Continuous-time Signals and Systems Lecture
Digital Signals and Systems are everywhere. Digital 1D signals, 2D signals (images) and 3D signals (video) encompass the vast majority of digital information nowadays in several disciplines:
-Digital Media, Social Media (music, images, video),
-Biomedical Signal/Image Analysis and Diagnosis,
-Autonomous cars, drones, marine vessels, robots
-Big Data Analytics,
-Internet and Communications (media broadcasting, streaming).
-Scientific signal acquisition of any sort, e.g., Remote Sensing, Environment Sensing, Geophysical Prospecting.
Digital Systems can model every aspect of the world, e.g., :
-Financial systems and Engineering
-Biomedical and Biology Systems
-Power plants
-Autonomous Systems and Robotics.
-Neural Networks.
-Social Networks, Complex Networks.
Much confusion exists nowadays in CVML literature, as even mature ML scientists have no background on Signals and Systems and confuse even basic notions, e.g., convolutions and correlations. SS principles are overviewed, while focusing on fast convolution algorithms, particularly on 2D convolution algorithms that are an absolute must for CNN libraries/frameworks and many computer vision tasks.
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.