In-place in-order mixed radix fast Hartley transforms

Abstract

This paper presents two Fortran programs that calculate the mixed radix discrete Hartley transform (DHT) using a general odd length p-point DHT module and several short length Winograd DHT (WDHT) modules. Each program has its own advantages such as simplicity for implementation or minimum arithmetic complexity. New efficient radix-3, odd radix-p FHT algorithms and short WDHT modules have been developed to be incorporated into a general FHT algorithm. It allows a much wider selection of transform sizes, and calculates the DHT in order.