Re: "Discrete Hartley transform" vs " Discrete Fouuier transform"

On Fri, 10 Oct 2008 11:54:52 -0500, Richard Owlett
<rowlett@[EMAIL PROTECTED]
> wrote:

>julius wrote:
>> On Oct 9, 9:02 pm, Richard Owlett <rowl...@[EMAIL PROTECTED]
> wrote:
>> 
>>>I'm interested in Magnitude vs Frequency.
>>>I have a strictly Real input sequence.
>>>There's Fast Hartley transform code available for my preferred
language.
>>>Relative speed is not an issue as I'm working on stored data.
>>>
>>>What gotcha's should I watch out for?
>>>Is the a good comparison on the web of their practical differences?
>>>
>>>TIA
>> 
>> 
>> Richard, maybe it's better if you tell us what your intended
>> application
>> is.  Right now it sounds a bit like asking whether you should buy a
>> sedan
>> or a hatchback :-P.  There will be lots of opinions, but they are
>> worthless
>> depending on your situation and application.
>
>Well, my app is about as simple as it gets.
>I have a time sequence f(t) and I want a measure of abs(f(omega))
>Signal so far has been audio, but don't think that bears on question.
>I'm not going to filter/process/... the transformed data, just plot it.
>I have been using an FFT so far.
>I wish to change hardware/OS/etc.
>There is existing FHT code that I can cut and paste.
>Wikipedia article seemed to imply FHT lost favor to FFT when faster FFT 
>algorithms were developed.

Back when processing power and memory were hard to come by I used to
use FHTs a lot.  As you mention, they're very good when the input is
real-valued, and if you only need the magnitude output for a plot
it'll be pretty efficient.

Since processing power and memory are cheap these days everybody just
plugs in FFTs.   When computing or memory resources are hard to come
by, though, the FHT can have some real advantages.

There's a book called "The Hartley Transform" by Bracewell that is a
good reference if you can find it or need it.   The output symmetries
of the FHT can be non-obvious at first, but once you sort them out it
is very easy to use and functionally equivalent to the FFT.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php