Need proofs about digital comminucation

"Richard Owlett" <rowlett@atlascomm.net> wrote in message
news:1085l9bod8nts82@corp.supernews.com...
> (apologies to J. Swift ;)
>
> Since Jerry threw my hat into the ring of those who might ask student
> type questions ( not having been in engineering classroom in 30+ tears
> and wishing I knew half of what he's probably forgotten ) I've an idea.
>
> A set of presuppositions, 'homework' posters may be:
> 1. lazy and incompetent
> 2. incompetent, knowing they are ignorant
> 3. competent but totally lost ( similar to #2)
> 4. unclassifiable independent learners ( Jerry and I )
>
>
> I would suggest that the first person recognizing the post as a
> "homework question" post a response in the following form:
>
> "This appears to be a homework question. We are willing to help
> students who demonstrate willingness to learn.
>
> If you are a student, please identify the course and give an
> indication of why you are having trouble answering the question.
>
> If you are not a student, please give us an idea of your background. A
> valid answer from the wrong point of view may not only be useless but
> misleading."

I agree with this.  It is not that I advocate intentionally misleading or
ignoring students (I don't).  Encouragement for the student to do their own
work is a good answer.

"Ronald H. Nicholson Jr." <rhn@mauve.rahul.net> wrote in message
news:c5vc1n$puo$3@blue.rahul.net...
> In article <9fe525a9.0404150420.48a5d0ba@posting.google.com>,
> ford <ford_usa_mustang@yahoo.fr> wrote:
> >2)Show that the sinc-pulse:
> >p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform
> >of the spectrum
> >P(f) = T^0.5 for |f| < 1 / (2T)
> >       0   for |f| > 1 / (2T)
>
> There seem to be a infinite number of different pulse shapes which might
> be the iFT of that spectrum, unless you are assuming some unstated
> phase specifications as well.
>
>
> IMHO. YMMV.
> -- 
> Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/
> #include <canonical.disclaimer>        // only my own opinions, etc.

Hello Ron,

I see the phase info as being given as the actual function and not just its
magnitude is given. Plus also given the context of these questions being
from an introductory course and the sinc/rect functions being a well known
Fourier pair, I'm sure the prof didn't throw an arbitrary phase curveball.

Now a more advanced question would be to use the defn of the FT to directly
find the transform of the sinc function via integration.

Clay

-- 
Clay S. Turner, V.P.
Wireless Systems Engineering, Inc.
Satellite Beach, Florida 32937
(321) 777-7889
www.wse.biz
csturner@wse.biz

"Clay S. Turner" <CSTurner@WSE.Biz> wrote in message news:<NyQgc.45308$951.14600@bignews3.bellsouth.net>...
> "Ronald H. Nicholson Jr." <rhn@mauve.rahul.net> wrote in message
> news:c5vc1n$puo$3@blue.rahul.net...
> > In article <9fe525a9.0404150420.48a5d0ba@posting.google.com>,
> > ford <ford_usa_mustang@yahoo.fr> wrote:
> > >2)Show that the sinc-pulse:
> > >p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform
> > >of the spectrum
> > >P(f) = T^0.5 for |f| < 1 / (2T)
> > >       0   for |f| > 1 / (2T)
> >
> > There seem to be a infinite number of different pulse shapes which might
> > be the iFT of that spectrum, unless you are assuming some unstated
> > phase specifications as well.
> >
> >
> > IMHO. YMMV.
> > -- 
> > Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/
> > #include <canonical.disclaimer>        // only my own opinions, etc.
> 
> Hello Ron,
> 
> I see the phase info as being given as the actual function and not just its
> magnitude is given. Plus also given the context of these questions being
> from an introductory course and the sinc/rect functions being a well known
> Fourier pair, I'm sure the prof didn't throw an arbitrary phase curveball.
> 
> Now a more advanced question would be to use the defn of the FT to directly
> find the transform of the sinc function via integration.

Well, during my time in DSP (which is limited to the last 15 years or so, 
I'm a relative newbie compared to some of the guys hanging out here)
I have never seen that sort of thing been done by formal integration. 
The only DSP textbook I have seen that attacs those kinds of problems 
from a formal point of view, is the Oppenheim and Schafer 1975 edition.

All other books apprach the "show that the sinc(w) is the FT of the 
rect(t)" problems by using the "by the Fourier Transform pair theorem 
the rect(t) must be the IFT of the sinc(w)" argument to establish 
the "proof". I guess a trained mathematician or mathematical physicist 
may get sezures from this sort of "proof", but this is how things are 
done in DSP texts.

Ouch! I may just have given away the answer of that assignment!
Oh well, the work still has to be done.

Rune

"Clay S. Turner" <CSTurner@WSE.Biz> wrote in message news:<NyQgc.45308$951.14600@bignews3.bellsouth.net>...
> "Ronald H. Nicholson Jr." <rhn@mauve.rahul.net> wrote in message
> news:c5vc1n$puo$3@blue.rahul.net...
> > In article <9fe525a9.0404150420.48a5d0ba@posting.google.com>,
> > ford <ford_usa_mustang@yahoo.fr> wrote:
> > >2)Show that the sinc-pulse:
> > >p(t) =sin((pi*t)/T) /((pi*t)/T) T^0.5 is the inverse Fourier transform
> > >of the spectrum
> > >P(f) = T^0.5 for |f| < 1 / (2T)
> > >       0   for |f| > 1 / (2T)
> >
> > There seem to be a infinite number of different pulse shapes which might
> > be the iFT of that spectrum, unless you are assuming some unstated
> > phase specifications as well.
> >
> >
> > IMHO. YMMV.
> > -- 
> > Ron Nicholson   rhn AT nicholson DOT com   http://www.nicholson.com/rhn/
> > #include <canonical.disclaimer>        // only my own opinions, etc.
> 
> Hello Ron,
> 
> I see the phase info as being given as the actual function and not just its
> magnitude is given. Plus also given the context of these questions being
> from an introductory course and the sinc/rect functions being a well known
> Fourier pair, I'm sure the prof didn't throw an arbitrary phase curveball.
> 
> Now a more advanced question would be to use the defn of the FT to directly
> find the transform of the sinc function via integration.

Well, during my time in DSP (which is limited to the last 15 years or so, 
I'm a relative newbie compared to some of the guys hanging out here)
I have never seen that sort of thing been done by formal integration. 
The only DSP textbook I have seen that attacs those kinds of problems 
from a formal point of view, is the Oppenheim and Schafer 1975 edition.

All other books apprach this type of problem along the lines of "first 
show that the sinc(w) is the FT of the rect(t), then use the Fourier 
Transform pair theorem to explain why rect(t) must be the IFT of the 
sinc(w)" to establish the "proof". I guess a trained mathematician or 
mathematical physicist may get sezures from this sort of "proof", but 
this is how things are done in DSP texts.

Ouch! I may just have given away the answer of that assignment!
Oh well, the work still has to be done.

Rune

On Sun, 18 Apr 2004 21:14:56 GMT, glen herrmannsfeldt
<gah@ugcs.caltech.edu> wrote:

  (snipped)
>
>I now have a copy of a book called "The Darwin Awards".  If you
>have read that book you will have an idea of what I mean by
>obvious after a little thought, and the results of applying
>no thought to a life risking question.
>
>-- glen

Hi Glen,

  I've heard of the Darwin Awards, but the stories 
seem unbelievable to me.

Did that guy really put huge helium balloons on a lawn 
chair and end up high in the sky?

Thanks,
[-Rick-]

"Rick Lyons" <r.lyons@_BOGUS_ieee.org> wrote in message
news:4084f5fb.987836953@news.sf.sbcglobal.net...
> On Sun, 18 Apr 2004 21:14:56 GMT, glen herrmannsfeldt
> <gah@ugcs.caltech.edu> wrote:
>
>   (snipped)
> >
> >I now have a copy of a book called "The Darwin Awards".  If you
> >have read that book you will have an idea of what I mean by
> >obvious after a little thought, and the results of applying
> >no thought to a life risking question.
> >
> >-- glen
>
> Hi Glen,
>
>   I've heard of the Darwin Awards, but the stories
> seem unbelievable to me.
>
> Did that guy really put huge helium balloons on a lawn
> chair and end up high in the sky?
>

That story is actually true
(http://www.snopes.com/spoons/noose/balloon.htm), but for the most part, the
Darwin Awards are made up.  I stopped reasing them several years ago when it
because obvious that they were becoming more of a contest to see who could
come up with the stupidest story.

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
news:f56893ae.0404192149.23b1fb9b@posting.google.com...
>
> Ouch! I may just have given away the answer of that assignment!
> Oh well, the work still has to be done.
>
> Rune

I rather doubt it.  My bet is that the assignment's due date was the day
after the original poster made his post.  Odds are that they haven't
followed this thread, and that even if they did, they won't have the
mathematical expertise to grasp what it is you're saying.

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
news:f56893ae.0404192155.46a9540e@posting.google.com...
> "Clay S. Turner" <CSTurner@WSE.Biz> wrote in message
news:<NyQgc.45308$951.14600@bignews3.bellsouth.net>...
> >
> > Now a more advanced question would be to use the defn of the FT to
directly
> > find the transform of the sinc function via integration.
>
> Well, during my time in DSP (which is limited to the last 15 years or so,
> I'm a relative newbie compared to some of the guys hanging out here)
> I have never seen that sort of thing been done by formal integration.
> The only DSP textbook I have seen that attacs those kinds of problems
> from a formal point of view, is the Oppenheim and Schafer 1975 edition.
>
> All other books apprach this type of problem along the lines of "first
> show that the sinc(w) is the FT of the rect(t), then use the Fourier
> Transform pair theorem to explain why rect(t) must be the IFT of the
> sinc(w)" to establish the "proof". I guess a trained mathematician or
> mathematical physicist may get sezures from this sort of "proof", but
> this is how things are done in DSP texts.
>
> Ouch! I may just have given away the answer of that assignment!
> Oh well, the work still has to be done.
>
> Rune

Hello Rune,
My 1st attack on the problem would be the standard one where the uniqueness
and invertibility of the transform are exploited as you described - and I
think this is what the prof really desires. But it can be done the "old
fashioned way." I scribbled a simple proof outlining the major details. It
may be found at the following link. The trick I used is not well known, but
it is very good for these types of integrals.

http://personal.atl.bellsouth.net/p/h/physics/proof.pdf

Clay

-- 
Clay S. Turner, V.P.
Wireless Systems Engineering, Inc.
Satellite Beach, Florida 32937
(321) 777-7889
www.wse.biz
csturner@wse.biz

Rick Lyons wrote:

> On Sun, 18 Apr 2004 21:14:56 GMT, glen herrmannsfeldt

>>I now have a copy of a book called "The Darwin Awards".  If you
>>have read that book you will have an idea of what I mean by
>>obvious after a little thought, and the results of applying
>>no thought to a life risking question.

>   I've heard of the Darwin Awards, but the stories 
> seem unbelievable to me.

> Did that guy really put huge helium balloons on a lawn 
> chair and end up high in the sky?

Some are verified, some aren't.

I remember the lawn chair story being in the news when
it happened.

I also remember the Yosemite parachute story being in the
news when it happened.

One that I remember, but which isn't in the book, came not long
after our family vacation in Yellowstone.  Someone was vacationing
in Yellowstone, opened the motorhome door, had the dog jump out
and immediately jump into a pool of boiling water.  The owner
then jumped in to rescue the dog.  Both died.

Some are urban legends and are so marked.

-- glen

Tim Wescott <tim@wescottnospamdesign.com> wrote in message news:<10800frpq46ls07@corp.supernews.com>...

> kal wrote:
> > I think the law of large numbers are at work here. I am sure the
> > letters from nigerian princes which want to transfer money to US and
> > give you some portion of it are pretty obviously bogus to you but
> > still they get some people. As the reach of comp.dsp is getting
> > larger, I am sure some people are responding to even the most obvious
> > homework problems.
> 
> So if there's a FAQ for the list (is there a FAQ?) then "how can I do my 
> homework using the list" should say "hit the books?".

Not necessarily.

> I wonder how many of these people are just lazy and how many are truly 
> desperate.  Some scholarship programs can be pretty harsh about low 
> grades, and you often don't realize that you're bombing a class until 
> it's too late to withdraw.  Not that we should all jump in and do 
> everyone's spring exams, mind, but the thought does keep me from typing 
> in a lot of snide comments.

For a student on harsh scholarship programs with a strict requirement
of grades, when he post his homework question or even take-home exam
question in comp.dsp, an honest student (who do not plagiarize others'
term papers) would have mentioned
* This is a homework (or take-home exam) question, and
* I have tried using this method but hit a stonewall and I
  cannot go further, or something else showing he does his
  best and got stucked.

In this case I do not think anyone in comp.dsp will object to helping
him.  There might be people solving the problem directly for him (free
consultation), and some others might offer further hints and lead him
step by step towards the direction, but in general he did not cheat
and he did not attempt to cheat.  He is honest and other DSP experts
can and should give him a hand.

For a question which looks "obviously" legitimate for an industry
issue instead of an academic one, there is no controversy either.

So now the problem is still -- what to do with a question in comp.dsp
which looks suspiciously similar to a textbook question or even a
homework/exam question when the original poster didn't elaborate it. 
Some people have suggested micellaneous ways to let the poster know
what he missed (an honesty statement/disclaimer).  Some people
suggested to err on this side (definitely not to help a cheater) and
some other people suggested the other way (what if he is under
scholarship pressure on his grades).

I would like to add one possible proposal: Knowledgeable people in
comp.dsp can write something similar to the followings upon a
suspicious homework question:

    Your question looks very similar to a textbook question,
    or a homework/exam one, but you did not say it is one nor
    it is not one.

    I and many other comp.dsp participants decide to put a
    hold on this question for 7 days before we start discussing
    and helping you, unless you elaborate on whether this is
    a homework question, and how much you have done if it is
    one.

Homework and take-home exam questions have their due dates, and I
assume 1 week is good enough to cover most cases so that the delay
will indirectly mean the discussion will not help a cheater in
schools.  On the other hand, if a guy thinks of a curious and
interesting DSP question and ask for others' opinions (like Jerry Avin
does), or the DSP question arises from a development project
encountered in real-life, I do not think a delay of 1 week would hurt.