Statistics and probabilities for spectral analysis

Abstract

Spectral analysis of data plays a central role in many signal processing applications, and comparing the relative output levels between filters often provides clues about the actual signals present in the data. Since data are often corrupted by noise, interference, or some other source of randomness, these filter outputs are also subject to random variations. Proper interpretation of these filter outputs is made possible by an awareness of the nature of their statistical variability. Thus, homework problems that illustrate how basic fundamental properties of random variables/vectors lend significant insight into the nature of such filter output comparisons are of great value in engineering practice. This talk will describe a handful of interesting problems that help with the interpretation of filtered data outputs used in some form of spectral analysis (e.g., FFT filters, beamformers, etc.). The problems considered will leverage notions of invariances, regeneration properties, and a basic algebra of random variables.