Applications of Regularized Fast Hartley Transform

Abstract

This chapter discusses the application of the regularized FHT to a number of computationally-intensive DSP-based functions that may benefit from the adoption of a transform-space solution, and in particular, where the data in question is real valued so that the processing may be efficiently carried out in Hartley space. The functions discussed are those of up-sampling, differentiation, correlation – both auto-correlation and cross-correlation – and channelization. Efficient channelization, for the case of a single channel (or small number of channels), may be achieved by means of a DDC process where the filtering is performed via fast Hartley-space convolution, whilst for the case of multiple channels, efficiency may be achieved via the application of the polyphase DFT filter bank. Each such function might typically be encountered in that increasingly important area of wireless communications relating to the geolocation of signal emitters, with each potentially able to yield both conceptually and computationally simplified solutions when solved via the regularized FHT. A discussion is finally provided relating to the results obtained in the chapter.