Random Signal Processing National University of Defense Technology

Stochastic signal processing is a core course for graduate students in electronics and communications engineering. This course mainly studies the basic theories of stochastic process foundation, parameter estimation, optimal filtering and signal detection. Stochastic process foundation mainly introduces the basic concepts of stochastic process and the linear process of stochastic process. System analysis, including definition and classification, statistical description, stationary random process and power spectrum, linear system analysis, commonly used time series models, matched filter theory, etc.; through the study of parameter estimation theory, master the general methods of parameter estimation and the basic principles of estimation and performance evaluation methods; through the study of optimal filtering theory, master the basic concepts of optimal filtering, master the basic theory of Kalman filtering, and be proficient in the derivation method of the Kalman filtering algorithm, the application of the algorithm, and the performance (simulation) evaluation method. Master the basic concepts and methods of nonlinear filtering (extended Kalman filtering method), be able to establish signal and observation models based on actual problems, establish corresponding algorithms, and use computers to analyze (simulate) algorithm performance. Signal detection includes two parts: the basic theory of hypothesis testing and signal detection in noise. Master the concepts and judgment criteria of hypothesis testing (including compound hypothesis testing), and be able to construct statistical models for hypothesis testing and select appropriate judgment criteria for practical problems. Analyze the performance of decisions. Be able to apply the mathematical theory of hypothesis testing to the problem of signal detection in noise, deduce the structure of the optimal receiver in Gaussian noise environment, and master the basic form of the optimal receiver in Gaussian noise, the performance analysis method of the receiver and the optimal Optimal signal design issues. Master the methods of signal detection in non-Gaussian noise.

• Chapter 1：Definition and Classification (12 minutes and 49 seconds)

• Chapter 2：Probability Distribution and Probability Density - Definition of Distribution (8 minutes and 25 seconds)

• Chapter 3：Probability distribution and probability density-calculation examples (10 minutes and 34 seconds)

• Chapter 4：Numerical Characteristics - Definition of Numerical Characteristics (7 minutes and 28 seconds)

• Chapter 5：Numerical Characteristics - Calculation Examples (11 minutes and 32 seconds)

• Chapter 6：Stationary stochastic process - ergodic process (7 minutes and 54 seconds)

• Chapter 7：Stationary stochastic process - properties of correlation functions (9 minutes and 58 seconds)

• Chapter 8：Stationary stochastic process - definition of stationary (12 minutes and 11 seconds)

• Chapter 9：Power Spectrum - The power spectrum of a random sequence (9 minutes and 19 seconds)

• Chapter 10：Power Spectrum - Power Spectrum of Continuous Time Stochastic Processes (14 minutes and 25 seconds)

• Chapter 11：typical random process (7 minutes and 23 seconds)

• Chapter 12：Analysis of sea clutter characteristics (14 minutes and 14 seconds)

• Chapter 13：Concepts and Theorems of Transformation (8 minutes and 43 seconds)

• Chapter 14：Stochastic process analysis through linear systems-impulse response method (9 minutes and 9 seconds)

• Chapter 15：Stochastic Process Analysis via Linear Systems - Spectral Method (6 minutes and 11 seconds)

• Chapter 16：Stochastic process analysis through linear systems - calculation examples (12 minutes and 3 seconds)

• Chapter 17：Random Sequence Analysis via Discrete Linear Systems - Commonly Used Time Series Models (11 minutes and 5 seconds)

• Chapter 18：Analysis of random sequence over-discrete linear systems-two analysis methods (10 minutes and 19 seconds)

• Chapter 19：The best linear filter with the highest signal-to-noise ratio (12 minutes and 12 seconds)

• Chapter 20：Matched filter - definition and properties (10 minutes and 43 seconds)

• Chapter 21：Matched filter - calculation example (9 minutes and 24 seconds)

• Chapter 22：Signal processing example-matched filtering of chirp signals (18 minutes and 8 seconds)

• Chapter 23：Overview of Estimation Theory - Statistical Models for Estimation Problems (6 minutes and 40 seconds)

• Chapter 24：Overview of Estimation Theory-Basic Methods of Estimation (14 minutes and 9 seconds)

• Chapter 25：Overview of Estimation Theory - Performance Evaluation of Estimators (7 minutes and 30 seconds)

• Chapter 26：CRLB-CRLB theorem for parameter estimation (15 minutes and 32 seconds)

• Chapter 27：CRLB-CRLB calculation example for parameter estimation (6 minutes and 9 seconds)

• Chapter 28：CRLB of signal parameters in Gaussian white noise (10 minutes and 16 seconds)

• Chapter 29：Monte Carlo simulation to estimate performance (9 minutes and 9 seconds)

• Chapter 30：maximum likelihood estimation (14 minutes and 32 seconds)

• Chapter 31：Asymptotic Properties of Maximum Likelihood Estimation (17 minutes and 1 seconds)

• Chapter 32：Delay estimation (14 minutes and 37 seconds)

• Chapter 33：General concepts of Bayesian estimation-prior information and estimation (8 minutes and 18 seconds)

• Chapter 34：General concepts of Bayesian estimation-posterior distribution and estimation (16 minutes and 58 seconds)

• Chapter 35：Derivation of least mean squares estimate (8 minutes and 52 seconds)

• Chapter 36：Properties of Least Mean Square Estimation (4 minutes and 4 seconds)

• Chapter 37：Minimum mean square estimation calculation example (7 minutes and 38 seconds)

• Chapter 38：maximum posterior probability estimate (10 minutes and 14 seconds)

• Chapter 39：Bayesian estimation of hit probability (21 minutes and 13 seconds)

• Chapter 40：The principle of linear least mean squares estimation (10 minutes and 36 seconds)

• Chapter 41：Properties of Linear Least Mean Squares Estimators (5 minutes and 6 seconds)

• Chapter 42：Linear least mean square estimation calculation example (17 minutes and 0 seconds)

• Chapter 43：Linear Least Mean Square Estimation Based on Random Vector Space (10 minutes and 34 seconds)

• Chapter 44：Geometric Interpretation of Linear Least Mean Square Estimation - Calculation Example (6 minutes and 20 seconds)

• Chapter 45：Recursive Linear Least Mean Square Estimation(1) (11 minutes and 58 seconds)

• Chapter 46：Recursive Linear Least Mean Square Estimation(2) (10 minutes and 54 seconds)

• Chapter 47：Kalman filter overview (16 minutes and 53 seconds)

• Chapter 48：The definition and properties of orthogonal projection (8 minutes and 50 seconds)

• Chapter 49：Kalman filter algorithm derivation (21 minutes and 21 seconds)

• Chapter 50：Calculation example (17 minutes and 59 seconds)

• Chapter 51：Several issues in application-Kalman filtering in colored noise (13 minutes and 33 seconds)

• Chapter 52：Several problems in application-filter divergence problem (12 minutes and 19 seconds)

• Chapter 53：Kalman filter application example-target tracking (21 minutes and 31 seconds)

• Chapter 54：Extended Kalman filter model and algorithm derivation (17 minutes and 18 seconds)

• Chapter 55：Extended Kalman filter calculation example (7 minutes and 6 seconds)

• Chapter 56：Extended Kalman filter application example-target tracking (12 minutes and 58 seconds)

• Chapter 57：Basic concepts of signal detection (14 minutes and 32 seconds)

• Chapter 58：Bayesian criterion (16 minutes and 7 seconds)

• Chapter 59：Neyman-Pearson criterion (8 minutes and 33 seconds)

• Chapter 60：Detection performance analysis-Detection performance analysis (15 minutes and 23 seconds)

• Chapter 61：Multiple Hypothesis Testing-Multiple Hypothesis Testing (14 minutes and 33 seconds)

• Chapter 62：Basic concepts of composite hypothesis testing (18 minutes and 39 seconds)

• Chapter 63：Generalized likelihood ratio test calculation (6 minutes and 55 seconds)

• Chapter 64：Local maximum potential test (12 minutes and 56 seconds)

• Chapter 65：matched filter (10 minutes and 25 seconds)

• Chapter 66：Matched filter performance analysis (8 minutes and 43 seconds)

• Chapter 67：Generalized matched filter (7 minutes and 5 seconds)

• Chapter 68：Generalized Matched Filter Performance Analysis (10 minutes and 33 seconds)

• Chapter 69：Matched filtering for general linear models (5 minutes and 52 seconds)

• Chapter 70：Minimum distance receiver (14 minutes and 49 seconds)

• Chapter 71：Deterministic signal detection of unknown parameters (14 minutes and 53 seconds)

• Chapter 72：Sinusoidal signal detection (17 minutes and 13 seconds)

• Chapter 73：Correlation detection of random signals (20 minutes and 51 seconds)

• Chapter 74：Detection of general Gaussian signals (8 minutes and 29 seconds)

• Chapter 75：Analysis of radar detection performance of Swerling undulating targets (14 minutes and 44 seconds)

• Chapter 76：Random signal detection of unknown parameters (15 minutes and 35 seconds)

• Chapter 77：Linear model detection of deterministic signals with unknown parameters (12 minutes and 50 seconds)

• Chapter 78：Linear model detection of random signals (13 minutes and 36 seconds)

• Chapter 79：Signal detection when noise parameters are unknown (11 minutes and 43 seconds)

• Chapter 80：Signal detection in non-Gaussian noise (17 minutes and 12 seconds)

• Chapter 81：Signal processing example-radiation source individual target identification (17 minutes and 49 seconds)