals, Systems, Models, and Properties 信號、系統、模型及性質 31 1.1.1?System Properties 系統的性質 33 1.2?Linear,Time-Invariant Systems 線性時不變系統 35 1.2.1?Impulse-Response Representation of LTI Systems LTI系統的沖激響應表示 35 1.2.2?Eigenfunction and Transform Representation of LTI Systems? LTI系統的特徵函數和變換表示 36 1.2.3?Fourier Transforms? 傅裏葉變換 40 1.3?Deterministic Signals and Their Fourier Transforms? 確定性信號及其傅裏葉變換 41 1.3.1?Signal Classes and Their Fourier Transforms? 信號種類及其傅裏葉變換 41 1.3.2?Parseval’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 1.4?Bilateral Laplace and z-Transforms? 雙邊z變換和雙邊拉普拉斯變換 46 1.4.1?The Bilateral z-Transform? 雙邊z變換 46 1.4.2?The Bilateral Laplace Transform? 雙邊拉普拉斯變換 50 1.5?Discrete-Time Processing of Continuous-Time Signals? 連續時間信號的離散時間處理 51 1.5.1?Basic 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 1.5.2?DT Filtering and Overall CT Response? 離散時間濾波以及全局連續時間響應 54 1.5.3?Nonideal D/C Converters? 非理想的D/C轉換器 56 1.6?Further 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 2.1?Fourier Transform Magnitude and Phase? 傅裏葉變換的幅度和相位 92 2.2?Group Delay and the Effect of Nonlinear Phase? 群延遲和非線性相位的影響 96 2.2.1?Narrowband Input Signals? 窄帶輸入信號 96 2.2.2?Broadband Input Signals? 寬帶輸入信號 98 2.3?All-Pass and Minimum-Phase Systems? 全通系統與最小相位系統 103 2.3.1?All-Pass Systems? 全通系統 103 2.3.2?Minimum-Phase Systems? 最小相位系統 105 2.4?Spectral Factorization? 譜因式分解 108 2.5?Further Reading? 延伸閱讀 110 Problems? 習題 110 第3章?Pulse Amplitude Modulation? 脈沖幅度調制 132 3.1?Baseband Pulse Amplitude Modulation? 基帶脈沖幅度調制 133 3.1.1?The Transmitted Signal? 發送信號 133 3.1.2?The Received Signal? 接收信號 135 3.1.3?Frequency-Domain Characterizations? 頻域特性 135 3.1.4?Intersymbol Interference at the Receiver? 接收機處的碼間乾擾 138 3.2?Nyquist Pulses? 奈奎斯特脈沖 140 3.3?Passband Pulse Amplitude Modulation? 通帶脈沖幅度調制 143 3.3.1?Frequency-Shift Keying (FSK)? 頻移鍵控 144 3.3.2?Phase-Shift Keying (PSK)? 相移鍵控 144 3.3.3?Quadrature Amplitude Modulation (QAM)? 正交幅度調制 146 3.4?Further Reading? 延伸閱讀 148 Problems? 習題 149 第4章?State-Space Models? 狀態空間模型 163 4.1?System Memory? 系統記憶性 163 4.2?Illustrative Examples? 舉例說明 164 4.3?State-Space Models? 狀態空間模型 176 4.3.1?DT State-Space Models? 離散時間狀態空間模型 176 4.3.2?CT State-Space Models? 連續時間狀態空間模型 179 4.3.3?Defining Properties of State-Space Models? 狀態空間模型的典型性質 181 4.4?State-Space Models from LTI Input-Output Models? 基於LTI輸入輸出模型的狀態空間模型 183 4.5?Equilibria 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 4.5.1?Equilibrium? 平衡狀態 188 4.5.2?Linearization? 線性化 191 4.6?Further 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 5.1?Continuous-Time and Discrete-Time LTI Models? 連續時間和離散時間LTI模型 204 5.2?Zero-Input Response and Modal Representation? 零輸入響應和模態表示 207 5.2.1?Undriven CT Systems? 未驅動的連續時間系統 207 5.2.2?Undriven DT Systems? 未驅動的離散時間系統 215 5.2.3?Asymptotic Stability of LTI Systems? LTI系統的漸進穩定性 217 5.3?General Response in Modal Coordinates? 模態坐標下的通用響應 221 5.3.1?Driven CT Systems? 被驅動的連續時間系統 221 5.3.2?Driven DT Systems? 被驅動的離散時間系統 224 5.3.3?Similarity Transformations and Diagonalization? 相似變換和對角化 226 5.4?Transfer Functions, Hidden Modes, Reachability, and Observability? 傳輸函數、隱藏模式、可達性和可觀測性 232 5.4.1?Input-State-Output Structure of CT Systems? 連續時間系統的輸入狀態輸出結構 232 5.4.2?Input-State-Output Structure of DT Systems? 離散時間系統的輸入狀態輸出結構 240 5.5?Further 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 6.1?Plant and Model? 設備和模型 267 6.2?State Estimation and Observers? 狀態估計和觀測器 269 6.2.1?Real-Time Simulation? 實時模擬 269 6.2.2?The State Observer? 狀態觀測器 271 6.2.3?Observer Design? 觀測器設計 273 6.3?State Feedback Control? 狀態反饋控制 282 6.3.1?Open-Loop Control? 開環控制 282 6.3.2?Closed-Loop Control via LTI State Feedback? 經由LTI狀態反饋的閉環控制 283 6.3.3?LTI State Feedback Design? LTI狀態反饋設計 284 6.4?Observer-Based Feedback Control? 基於觀測器的反饋控制 292 6.5?Further Reading? 延伸閱讀 297 Problems? 習題 297 第7章?Probabilistic Models? 概率模型 309 7.1?The Basic Probability Model? 基本概率模型 309 7.2?Conditional Probability, Bayes’ Rule, and Independence? 條件概率、貝葉斯法則和事件的獨立性 310 7.3?Random Variables? 隨機變量 313 7.4?Probability Distributions? 概率分佈 313 7.5?Jointly Distributed Random Variables? 聯合分佈的隨機變量 315 7.6?Expectations, Moments, and Variance? 期望、矩和方差 317 7.7?Correlation and Covariance for Bivariate Random Variables? 二元隨機變量的相關性和協方差 320 7.8?A Vector-Space Interpretation of Correlation Properties? 向量空間中的相關性質 324 7.9?Further Reading? 延伸閱讀 326 Problems? 習題 327 第8章?Estimation? 估計算法 336 8.1?Estimation of a Continuous Random Variable? 單個連續隨機變量的估計 337 8.2?From Estimates to the Estimator? 從估計到估計器 342 8.2.1?Orthogonality? 正交性 347 8.3?Linear Minimum Mean Square Error Estimation? 線性最小均方誤差估計 348 8.3.1?Linear 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?Multiple Measurements? 多重量測 353 8.4?Further Reading? 延伸閱讀 357 Problems? 習題 358 第9章?Hypothesis Testing? 假設檢驗 373 9.1?Binary Pulse-Amplitude Modulation in Noise? 噪聲中的二進制脈沖幅度調制 373 9.2?Hypothesis Testing with Minimum Error Probability? 最小差錯概率下的假設檢驗 375 9.2.1?Deciding with Minimum Conditional Probability of Error? 最小條件差錯概率的判決 376 9.2.2?MAP Decision Rule for Minimum Overall Probability of Error? 最小化總體差錯概率的MAP判決準則 377 9.2.3?Hypothesis Testing in Coded Digital Communication? 編碼數字通信中的假設檢驗 380 9.3?Binary Hypothesis Testing? 二元假設檢驗 383 9.3.1?False Alarm, Miss, and Detection? 虛警、漏警和檢測 384 9.3.2?The Likelihood Ratio Test? 似然比檢驗 386 9.3.3?Neyman-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 9.4?Minimum Risk Decisions? 最小風險判決 391 9.5?Further Reading? 延伸閱讀 393 Problems? 習題 393 第10章?Random Processes? 隨機過程 410 10.1?Definition and Examples of a Random Process? 隨機過程的定義和舉例 410 10.2?First-and Second-Moment Characterization of Random Processes? 隨機過程的一階矩和二階矩特性 415 10.3?Stationarity? 平穩性 416 ?10.3.1?Strict-Sense Stationarity? 嚴格平穩性 416 ?10.3.2?Wide-Sense Stationarity? 廣義平穩性 416 ?10.3.3?Some Properties of WSS Correlation and Covariance Functions? WSS相關函數和協方差函數的性質 418 10.4?Ergodicity? 各態歷經性 421 10.5?Linear Estimation of Random Processes? 隨機過程的線性估計 422 ?10.5.1?Linear Prediction? 線性預測 422 ?10.5.2?Linear FIR Filtering? 線性FIR濾波 424 10.6?LTI Filtering of WSS Processes? WSS過程的LTI濾波 425 10.7?Further Reading? 延伸閱讀 431 Problems? 習題 431 第11章?Power Spectral Density? 功率譜密度 451 11.1?Spectral Distribution of Expected Instantaneous Power? 瞬時功率期望的頻譜分佈 452 ?11.1.1?Power Spectral Density? 功率譜密度 452 ?11.1.2?Fluctuation Spectral Density? 波動譜密度 456 ?11.1.3?Cross-Spectral Density? 互譜密度 461 11.2?Expected 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 11.3?Applications? 應用 467 ?11.3.1?Revealing Cyclic Components? 揭示循環分量 467 ?11.3.2?Modeling Filters? 模型濾波器 469 ?11.3.3?Whitening Filters? 白化濾波器 473 ?11.3.4?Sampling Bandlimited Random Processes? 帶限隨機過程的採樣 474 11.4?Further Reading? 延伸閱讀 474 Problems? 習題 475 第12章?Signal Estimation? 信號估計 494 12.1?LMMSE Estimation for Random Variables? 隨機變量的LMMSE估計 495 12.2?FIR Wiener Filters? FIR維納濾波器 497 12.3?The Unconstrained DT Wiener Filter? 無約束的離散時間維納濾波器 502 12.4?Causal DT Wiener Filtering? 離散時間的因果維納濾波 510 12.5?Optimal Observers and Kalman Filtering? 最佳觀測器和卡爾曼濾波 517 ?12.5.1?Causal Wiener Filtering of a Signal Corrupted by Additive Noise 受加性噪聲乾擾的信號的因果維納濾波 517 ?12.5.2?Observer Implementation of the Wiener Filter? 維納濾波器的觀測器實現 519 ?12.5.3?Optimal State Estimates and Kalman Filtering? 最佳狀態估計和卡爾曼濾波 521 12.6?Estimation of CT Signals? 連續時間信號的估計 522 12.7?Further Reading? 延伸閱讀 523 Problems? 習題 523 第13章?Signal Detection? 信號檢測 541 13.1?Hypothesis Testing with Multiple Measurements? 基於多重量測的假設檢驗 542 13.2?Detecting a Known Signal in I.I.D. Gaussian Noise? 獨立同分佈高斯噪聲中已知信號的檢測 544 ?13.2.1?The Optimal Solution? 最佳檢測方案 545 ?13.2.2?Characterizing Performance? 性能描述 547 ?13.2.3?Matched Filtering? 匹配濾波 549 13.3?Extensions of Matched-Filter Detection? 匹配濾波器檢測的推廣 552 ?13.3.1?Infinite-Duration, Finite-Energy Signals? 無限長度的有限能量信號 552 ?13.3.2?Maximizing SNR for Signal Detection in White Noise? 白噪聲中信號檢測的SNR最大化 552 ?13.3.3?Detection in Colored Noise? 有色噪聲中的檢測 555 ?13.3.4?Continuous-Time Matched Filters? 連續時間匹配濾波器 558 ?13.3.5?Matched Filtering and Nyquist Pulse Design? 匹配濾波和奈奎斯特脈沖設計 559 ?13.3.6?Unknown Arrival Time and Pulse Compression? 未知的到達時間和脈沖壓縮 560 13.4?Signal Discrimination in I.I.D. Gaussian Noise? 獨立同分佈高斯噪聲中的信號識別 562 13.5?Further Reading? 延伸閱讀 568 Problems? 習題 568 Bibliography? 參考文獻 585 Index? 索引