This lecture presents Laplace Transform (LT) and its region of convergence. Its relation to Laplace transform is presented. Notable LT properties are reviewed: time shift, convolution, signal differentiation/integration. Its use in defining Linear Time-Invariant (LTI) continuous-time systems transfer function is also presented and stability issues are overviewed. Various types of such systems are presented with… Continue reading Laplace Transform
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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… Continue reading Fourier Transform
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… Continue reading Discrete-time Signals and Systems
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… Continue reading Continuous-time Signals and Systems
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.