Orthogonal Signal Transforms. Fourier Series

This lecture overviews Orthogonal Signal Transforms. Fourier Series that has many applications in signal processing, analysis and compression. It covers the following topics in detail: Vector calculus, Orthogonal functions, Trigonometric Fourier Series, Exponential Fourier Series, Triangular Fourier Series, Discrete Orthogonal Signals, Discrete Fourier Transform, Discrete Cosine Transform.

Fourier Transform

This lecture overviews the topics of continuous-time periodic signals, signal frequencies and Fourier Transform (FT).  Its relation to Laplace transform is presented. Notable FT properties are review: time shift, time scaling, convolution, signal differentiation/integration, energy preservation. Its use in defining Linear Time-Invariant (LTI) continuous-time systems frequency response is presented. Various types of such systems, notably low-pass, high-pass, band-pass are presented with examples (e.g., RC and RLC electric filters).

Discrete-time Signals and Systems

This lecture overviews discrete-time Signals and Systems topics. Discrete-time signals are presented: periodic signals, delta signal, unit step signal, exponential signal, trigonometric signals, complex exponential signal. Linear Shift-Invariant (LSI) systems are then presented in detail. 1D convolution and correlation, their properties and several examples are coming next. Finally, FIR and IIR systems are overviewed and examples are given, e.g., moving average filter, numerical differentiator.

Continuous-time Signals and Systems

This lecture overviews continuous-time Signals and Systems topics. Continuous-time signals are presented: periodic signals, delta function, unit step signal, exponential signal, trigonometric signals, complex exponential signal. Linear Time-Invariant (LTI) continuous-time systems are then presented in detail. 1D convolution and correlation, their properties and several examples are coming next. Finally, LTI system description by differential equations are overviewed. Examples are given, e.g., RC circuit and diffusion processes modeling by differential equations.

Introduction to Signals and Systems

This lecture overviews Signals and Systems. 1D signals, 2D signals (images), 3D signals (videos, medical volumes) are presented. Multichannel signals come next. Special signals, e.g., Proteomic sequences, DNA sequences, text sequences are overviewed. Graph signals are presented. Signal processing and signal analysis are defined and their differences from other related disciplines are explained.

Robust Statistics

This lecture overviews Robust Statistics that has many applications in Data Analytics and Digital Signal Processing and Analysis. It covers the following topics in detail: Outliers. Measures of Robustness: Sensitivity Curve (SC), The Influence Function, Breaking Point. Robust Estimators: L – Estimators, M – Estimators, S – Estimators.