This video introduces the frequency-domain description of stationary processes, through the equivalent but conceptually different ideas of stochastic decompositions and Fourier transforms of moments (such as the autocorrelation or autocovariance). The video considers the conceptual equivalence of a random spectrum and random time-series. The power-spectral density is developed in an informal method by calculating the second moment of the Fourier transforms of the realisations of the random signals. This is then formalised as a limiting process, to develop the infamous Wiener-Khinchin(-Einstein-Kolmogorov) theorem. The video considers the conceptual traps that you should be aware of, although ultimately the theory all leads to the definition that the power-spectral density is the Fourier Transform of the autocorrelation sequence.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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