In mathematics and engineering, the sinc function, denoted by sinc(x), has two slightly different definitions.
In mathematics, the historical unnormalized sinc function is defined by
:\mathrm{sinc}(x) = \frac{\sin(x)}{x}.\,\!
In digital signal processing and information theory, the normalized sinc function is commonly defined by
:\mathrm{sinc}(x) = \frac{\sin(\pi x)}{\pi x}.\,\!
The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of π). As a further useful property, a...