The Continuous-Time Impulse
An impulse in continuous time must have ``zero width'' and unit area under it. One definition is
An impulse can be similarly defined as the limit of any integrable pulse shape which maintains unit area and approaches zero width at time 0. As a result, the impulse under every definition has the so-called sifting property under integration,
provided






An impulse is not a function in the usual sense, so it is called instead a distribution or generalized function [12,38]. (It is still commonly called a ``delta function'', however, despite the misnomer.)
Next Section:
Relation of the DFT to Fourier Series
Previous Section:
Existence of the Fourier Transform