Smithsonians_Discrete_Hilbert_Fourier_Hartley_Transforms

An implementation from the Smithsonian Astrophysical Observatory of some notorious transforms ready to use in c/c++

"Smithsonians_Discrete_Hilbert_Fourier_Hartley_Transforms/am_sysdep.h" from the authors:

• For optimum performance, the default processor data cache size settings here can be overridden by target-specific definitions supplied at compile time.

  • Line-by-line and CIA computations are blocked to fit in L1 cache. If the cache size is set to 0, cache blocking is turned off.

  • For FFTs and FHTs, the L1 cache size setting controls the point at which the computation switches over from recursive to iterative.

CAREFULLY READ COMMENTS OF THE AUTHORS ABOVE THEIR FUNCTIONS IN "transforms.c" BEFORE USING THEM.

I did not write those functions, the Smithsonian Astrophysical Observatory did. I just isolated the references for the transforms from a much bigger project (https://www.cfa.harvard.edu/~spaine/am/) and provided an example on how to use them in c++.

NOTE THAT

the transforms themselves are written in c.

NOTE THAT

the phase shift of the Hilbert transform is 90 degrees and not - 90 as in MATLAB, as you can check here, comparing the result with the main_example.cpp output. To obtain matlab tranform multiply the output's component orthogonal to the input by EXP(j * PI) = -1, which translates in mutiplying the output's imaginary part by -1 when the input is real.

Jacopo Piccirillo

13/10/2020