nonuniform discrete Fourier transform of type II

[kylematoba]

If I read

https://en.wikipedia.org/wiki/Non-uniform_discrete_Fourier_transform#Definition

correctly, then "adjoint nonuniform DFT" (also called "nonuniform discrete Fourier transform of type II") would entail interpolating in space.

Thus, I expect that KbNufftAdjoint would not operate in frequency space, as seems to be suggested by the docs. Is there a standard reduction in this field that allows me to interpolate in space using this logic please?

[mmuckley]

Hello @kylematoba, in our case we define a forward NUFFT as a linear operator that applies an FFT followed by a linear interpolation with a Kaiser-Bessel function. Since it is a linear operator, the adjoint is defined as the adjoint of these individual operations in reverse order.

I think what you are describing would be some sort of Non-uniform inverse fast Fourier Transform (NUIFFT) operator, which would have its own distinct adjoint separate from any implemented in this package.

[apt-get-nat]

So, do I understand correctly that there is no way to use your package to perform a Fourier transform with data that is nonuniform in space to modes that are uniform in frequency?

[mmuckley]

@apt-get-nat using the duality property you may be able to approximate this operation using the package.

[mmuckley]

Closing as this does not document a bug.