Discrete Time Gauss Spectrum and Caushy-Schwartz Inequality

Uncertainty Principle for Discrete Time Signal

Abstract

By Applying Caushy-Schwartz inequality to discrete Fourier transform we derive uncertainty principle of discrete time signal. The inequality of the obtained uncertainty principle holds with equality sign if the discrete time signal has an upward or a downward convex Gauss spectrum. The lower bound of uncertainty principle for discrete time signal is not constant.