A narrow enough window is chosen to localize the signal in time and, according to Heisenberg's uncertainty principle, it results in have significant enough uncertainty in frequency. If one chooses a wide enough window it, according to the same principle, will increase time uncertainty. Thus, if the signal is narrowly localized in time its spectrum, on the contrary, is spread on the complete axis of frequencies, and vice versa.

Galaxy tab s6 lite book coverHeisenberg's Uncertainty Principle implies that no mind can completely know the momentum of a particle at a particular position in space, or the energy of a particle at a particular moment in time. The finiteness of the speed of light limits how big and nimble a material mind can be, as well as how far it can sense or influence circumstances.

-- which is true. The formula therefore is true for every natural number. In the Appendix to Arithmetic, we show directly that that is true.. Problem 1. According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove.