Frequency Domain Interpolation Convolution with Sinc Function

1. What is the Fourier transform of sinc function?
2. What happens to convolution in frequency domain?
3. Is sinc a low pass filter?

What is the Fourier transform of sinc function?

The Fourier transform of the sinc function is a rectangle centered on ω = 0. This gives sinc(x) a special place in the realm of signal processing, because a rectangular shape in the frequency domain is the idealized “brick-wall” filter response.

What happens to convolution in frequency domain?

The inverse transform of a convolution in the frequency domain returns a product of time-domain functions. If these equations seem to match the standard identities and convolution theorem used for time-domain convolution, this is not a coincidence.

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.