### Cosine-sum filters for resampling

Posted:

**2019-08-30T00:50:31-07:00**Cosine-sum filters for resampling are filters that are designed as a sum of cosine functions, which is then truncated to a desired width.

An example formula for width-4 (range from -2 to 2) cosine-sum filters would be:

a+b×cos(90°×input)+c×cos(180°×input)+d×cos(270°×input)+e×cos(450°×input)+f×cos(540°×input)+g×cos(630°×input)+...

Omitting 360°, 720°, etc. because they don't produce a constant when tiled indefinitely. For width-6 filters use multiples of 60° instead of 90°.

Those parameters look like some sort of digitization of the Gaussian function: the digital Gaussian is a=0.25, b=0.375, c=0.15, d=0.025.

Those parameters produce a cardinal function (assuming "tensor" resampling) with the first derivative of points at -1 and 1 being set to 0.5 and -0.5 respectively: a=0.25, b=0.45458, c=0.25, d=0.045423

Are such filters already known and researched in the community?

An example formula for width-4 (range from -2 to 2) cosine-sum filters would be:

a+b×cos(90°×input)+c×cos(180°×input)+d×cos(270°×input)+e×cos(450°×input)+f×cos(540°×input)+g×cos(630°×input)+...

Omitting 360°, 720°, etc. because they don't produce a constant when tiled indefinitely. For width-6 filters use multiples of 60° instead of 90°.

Those parameters look like some sort of digitization of the Gaussian function: the digital Gaussian is a=0.25, b=0.375, c=0.15, d=0.025.

Those parameters produce a cardinal function (assuming "tensor" resampling) with the first derivative of points at -1 and 1 being set to 0.5 and -0.5 respectively: a=0.25, b=0.45458, c=0.25, d=0.045423

Are such filters already known and researched in the community?