Sinc Low pass and transients

1. Is sinc a low-pass filter?
2. What kind of filter is sinc function?
3. Are sinc functions stable?

Is sinc a low-pass filter?

A sinc filter is essentially a low-pass filter that converts the input SD modulated bitstream into high resolution digital data by digital filtering and decimation. In this slide, I've shown the z transform of n-th order sinc filter and its simplified block diagram.

What kind of filter is sinc function?

and its frequency response is a rectangular function. It is an "ideal" low-pass filter in the frequency sense, perfectly passing low frequencies, perfectly cutting high frequencies; and thus may be considered to be a brick-wall filter.

Are sinc functions stable?

Windowed-sinc filters are used to separate one band of frequencies from another. They are very stable, produce few surprises, and can be pushed to incredible performance levels.