ABSTRACT
In order to achieve time-localization of spectral characteristics of a time varying signal, a “window function” is introduced into the Fourier transform. Multiplying a signal by a window function before taking its Fourier transform has the effect of restricting the spectral information of the signal to the domain of influence of the window function. Using translates of the window function on the time axis to cover the entire time domain, the signal is analyzed for spectral information in localized neighborhoods in time. Heisenberg’s Uncertainty Principle is an important principle with far reaching consequences in quantum mechanics. It imposes a lower bound on the product of the mean square errors incurred in the simultaneous measurement of the two complementary parameters of a function with respect to the Fourier transform.
