Efficient Digital FFT Convolution with Boundary Kernel Renormalisation

This paper describes a correction method for Fast Fourier Transform (FFT) convolution that limits boundary contamination artefacts resulting from convolution padding methods. The proposed correction method makes a single data-driven boundary condition assumption and only uses information contained within the original input signal to produce consistent convolution results and maintain data integrity. An analysis of the algorithm shows that it performs identically to the standard convolution approach with the only discernible differences being resolved at the level of machine rounding errors. The correction method can be applied at minimal cost to performance and has valuable applications for scientific data processing where algorithm efficiency and data accuracy are imperative.