Hardware implementation of a series of transform matrices based on discrete hirschman transform

In this work, we present a fast computational structure for the discrete Hirschman Transform (FHT) family on Field Programmable Gate Arrays (FPGAs). Compared to the traditional FFT, the FHT has better performance in spectral estimation, FIR convolution, and especially in Compressive Sensing (CS). We implement our design of the DHT by using circular shifting of shorter terms of the FFT. This algorithm generates a series of DHT matrices of dimension N based on integer multiplications of N = K L which provides us alternative choices that have varying computational efficiencies and accuracies. Our design is presented on the Cyclone II DE2 board. Its simulation shows that the FHT is superior to the FFT in computational speed, space requirements, and rounding error performance.