目 錄
第 1 章 信號與系統(tǒng)導(dǎo)論 ···················································································.1
1.1 信號的概念 ···························································································.1
1.1.1 信號的定義和描述 ·················································································.1
1.1.2 信號的分類 ·························································································.2
1.1.3 信號的運(yùn)算和獨(dú)立變量變換 ·······································································.6
1.2 基本信號 ·····························································································.10
1.2.1 正弦信號 ···························································································.10
1.2.2 指數(shù)信號 ···························································································.12
1.2.3 單位階躍信號 ·····················································································.14
1.2.4 單位沖激信號 ·····················································································.16
1.2.5 抽樣函數(shù) ···························································································.23
1.3 系統(tǒng) ···································································································.24
1.3.1 系統(tǒng)的基本概念 ···················································································.24
1.3.2 系統(tǒng)特性及 LTI 系統(tǒng) ··············································································.27
1.3.3 SISO 系統(tǒng)的時(shí)域描述 ·············································································.33
1.4 信號與系統(tǒng)的基本問題和基本內(nèi)容 ····························································.34
*1.5 Matlab 實(shí)踐入門 ··················································································.35
1.5.1 Matlab 中信號的表示 ··············································································.35
1.5.2 輸出圖形的修飾 ···················································································.41
1.5.3 應(yīng)用舉例 ···························································································.43
習(xí)題 ··········································································································.45
第 2 章 信號與系統(tǒng)的時(shí)域分析 ·········································································.50
2.1 離散時(shí)間 LTI 系統(tǒng)的零狀態(tài)響應(yīng)：卷積和 ···················································.50
2.1.1 LTI 系統(tǒng)響應(yīng)求解的基本思想 ····································································.50
2.1.2 零狀態(tài)響應(yīng)的卷積和求解 ·········································································.50
2.1.3 卷積和的計(jì)算 ·····················································································.52
2.1.4 卷積和的性質(zhì) ·····················································································.57
2.2 連續(xù)時(shí)間 LTI 系統(tǒng)的零狀態(tài)響應(yīng)：卷積積分 ················································.60
2.2.1 零狀態(tài)響應(yīng)的卷積積分求解 ······································································.60
2.2.2 卷積積分的計(jì)算 ···················································································.61
2.2.3 卷積積分的性質(zhì) ···················································································.64
2.3 系統(tǒng)沖激響應(yīng)的性質(zhì) ··············································································.66
2.3.1 系統(tǒng)特性與沖激響應(yīng) ··············································································.66
2.3.2 理想系統(tǒng)的沖激響應(yīng) ··············································································.67
信號與系統(tǒng) X
2.3.3 互聯(lián)系統(tǒng)的沖激響應(yīng) ··············································································.67
*2.4 系統(tǒng)的方框圖表示 ···············································································.69
2.4.1 微分方程描述系統(tǒng)的方框圖表示 ·································································.69
2.4.2 差分方程描述系統(tǒng)的方框圖表示 ·································································.72
*2.5 相關(guān)分析 ···························································································.74
2.5.1 連續(xù)時(shí)間信號相關(guān)函數(shù) ···········································································.74
2.5.2 離散時(shí)間信號相關(guān)函數(shù) ···········································································.81
*2.6 正交分析 ···························································································.82
2.6.1 信號正交的概念和定義 ···········································································.82
2.6.2 信號的正交分解與近似 ···········································································.85
*2.7 Matlab 實(shí)踐 ························································································.88
2.7.1 卷積和的計(jì)算 ·····················································································.88
2.7.2 系統(tǒng)響應(yīng)求解 ·····················································································.89
2.7.3 相關(guān)函數(shù)的計(jì)算 ···················································································.91
習(xí)題 ··········································································································.92
第 3 章 連續(xù)時(shí)間信號與系統(tǒng)的傅里葉分析 ··························································.95
3.1 傅里葉分析的意義 ·················································································.95
3.2 周期信號的傅里葉級數(shù)分析 ·····································································.96
3.2.1 周期信號的傅里葉級數(shù)展開 ······································································.96
3.2.2 復(fù)指數(shù)展開式系數(shù)的基本性質(zhì) ·································································.101
3.2.3 周期信號的頻譜 ·················································································.103
*3.2.4 關(guān)于傅里葉級數(shù)的幾點(diǎn)補(bǔ)充 ···································································.105
3.3 非周期信號的傅里葉變換分析 ································································.106
3.3.1 非周期信號的傅里葉變換表示 ·································································.106
3.3.2 傅里葉變換的性質(zhì)—X(?)的特點(diǎn) ·····························································.111
3.3.3 傅里葉變換的性質(zhì)—信號運(yùn)算的傅里葉變換 ················································.112
3.3.4 周期信號的傅里葉變換 ·········································································.125
3.3.5 傅里葉變換與信號頻譜 ·········································································.129
*3.3.6 能量譜密度和功率譜密度 ·····································································.133
3.4 連續(xù)時(shí)間 LTI 系統(tǒng)的頻域分析 ································································.137
3.4.1 連續(xù)時(shí)間 LTI 系統(tǒng)的頻域表示··································································.137
3.4.2 理想傳輸系統(tǒng)和濾波器 ·········································································.139
*3.4.3 因果穩(wěn)定系統(tǒng)的頻率響應(yīng)特性 ································································.141
3.5 信號的抽樣 ························································································.142
3.5.1 時(shí)域抽樣分析和時(shí)域抽樣定理 ·································································.142
*3.5.2 模擬信號的數(shù)字處理系統(tǒng) ·····································································.149
*3.5.3 頻域抽樣分析和頻域抽樣定理 ································································.152
*3.6 希爾伯特變換 ···················································································.153
3.6.1 希爾伯特變換及其有關(guān)概念 ····································································.153
*3.6.2 解析信號 ·······················································································.157
目 錄 XI
3.7 Matlab 實(shí)踐 ························································································.159
3.7.1 周期信號的分解與合成—傅里葉級數(shù) ·······················································.159
3.7.2 非周期信號的頻譜—傅里葉變換 ····························································.161
3.7.3 信號時(shí)域抽樣 ···················································································.162
3.7.4 希爾伯特變換在 AM 信號解調(diào)中的應(yīng)用—包絡(luò)檢波 ·······································.165
附錄 ········································································································.166
習(xí)題 ········································································································.168
第 4 章 離散時(shí)間信號與系統(tǒng)的傅里葉分析 ························································.174
4.1 周期序列的傅里葉級數(shù)分析 ···································································.174
4.1.1 離散傅里葉級數(shù)（DFS） ·······································································.174
4.1.2 DFS 的性質(zhì)—周期序列頻譜 ck的特點(diǎn) ······················································.176
4.1.3 復(fù)指數(shù)諧波序列及其性質(zhì) ·······································································.178
4.1.4 周期序列的頻譜及其特征 ·······································································.180
4.2 非周期序列的傅里葉變換分析 ································································.181
4.2.1 離散時(shí)間傅里葉變換（DTFT） ································································.181
4.2.2 DTFT 的性質(zhì)—頻譜函數(shù) j X (e ) ? 的特點(diǎn) ····················································.184
4.2.3 DTFT 的性質(zhì)—變換的性質(zhì) ··································································.187
4.2.4 非周期序列的頻譜及其特征 ····································································.192
*4.2.5 周期序列的傅里葉變換 ········································································.194
*4.2.6 序列內(nèi)插零和序列抽取的頻譜分析 ···························································.196
4.3 離散傅里葉變換（DFT） ······································································.201
4.3.1 序列頻譜的離散化和 DFT 的定義 ······························································.201
4.3.2 DFT 和 DFS 的關(guān)系 ·············································································.203
*4.3.3 周期卷積與圓周卷積 ··········································································.208
4.3.4 DFT 的性質(zhì)—X[k]的特性 ····································································.213
*4.3.5 DFT 的性質(zhì)—變換的性質(zhì) ··································································.215
*4.3.6 DFT 的譜線間隔分析— j X (e ) ? 的頻域抽樣 ···············································.224
*4.3.7 快速傅里葉變換（FFT） ······································································.225
4.4 離散時(shí)間系統(tǒng)與連續(xù)時(shí)間系統(tǒng) ································································.228
4.4.1 離散時(shí)間系統(tǒng)頻率響應(yīng) ·········································································.229
4.4.2 連續(xù)時(shí)間頻率和離散時(shí)間頻率 ·································································.232
4.4.3 連續(xù)時(shí)間和離散時(shí)間信號頻譜之間的關(guān)系 ····················································.234
4.4.4 連續(xù)時(shí)間和離散時(shí)間頻率響應(yīng)函數(shù)之間的關(guān)系 ···············································.235
*4.5 數(shù)字濾波—FIR 濾波器 ·····································································.236
4.5.1 數(shù)字濾波的核心原理—脈沖響應(yīng)不變法 ····················································.236
4.5.2 FIR 濾波器 ·······················································································.238
*4.6 Matlab 實(shí)踐 ······················································································.243
4.6.1 fft 函數(shù)調(diào)用和譜線分析 ·········································································.243
4.6.2 數(shù)字濾波函數(shù)調(diào)用和信號的數(shù)字濾波 ··························································.246
習(xí)題 ········································································································.250
信號與系統(tǒng) XII
第 5 章 連續(xù)時(shí)間信號與系統(tǒng)的 s 域分析 ···························································.254
5.1 拉普拉斯變換 ·····················································································.254
5.1.1 拉普拉斯變換的定義及收斂域 ·································································.254
5.1.2 拉普拉斯變換的性質(zhì) ············································································.263
5.1.3 拉普拉斯逆變換求解 ············································································.274
*5.1.4 單邊周期信號的拉普拉斯變換 ································································.281
5.2 系統(tǒng)響應(yīng)的 s 域求解 ············································································.282
5.2.1 微分方程描述系統(tǒng)的響應(yīng)求解 ·································································.283
*5.2.2 電路的 s 域分析 ················································································.285
*5.2.3 自由響應(yīng)與強(qiáng)迫響應(yīng)、穩(wěn)態(tài)響應(yīng)與暫態(tài)響應(yīng) ·················································.288
5.3 系統(tǒng)的 s 域分析 ··················································································.290
5.3.1 系統(tǒng)函數(shù)與系統(tǒng)特性 ············································································.290
5.3.2 系統(tǒng)函數(shù)與系統(tǒng)頻率響應(yīng)特性 ·································································.293
*5.3.3 全通系統(tǒng)和最小相位系統(tǒng) ·····································································.298
*5.3.4 物理可實(shí)現(xiàn)系統(tǒng) ················································································.301
*5.4 模擬濾波器設(shè)計(jì) ················································································.303
5.4.1 巴特沃斯低通濾波器 ············································································.303
*5.4.2 切比雪夫低通濾波器 ··········································································.308
5.4.3 低通到高通、帶通和帶阻濾波器的變換 ·······················································.310
*5.5 Matlab 實(shí)踐 ······················································································.313
5.5.1 拉普拉斯變換求解 ··············································································.313
5.5.2 部分分式展開及逆變換求解 ····································································.314
5.5.3 系統(tǒng)零極點(diǎn)和系統(tǒng)頻率響應(yīng) ····································································.315
5.5.4 模擬濾波器設(shè)計(jì) ·················································································.317
附錄 ········································································································.320
習(xí)題 ········································································································.322
第 6 章 離散時(shí)間信號與系統(tǒng)的 z 域分析 ···························································.327
6.1 z 變換 ·······························································································.327
6.1.1 z 變換的定義及收斂域 ··········································································.327
6.1.2 z 變換的性質(zhì) ····················································································.333
6.1.3 逆 z 變換的求解 ·················································································.340
*6.1.4 單邊周期序列的 z 變換 ········································································.346
6.2 系統(tǒng)響應(yīng)的 z 域求解 ············································································.349
6.2.1 差分方程描述系統(tǒng)的響應(yīng)求解 ·································································.349
6.2.2 方框圖描述系統(tǒng)的響應(yīng)求解 ····································································.351
*6.2.3 完全響應(yīng)的分解及響應(yīng)分量的 z 域求解 ······················································.351
6.3 系統(tǒng)的 z 域分析 ··················································································.354
6.3.1 系統(tǒng)函數(shù)與系統(tǒng)特性 ············································································.354
6.3.2 系統(tǒng)函數(shù)與系統(tǒng)頻率響應(yīng)特性 ·································································.357
*6.3.3 全通系統(tǒng)和最小相位系統(tǒng) ·····································································.359
目 錄 XIII
*6.3.4 因果穩(wěn)定性和可實(shí)現(xiàn)性 ········································································.361
*6.4 z 變換與拉普拉斯變換 ········································································.362
6.4.1 從拉普拉斯變換到 z 變換 ·······································································.362
6.4.2 s 平面和 z 平面之間的映射關(guān)系 ································································.363
*6.5 數(shù)字濾波—IIR 濾波器 ······································································.364
6.5.1 雙線性變換法 ···················································································.364
6.5.2 IIR 濾波器的設(shè)計(jì)與實(shí)現(xiàn) ········································································.367
*6.6 Matlab 實(shí)踐 ······················································································.369
6.6.1 離散時(shí)間系統(tǒng)頻率響應(yīng) ·········································································.369
6.6.2 IIR 數(shù)字濾波器設(shè)計(jì)與實(shí)現(xiàn) ·····································································.370
附錄 ········································································································.372
習(xí)題 ········································································································.373
第 7 章 狀態(tài)方程與 MIMO 系統(tǒng) ······································································.375
7.1 系統(tǒng)的狀態(tài)方程描述 ············································································.375
7.1.1 離散時(shí)間狀態(tài)方程 ··············································································.375
7.1.2 連續(xù)時(shí)間狀態(tài)方程 ··············································································.377
*7.1.3 狀態(tài)方程描述的特點(diǎn)及相關(guān)問題的討論 ······················································.378
7.2 卡爾曼濾波 ························································································.379
7.2.1 卡爾曼濾波的基本原理和迭代公式 ····························································.379
7.2.2 卡爾曼增益和卡爾曼濾波的核心概念 ··························································.387
7.2.3 協(xié)方差矩陣和誤差傳播 ·········································································.389
7.2.4 一維卡爾曼濾波的收斂性分析 ·································································.390
7.2.5 卡爾曼濾波的初始賦值 ·········································································.393
*7.2.6 卡爾曼濾波和頻域?yàn)V波 ········································································.395
*7.3 貝葉斯濾波 ······················································································.395
7.3.1 狀態(tài)值的貝葉斯估計(jì) ············································································.396
7.3.2 貝葉斯濾波算法 ·················································································.397
7.3.3 概率濾波和高斯濾波 ············································································.401
7.3.4 貝葉斯濾波框架下的線性卡爾曼濾波 ··························································.402
*7.4 非線性卡爾曼濾波 ·············································································.403
7.4.1 擴(kuò)展卡爾曼濾波（EKF） ·······································································.403
7.4.2 無跡卡爾曼濾波（UKF） ······································································.406
7.5 MIMO 系統(tǒng) ························································································.412
7.5.1 MIMO 系統(tǒng)的描述 ··············································································.412
7.5.2 MIMO LTI 系統(tǒng)的變換域求解 ··································································.417
*7.6 MIMO 與神經(jīng)網(wǎng)絡(luò) ·············································································.420
7.6.1 人腦神經(jīng)系統(tǒng)的 MIMO 建模 ···································································.420
7.6.2 神經(jīng)網(wǎng)絡(luò)的基本原理 ············································································.422
7.6.3 多層神經(jīng)網(wǎng)絡(luò)的反向傳播算法 ·································································.426
7.6.4 神經(jīng)網(wǎng)絡(luò)與分類 ·················································································.429
信號與系統(tǒng) XIV
7.6.5 深度學(xué)習(xí) ·························································································.432
7.6.6 卷積神經(jīng)網(wǎng)絡(luò) CNN ·············································································.434
*7.7 Matlab 實(shí)踐 ······················································································.435
7.7.1 卡爾曼濾波應(yīng)用一：勻速平面行駛車輛的位置跟蹤 ··········································.436
7.7.2 卡爾曼濾波應(yīng)用二：系統(tǒng)控制設(shè)計(jì) ····························································.438
附錄 ········································································································.439
附錄 A 矢量和矩陣的基本概念及公式 ·······························································.439
附錄 B 隨機(jī)變量和高斯分布的基本概念及公式 ·····················································.444
習(xí)題 ········································································································.451
參考文獻(xiàn) ·····································································································.453