A consequence of Fourier transforms being built from is that narrowing a function in one domain widens it in the other domain. Scaling implies inverse scaling of t to keep the product constant. A pure sinusoidal wave has a clearly defined frequency, but it is spread over the infinitely long time axis. In this section we examine how the width of a function in one domain relates to that in the other. This inequality is the uncertainty principle .
Strong inequality arises from all-pass filter s.