Hartley transforms

Thread View: comp.dsp

2 messages

[T] Back to Threads [V] Tree View [G] Group Articles

2 total messages Started by Thomas M. Breuel Sun, 05 Aug 1990 00:49

#902

Author: Thomas M. Breuel
Date: Sun, 05 Aug 1990 00:49

25 lines
1643 bytes

Does anyone know or have pointers to the literature or code about how
to do multidimensional Hartley transforms (i.e., is it obvious that a
2D HT is the same as 2 1D HT's, or do I need some correction), and what
the correlation and convolution theorems look like for multidimensional
Hartley transforms?

A straightforward derivation and implementation of the convolution/correlation 
theorems would give 4 times the number of multiplications for a convolution/
correlation as the corresponding (complex) Fourier method and not allow
the operation to be done "in place" (replacing one of the input
arrays). I think by rearranging terms I can fix this, but I would
rather not have to work it out myself.

Also, does anyone have code for the FHT (C/Fortran)? Currently, I am
using a REALFFT routine and re-arrange the output, which is probably
not very inefficient, but not quite as fast as it could be.  Have the
patent issues involving the FHT been resolved?

					Thanks, Thomas.
					tmb@ai.mit.edu

PS: the Hartley transform is a real transform that is
closely related to the Fourier transform and has some
practical advantages over it if all you want to do is
operate on real data.

Re: Hartley transforms

#909

Author: Dr. Robin Lake
Date: Mon, 06 Aug 1990 11:55

36 lines
1758 bytes

In article <9706@life.ai.mit.edu> tmb@ai.mit.edu writes:
| >Does anyone know or have pointers to the literature or code about how
| >to do multidimensional Hartley transforms (i.e., is it obvious that a
| >2D HT is the same as 2 1D HT's, or do I need some correction), and what
| >the correlation and convolution theorems look like for multidimensional
| >Hartley transforms?
| >
...
| >
| >Also, does anyone have code for the FHT (C/Fortran)? Currently, I am
| >using a REALFFT routine and re-arrange the output, which is probably
| >not very inefficient, but not quite as fast as it could be.  Have the
| >patent issues involving the FHT been resolved?
| >
| >					Thanks, Thomas.
| >					tmb@ai.mit.edu
| >
| >PS: the Hartley transform is a real transform that is
| >closely related to the Fourier transform and has some
| >practical advantages over it if all you want to do is
| >operate on real data.


Perhaps not right on target, but I find the following at hand:

R. N. Bracewell "Numerical Transforms"  Science, 11 May 1990, pg 697ff.

P. Duhamel and M.  Vetterli "Improved Fourier and Hartley Transform Algorithms ... "
IEEE Trans ASSP.  #6, June 1987, pg.818 ff.

Surprisingly, nothing in the books on Fast Algorithms or MultiDimensional
Signal Processing.

Rob Lake
BP Research
rbl@BP.COM

Thread Navigation

This is a paginated view of messages in the thread with full content displayed inline.

Messages are displayed in chronological order, with the original post highlighted in green.

Use pagination controls to navigate through all messages in large threads.

Back to All Threads