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Asked: 2026-05-12T18:20:40+00:00

I have to apply a convolution filter on each row of many images. The

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I have to apply a convolution filter on each row of many images. The classic is 360 images of 1024×1024 pixels. In my use case it is 720 images 560×600 pixels.

The problem is that my code is much slower than what is advertised in articles.

I have implemented the naive convolution, and it takes 2m 30s. I then switched to FFT using fftw. I used complex 2 complex, filtering two rows in each transform. I’m now around 20s.

The thing is that articles advertise around 10s and even less for the classic condition.
So I’d like to ask the experts here if there could be a faster way to compute the convolution.

Numerical recipes suggest to avoid the sorting done in the dft and adapt the frequency domain filter function accordingly. But there is no code example how this could be done.

Maybe I lose time in copying data. With real 2 real transform I wouldn’t have to copy the data into the complexe values. But I have to pad with 0 anyway.

EDIT: see my own answer below for progress feedback and further information on solving this issue.

Question (precise reformulation):

I’m looking for an algorithm or piece of code to apply a very fast convolution to a discrete non periodic function (512 to 2048 values). Apparently the discrete time Fourier transform is the way to go. Though, I’d like to avoid data copy and conversion to complex, and avoid the butterfly reordering.

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1 Answer

  1. Editorial Team

    FFT is the fastest technique known for convolving signals, and FFTW is the fastest free library available for computing the FFT.

    The key for you to get maximum performance (outside of hardware … the GPU is a good suggestion) will be to pad your signals to a power of two. When using FFTW use the ‘patient’ setting when creating your plan to get the best performance. It’s highly unlikely that you will hand-roll a faster implementation than what FFTW provides (forget about N.R.). Also be sure to be using the Real version of the forward 1D FFT and not the Complex version; and only use single (floating point) precision if you can.

    If FFTW is not cutting it for you, then I would look at Intel’s (very affordable) IPP library. The have hand tuned FFT’s for Intel processors that have been optimized for images with various bit depths.

    Paul
    CenterSpace Software

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