Fast Hartley transform

Discrete Hartley transform is an analogue of discrete Fourier transform for real data. The Hartley transform takes a real sequence as an input. The result is also a real sequence:

For some time it was considered that Hartley transform can be a faster alternative to the real Fourier transform, but later it was found out that there are FFT algorithms, which are a little more efficient than the corresponding FHT algorithms. Thus, at present the Hartley transform is rarely used in practice.

FHT implementation in ALGLIB

ALGLIB package does not contain a specialized code for fast Hartley transform. Instead, the Hartley transform is converted into a real FFT the results of which are processed in time O(N).