The normalized sinc is j0(πx). where Si(x) is the sine integral, λ sinc(λx) (not normalized) is one of two linearly independent solutions to the linear ordinary differential equation. The other is cos(λx)x, which is not bounded at x = 0, unlike its sinc function counterpart.
Where is sinc function used?
The sinc function is widely used in DSP because it is the Fourier transform pair of a very simple waveform, the rectangular pulse. For example, the sinc function is used in spectral analysis, as discussed in Chapter 9. Consider the analysis of an infinitely long discrete signal.