Southern Post Modern Signal Processing Final Exam (Summary of Review Outline for 2020)

Modern Digital Signal Processing Final Exam (Summary of Review Outline of China Post 2020)

Chapter One Introduction and Basics-Basics of Digital Signal Processing

1.1 Discrete time signal and system

1.1.1 序列
1.1.2 LTI系统
1.1.3 快速变换
1.1.4 滤波器设计

1.2, random signal basis

1.2.1 数字特征
1.2.2 严平稳/广义平稳
1.2.3 各态历经
1.2.4 相关函数与功率谱
1.2.5 功率谱特点
1.2.6 高斯过程
1.2.7 白噪声过程
1.2.8 谐波过程
1.2.9 有理分式模型
1.2.10通过线性系统
1.2.11谱分解定理
1.2.12参数模型法谱估计

1.3 The theoretical basis of spectrum estimation

1.3.1 自相关函数的估计

Related exercises:
1. Write down the basic numerical characteristics of a stationary random process: the definition of the mean, variance, and autocorrelation function.
2 . What is generalized stationary? What is each state traversal?
3. Write down the relationship between the autocorrelation function and power spectrum of the stationary random process, and the characteristics of the autocorrelation function and power spectrum of the white noise process.
4. Write down the characteristics, system functions and difference equations of the three signal models.
5. What is the relevant convolution theorem?

Chapter 2 Random Signal Spectrum Estimation

2.1. Overview

2.1.1 古典谱估计
2.1.2 现代谱估计

2.2, classical spectrum estimation

2.2.1 自相关法
2.2.2 周期图法

2.3 Spectrum estimation method based on AR model

2.3.1 Yule-Walker方程
	 (1) AR模型的参数求解（重点）
2.3.2 AR模型谱估计性质
	 (1) 与线性预测滤波等效
	 (2) 与最大熵谱估计等效
2.3.3 Levinson-Durbin算法
	 (1) 原理
	 (2) 算法
	 (3) 讨论
	 (4) 优缺点
2.3.4 Burg算法
	 (1) 前向预测和后向预测
	 (2) 原理
	 (3) 算法

2.4 Frequency estimation based on matrix eigendecomposition

2.4.1 自相关矩阵的特征分解
	 (1) 原理
	 (2) 结论
2.4.2 基于噪声子空间的频率估计
	 (1) PHD方法（考试不要求）
	 (2) MUSIC方法
		(2.1) 基本思路
		(2.2) 算法步骤

2.5, high-order spectrum estimation (not required for the exam)

Related exercises:
1. Write down these three basic ideas of power spectrum estimation: classical spectrum estimation, AR model spectrum estimation, and maximum entropy spectrum estimation.
2. What is the relationship between the AR model and the prediction error filter?
3. Write the expression of the regular equation of the AR model.
4. The 4 observations of the autoregressive process x(n)={2,4,1,3}, n={0,1,2,3}. Try autocorrelation method and covariance method to design a first-order linear predictor and calculate linear predictive coefficients.
5. Write the Levinson relationship.
6. Compare the Burg algorithm with the Levinson-Durbin algorithm.
7. What are signal subspace and noise subspace?
8. What is the basic idea of ​​PHD algorithm and MUSIC algorithm?

Chapter 3/4 Adaptive Signal Processing

3.1, optimal prediction and filtering

(1) 波形估计与动态估计
(2) 滤波与预测
(3) 维纳滤波、卡尔曼滤波、自适应滤波器(重点)

3.2. Optimal filtering theory

(1) 线性最优滤波器

3.3, the principle of orthogonality (no requirement)

3.4, Wiener filter

3.5, Kalman filter

4.1, the basic concept of adaptive filtering

4.2 Application of adaptive filtering (master four typical applications)

(1) 自适应系统辨识(如信道估计)；
(2) 自适应均衡(如均衡 )；
(3) 信号或时间序列的自适应预测；
(4) 自适应干扰消除。

4.3 Classification of adaptive filters

4.3.1、FIR自适应滤波器
	(1) 梯度下降算法
	(2) 横向LMS自适应滤波器
	(3) 横向RLS自适应滤波器

4.3.2, IIR adaptive filter

	(1) 输出误差法
	(2) 方程误差法

4.3.3, Laguerre adaptive filter

	(1) Laguerre 横向滤波器
	(2) Laguerre 格型滤波器

Related exercises:
1. Two kinds of optimal linear filtering (Wiener filtering/Kalman filtering) are summarized, including applicable conditions, optimal criteria, limitations, and estimation process.
2. Understand the orthogonality principle of Wiener filtering, and write the Wiener-Hopf equation of FIR Wiener filtering.
3. Summarize two adaptive algorithms: LMS algorithm and RLS algorithm, and compare their performance.
4. Draw the basic structure diagram of FIR adaptive filter, IIR adaptive filter, and Laguerre transversal filter.

Chapter 5 Multi-rate Signal Processing System

5.1 Overview of multi-rate signal processing

5.2. Sampling rate conversion (decimation and interpolation)

(1) 抽取器(decimator) Z-transform (频域) 分析 
(2) 内插器(interpolator) z-变换 (频域) 分析 

5.3, multi-rate system

(1) 多速率构件的互连 
(2) 多速率构件的互连 

5.4, ​​polyphase decomposition and polyphase filter

5.4.1 多相分解
(1)多相分解表示
(2)多相网络设计
(3)应用1：抽取滤波器的高效实现（二相结构）
(4)抽取滤波器的多相结构
(5)应用2：内插滤波器的高效实现（二相结构）
(6)内插滤波器的多相结构

5.4.2 Polyphase filter

(1)多相分解
(2)应用1：抽取滤波器的高效实现
(3)抽取滤波器的高效实现（多相结构）
(4)应用2：内插滤波器的高效实现（二相结构）
(5)内插滤波器的高效实现（多相结构）
(6)应用3：带通滤波器组的高效实现
(7)矩阵形式

5.5. Filter bank (no requirement for exam)

Chapter 6 Wavelet Transform

6.1 Limitations of Fourier analysis and solutions
6.2, Continuous wavelet transform
6.3, Discrete wavelet transform
6.4, Wavelet transform and multi-resolution analysis

Chapter 7 Artificial Neural Network

Exam requirements:
3 basic elements of ANN.
Neuron structure, transfer function and activation function.
3 types of common artificial neural networks.
3 types of neural network training algorithms and their common application scenarios.