Alias-free sampling: An alternative conceptualization and its applications

Abstract

A new concept of alias-free sampling of continuous-time processes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X = \{ X(t), -\infty &lt; t \infty \}</tex> is introduced. The new concept is shown to be distinct from the traditional concept [1]-[3]. various criteria for a given sampling scheme <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{t_{n}\}</tex> to be alias-free in the new sense are developed. The relationship of the new definition to the question of estimating the spectral density function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Phi(\lambda)</tex> of the continuous-time process <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</tex> from its samples <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{X(t_{t})\}</tex> is discussed.