I have not looked at the code, but this sounds like spectral leakage. This is a common artefact in the Fourier transform where it assumes the finite signal is one perfect, repeating period of an infinitely long signal. However, as this is rarely the case with real-world data, a sharp discontinuity is created between the signal's start and end points. This leads to spectral leakage, which can manifest as the high correlation you're observing. To minimise this, the standard method is to apply a window function (such as Hann or Hamming) to taper the signal's edges before the transform. Separately, you might also consider padding the signal, which can help by increasing the display resolution of the resulting spectrum.

Tim Albiges Thank you for your reply. the code consists of these steps:

1- the positions (x,y,z coorinates) of two proteins (receptor and the ligand) are read and stored in separate numpy arrays.

2- two separate grids (128 x 128 x 128) are formed with three values: 1 representing the protein surface, -15 representing the atoms interior, and 0 in other places.

3- the grids are then used with scipy rfftn function to perform the fft

4- then the conjugate of the protein grid fft is multiplied by the ligand fft then the inverse fft (irfftn in scipy) is performed to obtain the correlation

in your reply, you mentioned the padding of the signal. Does this mean adding more zeros at the edges after step 2 and before step 3? will this be solved if the grid was larger at step 2?

Thanks

You correct with your second point. The standard practice is to create a larger grid from the outset (e.g., 256x256x256) and then place your 128x128x128 protein data inside it. This procedure is performed after defining the protein grid (step 2) but before applying the FFT (step 3).

The crucial reason for this padding is to prevent 'wrap-around' errors. The FFT algorithm treats the grid as periodic, and without sufficient padding, a shifted ligand would incorrectly wrap from one side of the grid to the other, creating false correlation signals. Doubling the grid dimensions ensures a clean, linear correlation is calculated. Additionally, applying hamming function to the larger matrix may help your analysis by temping the edges. This can be achieved in numpy like this:

win_x = np.hamming(padded_size)

win_y np.hamming(padded_size)

win_z np.hamming (padded_size)

window_3d = win_x[:, np.newaxis, np.newaxis] * win_y[np.newaxis,

np.newaxis] * win_z [np.newaxis, np.newaxis,:]

receptor_grid_windowed = receptor_grid * window_3d

ligand_grid_windowed = ligand_grid * window_3d

Then continue with your analysis from step three.

Tim Albiges Hi, i tried adding padding then using the hamming function before doing the fft, then plotted the correlation. However, the peaks still appears in the corners. the same colab link was modified.

Hamming tapers the signal at around 0.08 of the signal, which might not be enough. Therefore, trying with a Hanning function might be better.

Additionally, after windowing and before rfftn, the amount of padding is crucial for reducing side effects, the standard padding is size calculation is 2n-1.