Sinc interpolation

[sglyon]

RE comment here

[roflmaostc]

I was thinking about a possible sinc interpolation implementation:

A naive (and probably the mathematically correct one?) sinc interpolation is to calculate the FFT of the samples, zero pad the FFT spectrum and calculate the IFFT of the padded spectrum.

However, this repository seems to calculate interpolations differently. It construct a itp object, which is able to calculate new values at all indices in between the original one.

A explicit sinc interpolation formula can be also written down, but it's evaluation is O(n) where n is the number of samples.

So what do you think? Is there a way that we adapt the whole API to a use case, where you need so specify a whole new grid beforehand?

Edit: I've found a similar discussion in #282 which indicates that we don't want to depend of FFTW.jl

[mkitti]

We probably would want to use https://github.com/JuliaMath/AbstractFFTs.jl . There a good point there that perhaps Fourier based interpolation should be a separate package.

Also see the lanczos support we added recently.

[roflmaostc]

I'm not sure whether AbstractFFT.jl helps.
Doesn't it provide a AbstractInterface for the bindings? At the end, the users still have to load a suitable FFT library.

[roflmaostc]

I started to work on a proper FFT interpolation and stumbled over certain problems and created a discourse post.
look here

Hopefully this helps in solving this properly and we could register this.