Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!iuvax!purdue!tut.cis.ohio-state.edu!pt.cs.cmu.edu!andrew.cmu.edu!steve+
From: steve+@andrew.cmu.edu (Stephen Webster)
Newsgroups: comp.dsp
Subject: Hartley xform
Message-ID: <wZ_UwgC00UkM8KM0RN@andrew.cmu.edu>
Date: 4 Oct 89 14:09:48 GMT
Organization: Information Technology Center, Carnegie Mellon, Pittsburgh, PA
Lines: 31


I believe the major distinguishing features between the FHT and the FFT
are:

*   The FHT uses a purely real kernel (sin + cos) instead of the FFT's
imaginary kernel (sin + j cos).  (Yes, ``j'', dammit.  I'm an engineer.)

*   Since you're only handling real data, you cut the number of
multiplies in half; that is, you don't have to carry around a real and
an imaginary part for each datum in the calculation.

*   What you actually get from the FHT is an asymmetric combination of
the magnitude & phase of your input time waveform.  Intuitively, one can
see that the symmetry of the FFT in magnitude & phase means that you're
doing "extra" calculations that you don't have to; the FHT exploits this.

*   This all means that the FHT is just great for finding power spectra
(wherein you don't care about mag & phase separately).  You _can_
convert the FHT output to magnitude & phase data, but the total number
of calculations required is the same, or greater, than a good FFT.

*   FHT algorithms for finding power spectra are (generally) shorter
than their FFT-based counterparts, while FHT algorithms for finding mag
& phase are (generally) longer.

*   I think R.N. Bracewell has actually gone and patented the FHT, while
the FFT is as public as the Pythagorean Theorem.  I wish him the best of
luck in enforcing that patent.

-steve webster
ITC/EE, CMU