Stochastic processes (random functions) in engineering: motivation, definitions, examples

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 15:40

*Enlace a Spanish version

Summary:

This video poses, in a very informal way, the concept of “stochastic process”, used in statistical analysis, as a formalization of what, in engineering terms, would be understood as a “signal corrupted by noise”.

Its definition as a random function is discussed, and examples in signal processing, audio-video, and vibrations are outlined. The overall goals of using stochastic processes in applications are also hinted.

At first glance, signal processing applications might be associated to only “functions of time” (time series, in statistical jargon). However, the ideas generalize to stochastic processes in “spatial” coordinates (say, colored noise in a photograph) or in both time+space (video signals).

Stochastic processes are also used in optimization, giving rise to the so-called Bayesian optimization techniques, see [BOmot1EN].

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.