My problem is similar to this but not the same.
Edit: Here is a description of Neumann boundary conditions for differential equations: Neumann-type boundary conditions means derivatives are specified at the end of the domain. In this case I refer to the specific case where the derivative vanishes at both the ends of the domain. Henceforth, such boundary condition is referred to as Neumann type.
I have 1D wavenumber domain equivalent to a fourier space with integer multiples of a fundamental mode. At the end of the domain neumann boundary conditions are satisfied.
As such, my spatial real signal has basis functions of cosine types. Due to neumann boundary conditions, to project the signal onto the fourier space, dct type 1 transform is used. Specifically, to accomplish this I use the REDFT00 transform of FFTW3 library.
Now, since it is DCT type 1, only half the length (plus 1) of spatial signal is stored in a 1D array with n bins. Subsequently, I compute the DCT type 1 store it in another array with another n bins. After that I'm confused how to compute the complex part of the hilbert analytic signal from DCT-type1.
It would be better (but not mandatory) to share a piece of code used with FFTW3 REDFT00.