c++ - Computing a 3D power spectrum in fftw -

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i trying compute 3d power spectrum -- is, averaged power in frequency shells. think i'm doing calculation of shell densities correctly, i'm not sure how determine frequency of each shell.

supposing sampling rate fs same in each dimension, , length of original samples in each dimension same value n. shell "index" idx = sqrt(i*i + j*j + k*k) i, j, , k extent in each direction. how compute frequency of shell?

it's simpler think: vector (i, j, k) wave vector, associated frequency taking length , dividing length of edge of cube.

f = sqrt(i*i + j*j + k*k)/edgelength

the result spacial frequency. if looking temporal frequency, need additional information links 2 together.

the thing need take care of, location of 0 frequency within fft transformed cube: algorithms place @ upper left corner, others place in center. wherever is, need take care don't misinterpret low frequency aliased high frequency in opposite direction, i. e. absolute value of i, j, k should less half width of cube.


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