Sinc

Convolution with sinc function

Convolution with sinc function
  1. What is the convolution of two sinc functions?
  2. What is integration of sinc function?
  3. Is sinc function stable?

What is the convolution of two sinc functions?

the convolution of two identical sinc functions (of the same BW) is the same sinc function. This is because the convolution of the two sinc's is the Fourier transform of their product of the transforms of the two sincs. The FT of the sinc is a rectangle in the frequency domain….

What is integration of sinc function?

The integral of a function is the value of its Fourier transform at zero, so sinc integrates to π. [ 1] By Plancherel's theorem, the integral of sinc2(x) is the integral of its Fourier transform squared, which equals π.

Is sinc function 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.

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