Shannon sampling theorem: Gaussian process version (1)

Antonio Sala, UPV

Difficulty: ** ,       Relevance: ,      Duration: 10:55

Summary:

This video presents the ‘statistical’ (Gaussian process) version of Shannon’s sampling theorem. The discussion will be split in two videos. The first one will only discuss motivation, reviewing of sampling theorem statements, presenting the power spectral density and auto-covariance (sinc function) of a band-limited stochastic process, and simulating realizations of such a process. The video ends with a motivational presentation of the principal-component analysis on a finite grid of points of the time domain: a 30-second fragment realization (31 samples, every second) gridded at 0.05 seconds can be described as a realization of just 34 independent random variables... We are almost there: we have 31 statistically independent samples... when the number of samples grows to infinity we reach perfect reconstruction from such samples. Details and Matlab examples will be deferred to video [shannonGP2EN].

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