Fourier properties
of the Magic Kernel Sharp algorithm, and discovered that it possesses high-order zeros at multiples of the sampling frequency, which explains why it produces such amazingly clear results: these high-order zeros greatly suppress any potential aliasing artifacts that might otherwise appear at low frequencies..."
[...]
>"Following that work, I analytically derived the
Fourier transform
of the Magic Kernel in closed form, and found, incredulously, that
it is simply the cube of the sinc function.
This implies that the Magic Kernel is just the
rectangular window function convolved with itself twice
-which, in retrospect, is completely obvious. This observation, together with a precise definition of the requirement of the Sharp kernel, allowed me to obtain an analytical expression for the exact Sharp kernel, and hence also for the exact Magic Kernel Sharp kernel, which I recognized is just the third in a sequence of fundamental resizing kernels. These findings allowed me to explicitly show why Magic Kernel Sharp is superior to any of the Lanczos kernels. It also allowed me to derive further members of this fundamental sequence of kernels, in particular the sixth member, which has the same computational efficiency as Lanczos-3, but has far superior properties."
Paper: http://www.johncostella.com/magic/mks.pdf
PDS: My thoughts: Absolutely fascinating! (Also, that the the "Magic Kernel is just the rectangular window function convolved with itself twice" -- was not obvious to me, so it's good you included that!)