The emperor's new clothes

Am I the only one feeling like this about the Fourier transform?

People often say or write in text books "Then you just take the Fourier
transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
dimension". But when it comes down to it, people don't know s... and
they can not help you because it is not that simple, and it can not be
written as a one-line equation.

"Oh, you have change the sign and take the complex conjugate", "Oh, it
is different for discrete values", "That is what the theory says, but
it will not work on your data", "hmm thats funny...."

Or maybe I am just the thickest guy on earth, that should step away
from my computer before I harm myself, because every one else gets it!

sorry, just tired after spending a few days getting nowhere....

happy holidays,
walther

Newbie to Newbie response

I think the gurus need more particulars ;}
Pose the PARTICULAR problem that frustrated you.
[P.S. there are several here that can testify that I'm so lost I 
confuse all. But they help me any way ;}


walther wrote:

> Am I the only one feeling like this about the Fourier transform?
> 
> People often say or write in text books "Then you just take the Fourier
> transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
> dimension". But when it comes down to it, people don't know s... and
> they can not help you because it is not that simple, and it can not be
> written as a one-line equation.
> 
> "Oh, you have change the sign and take the complex conjugate", "Oh, it
> is different for discrete values", "That is what the theory says, but
> it will not work on your data", "hmm thats funny...."
> 
> Or maybe I am just the thickest guy on earth, that should step away
> from my computer before I harm myself, because every one else gets it!
> 
> sorry, just tired after spending a few days getting nowhere....
> 
> happy holidays,
> walther

walther wrote:

> Am I the only one feeling like this about the Fourier transform?
> 
> People often say or write in text books "Then you just take the Fourier
> transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
> dimension". But when it comes down to it, people don't know s... and
> they can not help you because it is not that simple, and it can not be
> written as a one-line equation.
> 
> "Oh, you have change the sign and take the complex conjugate", "Oh, it
> is different for discrete values", "That is what the theory says, but
> it will not work on your data", "hmm thats funny...."
> 
> Or maybe I am just the thickest guy on earth, that should step away
> from my computer before I harm myself, because every one else gets it!
> 
> sorry, just tired after spending a few days getting nowhere....

Walther,

If you want to learn this correctly, I suggest getting ahold of Proakis
and Manolakis's "Digital Signal Processing" and also possibly Oppenheim's
old "Signals and Systems." Oppenheim (I believe, I can't check because my
books are at work) has a derivation of the convolution property for continuous-time
Fourier transforms. P&M have a really good section that shows how multiplying
in discrete-time using the Discrete Fourier Transform (DFT) is equivalent to
*circular* convolution. Check it out. And don't be surprised if you have to
spend a month of evenings reading and working problems. This stuff comes easy
for no one.
-- 
%  Randy Yates                  % "...the answer lies within your soul
%% Fuquay-Varina, NC            %       'cause no one knows which side
%%% 919-577-9882                %                   the coin will fall."
%%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

walther <-@-.-> wrote in message news:<221220032016528945%-@-.->...
> Am I the only one feeling like this about the Fourier transform?
> 

Hi Walther,

Maybe looking at the DFT as done on computers would help..

The way I sort of got the hang of the FT (not the maths) was to think
about it as _basically_ a number of FIR filters run over a window of
samples from your signal. The lowest frequency (above DC) that is
resolved would be the 1/WindowPeriod. The highest would be
SampleRate/2.

This FIR_Per_Frequency is done using cosine coefficients and sine
coefficients just in case the signal is not exactly in phase with one
or other.

I don't claim to understand the FT, but I've sort of got a feel for
it.

Good Luck

Robert

walther <-@-.-> wrote in message news:<221220032016528945%-@-.->...
> Am I the only one feeling like this about the Fourier transform?
> 
> People often say or write in text books "Then you just take the Fourier
> transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
> dimension". But when it comes down to it, people don't know s... and
> they can not help you because it is not that simple, and it can not be
> written as a one-line equation.
> 
> "Oh, you have change the sign and take the complex conjugate", "Oh, it
> is different for discrete values", "That is what the theory says, but
> it will not work on your data", "hmm thats funny...."
> 
> Or maybe I am just the thickest guy on earth, that should step away
> from my computer before I harm myself, because every one else gets it!
> 
> sorry, just tired after spending a few days getting nowhere....
> 
> happy holidays,
> walther

A few years ago I wrote a PhD thesis on signal processing of seismic waves. 
Here are just a few of the details I had to sort out:

- Electrical engineers define the Fourier Transform (FT) as

   X(w) = integral x(t) exp(-jwt) dt                   [1]

  while the mathematicians define the FT as

   X(w) = integral x(t) exp(iwt) dt.                   [2]

  Note the different -j and i. Some say that [1] and [2] are formally 
  equal because i=sqrt(-1) and j= -sqrt(-1). 

- In physics, you often have to transform the wave equation to 
  frequency-wavenumber domain:

   S(k,w) = double integral s(x,t) exp(i(wt-kx)) dxdt  [3]

  Note the different signs in the wt part and kx part in the exponent.

- Lots of the literature I used was written by earthquake seismologists, 
  who work on a global scale. To them, it's very convenient to work with 
  a spherical coordinate system where the range axis points outwards
  from the centrum of the earth. On the surface of the earth, that 
  translates to a vertical axis (z axis) pointing upwards. Now, I worked 
  with petroleum exploration seimsologists and they find it very useful 
  to use a cartesian coordinate system  with a vertical depth axis that 
  points downwards from the earth surface. The difference between the 
  two conventions is changing a sign in the Fourier exponent.

Sorting out these kinds of details delayed my writing the thesis
with about a year. So no, you aren't thick. It's just one of those 
things one have to learn the hard way, and then deal with as best 
one can.

Rune

"walther" <-@-.-> wrote in message news:221220032016528945%-@-.-...
> Am I the only one feeling like this about the Fourier transform?
>
> People often say or write in text books "Then you just take the Fourier
> transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
> dimension". But when it comes down to it, people don't know s... and
> they can not help you because "it" is not that simple, and "it" can not be
> written as a one-line equation. [quotation marks added]

Walther,

What is "it"?  The first line suggests the Fourier Transform but what
follows suggests something else - like operations involving Fourier
Transforms.

>
> "Oh, you have change the sign and take the complex conjugate", "Oh, it
> is different for discrete values",

Yes, sometimes it's easier to remember what happens when you start with real
numbers.  When the numbers are complex to start with, then I too have to
things up.  I never remember.  It's because it's so rarely an issue.  Just
remember that conjugates appear in some situations and use that awareness to
check.

>"That is what the theory says, but
> it will not work on your data", "hmm thats funny...."

Not funny.  Why should theory and practice necessarily diverge?  You must
have an example in mind.  I can think of my own but that's not nearly as
helpful.

Fred

Thank you for all the quick replies. 

Glad to hear I am not the only one strugling with the peculiarities of
the Fourier transform. Now I feel more at ease asking questions...

It is just that in books on image analysis, it is often presented on a
few pages, and you get the feeling that you should be able to use after
that. 

I will try and isolate my problem, and hopefully someone here can guide
me in the rigth direction.

Thank you,
Walther

perhaps the best way to understand the fourier transform and get a start:

"Mastering The Fourier Transform in One Day" at this site:
http://www.dspdimension.com/html/dftapied.html

regards
tathagatac

Walther Fledelius <-@-.dk> wrote in message news:<231220031104240710%-@-.dk>...
> Thank you for all the quick replies. 
> 
> Glad to hear I am not the only one strugling with the peculiarities of
> the Fourier transform. Now I feel more at ease asking questions...
> 
> It is just that in books on image analysis, it is often presented on a
> few pages, and you get the feeling that you should be able to use after
> that. 
> 
> I will try and isolate my problem, and hopefully someone here can guide
> me in the rigth direction.
> 
> Thank you,
> Walther

walther <-@-.-> wrote:

>Am I the only one feeling like this about the Fourier transform?
>
>People often say or write in text books "Then you just take the Fourier
>transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
>dimension". But when it comes down to it, people don't know s... and
>they can not help you because it is not that simple, and it can not be
>written as a one-line equation.
>
>"Oh, you have change the sign and take the complex conjugate", "Oh, it
>is different for discrete values", "That is what the theory says, but
>it will not work on your data", "hmm thats funny...."
>

'Tis the difference between being a Professor, and one slogging it out
in the real world of DSP applications.  Haha.

Robert

www.gldsp.com

( modify address for return email )

www.numbersusa.com
www.americanpatrol.com

may be i'm missing something here... dft method produces circular
convolution, not linear. circular one is aliased version of the linear conv.
if u want to use dft to produce linear conv, add a bunch of zeros (for
lengths M & N of 2 signals add zeros to both signals so that their lengths
become M+N-1) and then do the dft stuff

Ganesan



"Randy Yates" <yates@ieee.org> wrote in message
news:52OFb.5597$IM3.4539@newsread3.news.atl.earthlink.net...
> walther wrote:
>
> > Am I the only one feeling like this about the Fourier transform?
> >
> > People often say or write in text books "Then you just take the Fourier
> > transform" or "f(x)*g(x)=F(x)xG(x)" or "It generalizes to any
> > dimension". But when it comes down to it, people don't know s... and
> > they can not help you because it is not that simple, and it can not be
> > written as a one-line equation.
> >
> > "Oh, you have change the sign and take the complex conjugate", "Oh, it
> > is different for discrete values", "That is what the theory says, but
> > it will not work on your data", "hmm thats funny...."
> >
> > Or maybe I am just the thickest guy on earth, that should step away
> > from my computer before I harm myself, because every one else gets it!
> >
> > sorry, just tired after spending a few days getting nowhere....
>
> Walther,
>
> If you want to learn this correctly, I suggest getting ahold of Proakis
> and Manolakis's "Digital Signal Processing" and also possibly Oppenheim's
> old "Signals and Systems." Oppenheim (I believe, I can't check because my
> books are at work) has a derivation of the convolution property for
continuous-time
> Fourier transforms. P&M have a really good section that shows how
multiplying
> in discrete-time using the Discrete Fourier Transform (DFT) is equivalent
to
> *circular* convolution. Check it out. And don't be surprised if you have
to
> spend a month of evenings reading and working problems. This stuff comes
easy
> for no one.
> -- 
> %  Randy Yates                  % "...the answer lies within your soul
> %% Fuquay-Varina, NC            %       'cause no one knows which side
> %%% 919-577-9882                %                   the coin will fall."
> %%%% <yates@ieee.org>           %  'Big Wheels', *Out of the Blue*, ELO
> http://home.earthlink.net/~yatescr