Uncertainty in time/frequency domain representations - How accurately can we know when and how often?

In signal analysis we search for discrete structures in observed data. The art of signal processing is basically that of finding the optimal basis for a particular data set, so thar a representation in that basis clearly reveals such structures, The uncertainty principle, however, is a fundamental and inescapable property of nature which - in our perception of nature, as a matter of principle - conceals the details of its present state. This property is reflected in signals when observing a process or system, regardless of the domain in which information is transformed and presented. In the field of spectral estimation, effects of the uncertainty principle are perpetually present and to avoid fooling ourselves, we must consider these whenever applying our findings in conclusions concerning the phenomena as we try to identify, qualify and quantify. This article reviews the uncertainty principles in spectral estimations - whether using the discrete Fourier transform or real time filtering and/or other time-Frequency methods. The goal of the article is to make the reader aware of this fundamental curiosity of nature - or is ii in our minds? - which we must take into consideration whenever planning, executing and interpreting observations.