Signal Processing and Data Analysis

Table of Content:Chapter 1 Concepts and theoretical background in signals and systems1.1 Introduction1.2 Key concepts1.3 Linear time invariant system and convolution1.4 Characteristics of linear time invariant systemChapter 2 Fourier transform and frequency domain analysis2.1 Introduction2.2 Fourier series for continuous -time system2.3 Fourier series for discrete -time system2.4 Fourier transform for continuous -time system2.5 Fourier transform for discrete -time system2.6 Frequency domain analysis for signals and systemsChapter 3 Laplace transform and complex frequency domain analysis3.1 Introduction3.2 Laplace transform3.3 Continuous -time signal and complex frequency domain analysis3.4 Z transform3.5 Discrete -time signal and complex frequency domain analysisChapter 4 Discretization of continuous -time signal and serialization of discrete-time signal 4.1 Introduction4.2 Sampling continuous -time signal4.3 Interpolation and fitting for discrete-time signalChapter 5 Discrete Fourier transform and fast Fourier transform5.1 Introduction5.2 Discrete Fourier transform5.3 Problems in discrete Fourier transform5.4 Two dimensional Fourier transform5.5 Fast Fourier transform5.6 Application of Fast Fourier transformChapter 6 Digital filter and design6.1 Introduction6.2 Digital filter structure6.3 Infinite impulse response filter6.4 Finite impulse response filter6.5 Lattice structure for digital filter6.6 Infinite impulse response filter design6.7 Finite impulse response filter designChapter 7 Finite-length effect in digital signal processing7.1 Introduction7.2 Analog to digital converter7.3 Quantification of digital filter7.4 Finite-length effect in digital filter calculation7.5 Finite-length effect in discrete Fourier transformChapter 8 Error analysis and signal pre-treatment8.1 Introduction8.2 Concept and classification of error8.3 uncertainty of measurement8.4 Least square method in data analysis8.5 Regression analysis8.6 Trends and outliers8.7 Case study on temperature measurementChapter 9 Random signal processing9.1 Introduction9.2 Concepts and characteristics of random signal9.3 Stochastic process and stochastic signal9.4 Frequently0used stochastic signal and noise9.5 Stochastic signal for linear system9.6 Classical analysis for stochastic signal9.7 Parameter analysis for stochastic signalChapter 10 Correlation function estimation for stochastic signal and power spectral density estimation10.1 Introduction10.2 Correlation function and power spectral density10.3 Self-correlation10.4 Classical methods for spectral estimation10.5 Methods for spectral estimation after 1960s10.6 Cepstrum analysis10.7 Application of spectral estimation in signal processingChapter 11 Statistical optimal filter for stochastic signals11.1 Introduction11.2 Theoretical background of Wiener filter 11.3 Wiener predictor11.4 Kalman filterChapter 12 Adaptive filtering12.1 Introduction12.2 Adaptive transversal filter and stochastic gradient method12.3 Least mean square algorithm for adaptive filter12.4 Least square algorithm for adaptive filter12.5 Application of adaptive filterChapter 13 Statistic analysis of higher-order and Fractional lower-order signals13.1 Higher-order cumulant13.2 Higher-order spectrum and higher-order estimation13.3 a-stable process and lower-order statistics13.4 Application of lower-order signalsChapter 14 Modern signal processing14.1 Time-frequency analysis14.2 Wavelet analysis14.3 Hibert-Huang transformation