


Probability Theory
This lecture overviews Probability Theory that has many applications in a multitude of scientific and engineering disciplines, notably in Pattern Recognition and Machine Learning. It covers the following topics in detail:



State – Space Equations
This lecture overviews State –Space Equations that has many applications in digital filters, systems theory and deep learning.



Orthogonal Signal Transforms. Fourier Series
This lecture overviews Orthogonal Signal Transforms. Fourier Series that has many applications in signal processing, analysis and compression.



Z Transform
This lecture overviews Z Transform that has many applications in signal processing and systems theory.



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.



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.