Uncertainty principles for doubly periodic functions

Abstract

This paper studies uncertainty principles for doubly periodic functions. Firstly, the means and the variances of time and of frequency for doubly periodic signal functions are provided. Also, the phase and the amplitude derivatives of doubly periodic signal functions are properly defined. Based on these definitions, we establish two versions of uncertainty principles. An example is presented to illustrate these results.

The Uncertainty Principle with Fourier Transform Derivatives

“…In 1946, the simplest version of the uncertainty principle appeared [2]. After that, a rich form of the uncertainty principle appeared in the mathematical form [3][4][5][6][7]. We make ℎ: ℝ → ℝ be a signal function that is square integrable.…”