help -- Windzilla (high dynamic range windows)

I've been traveling the last week in areas with little wi-fi or even
cellular access, so my response has been delayed.

On Nov 2, 10:56 am, Fred Marshall <fmarshall_xremove_the...@xacm.org>
wrote:
> On 11/2/2010 10:59 AM, dbd wrote:
> ...

> Dale,
>
> You make some great points!  I'll have to ponder this further.
>
> I sure hope this isn't leading us into one of those silly arguments
> about delta functions!!  I'm a believer.
> Maybe that's why I relate the FT and DFT so readily?
> I do view them rather as "the same thing", if you will, because the
> integrals become sums going from continous to discrete and one can
> approach this in a "limit" sense, no?
> Is that agreeable at least?
>

I don't think the difference in viewpoints is based on delta functions
or limit arguments. I think that the FT and DFT are attempts to
perform the same operations, but they have access to much different
information. Because they do not have the same information, they
cannot do the same things.

> If not, then one would have to be able to argue that the discrete
> versions with sums have some special properties - is that reasonable?
>

Yes, the finite discrete sample sets available to the DFT don't
contain the information to allow the same properties as the FT.

> But, OK.  I'll try to paraphrase what we're saying:
>
> I've said that discrete finite sequences (and I'll say now "arbitrary
> sequences" to get away from any underlying signal periodicity issue),
> connected by a DFT, have a periodicity property that is assumed or
> implied or ....  (Well, of course, only the initial sequence can be
> arbitrary and the other follows from the transform - chicken and egg).
>
> You've said that the periodicity assumption is unnecessary and
> "harmful"?  I don't want to put words in your mouth here.
> ...
> Fred

There is a mathematics of the DFT based solely on finite data sets in
both domains. This has analogous but not equivalent properties to the
FT. If you carefully select your signals, you can find some (like the
ones you called herringbone) where the DFT is a subset of the FT (but
only for the right period and number of samples or you may actually
get to see the herringbone).

I shouldn't say that the statement: "The DFT is a special case of the
FT." is harmful. It's like a gun: guns don't shoot people, people
shoot people. There are many meanings that can be and have been given
to the statement. That is a good reason to avoid it.

"It is possible to define signals for which the DFT pair is a subset
of the FT pair." is a meaning that I would say is true.

"If you have a signal that is part of a FT pair there is a DFT pair
that is a subset of that FT pair." is a meaning that is not true of
the statement, but many people who ask questions about their ffts on
comp.dsp and comp.soft-sys.matlab have been led to believe. I think it
could be argued that those people have been harmed by incompetent
instruction.

Dale B. Dalrymple

"Fred Marshall" <fmarshall_xremove_the_xs@xacm.org> wrote in message 
news:v9Dzo.342220$Yn5.61629@en-nntp-14.dc1.easynews.com...
>
>
> I'm not saying that there aren't pitfalls in anything we do.  Once I was 
> building a sound source that was supposed to sound like a machine.  So, we 
> recorded some of the machine sound and put it into one of those "new" 
> digital shift-register memories to play it in an endless loop.  All we had 
> to do was match up the ends (like matching the time span of samples of a 
> periodic signal).  Oh!  But oops.  The length of the memory was too short 
> and the resulting spectral analysis looked like a herringbone.
>
> I think we need to use models that are meaningful for each of us.  I'll 
> leave it at that.
>

that's hysterical . 

"Steve Pope" <spope33@speedymail.org> wrote in message 
news:iab0a5$sob$1@blue.rahul.net...
>
> I guess I have a belief system that it really is a cosine transform
> I am doing; that f really is anywhere on the real line and is not
> discrete; and that while one can come up with a discrete transform
> that gives you the same answer for any particular case, it is
> (for me) not the most natural way of looking at it.
>


http://www.youtube.com/watch?v=DJIFDRjPySc