Parallel Architecture for Fast Transforms with Trigonometric Kernel

We present an unified parallel architecture for four of the most important fast orthogonal transforms with trigonometric kernel: Complex Valued Fourier (CFFT), Real Valued Fourier (RFFT), Hartley (FHT), and Cosine (FCT). Out of these, only the CFFT has a data flow coinciding with the one generated by the successive doubling method, which can be transformed on a constant geometry flow using perfect unshuffle or shufile permutations. The other three require some type of hardware modification to guarantee the constant geometry of the successive doubling method. We have defined a generalized processing section n data recirculations and the RFFT and FHT transforms in n-1 data recirculations, with R being the number of stages of a transform of length N = r n. Also, the efficiency of the partitioned parallel architecture is optimum because there is no cycle loss in the systolic computation of all the butterflies for each of the four transforms.