Correlation and convolution of image data using fermat number transform based on two's complement

The fast fermat number transform (FNT) enables fast correlation and fast convolution similar to fast correlation based on fast fourier transform (FFT). In contrast to fixed-point FFT with dynamic scaling, FNT is based on integer operations, which are free of rounding error, and maintains full dynamic range for convolution and correlation. In this paper, a technique to calculate FNT based on two's complement (TFNT) is presented and the correctness of the technique is proven. The TFNT is data flow driven without conditional assignments, which enables high performance pipelined implementations on digital signal processors and field programmable gate arrays. By taking the example of 2D correlation and based on a Radix-4 algorithm, it is shown that TFNT requires less operations than fixed-point FFT as well as less operations than FNT based on the previously presented diminished-1 approach.