A real-data FFT algorithm for image processing applications

This paper presents a new approach for the reduction of the number of mathematical operations and the amount of memory required for two dimensional Fast Fourier Transforms. The approach, developed to support special purpose high speed hardware, is based on the restriction that the input data is real. It leads to a reduction in the number of mathematical operations for both one and two dimensional transforms. The new representation of the spectrum requires half the amount of memory used in the conventional representation. Filtering, though it requires the same amount of calculations, needs some interpretation and some relations had to be developed to relate the spectrum of the filtered image to the filter and the original image.