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Lightning and Fourier transform of an impulse

Started by jnarino August 5, 2008
Dear list
I would like to ask the group, about a certain doubt I have. In an
examination, the professor asked 'why lighting causes disruptions to
TV and Radio signals?'. The answer supposedly is, since a lighting can
be seen as an electric 'impulse' signal (on the time domain), then in
the frequency domain we have white noise, thus, generating noise in
all frequencies. For the time being, let's ignore the electromagnetics
involved, and let only focus on the Fourier transform part.

The following explanation may be wrong, but the fact that the Fourier
transform(FT) of an impulse is white noise is due to the fact that for
FT 'localizing' a very short and abrupt event in time is very
difficult (we can see this in the Gibbs phenomenon), so all bases
(sines and cosines) are summed up and we end with the continuous
frequency representation, or 'white noise'.

However, a more advanced transform (like a Gabor transform), shows in
a Time frequency plane that the impulse is localized in time and
frequency.

I am highly confused of how to see on a real physical sense the
Fourier transform of an impulse function . Any insights?

regards

Juan Pablo
jnarino wrote:
> Dear list > I would like to ask the group, about a certain doubt I have. In an > examination, the professor asked 'why lighting causes disruptions to > TV and Radio signals?'. The answer supposedly is, since a lighting can > be seen as an electric 'impulse' signal (on the time domain), then in > the frequency domain we have white noise, thus, generating noise in > all frequencies. For the time being, let's ignore the electromagnetics > involved, and let only focus on the Fourier transform part. > > The following explanation may be wrong, but the fact that the Fourier > transform(FT) of an impulse is white noise is due to the fact that for > FT 'localizing' a very short and abrupt event in time is very > difficult (we can see this in the Gibbs phenomenon), so all bases > (sines and cosines) are summed up and we end with the continuous > frequency representation, or 'white noise'. > > However, a more advanced transform (like a Gabor transform), shows in > a Time frequency plane that the impulse is localized in time and > frequency. > > I am highly confused of how to see on a real physical sense the > Fourier transform of an impulse function . Any insights? > > regards > > Juan Pablo
Sometimes when I run into problems like this I start with the math and ponder it until the objecting brain cells are beaten into submission by their neighbors. From a mathematical standpoint this is easy: because the impulse has an infinitesimal duration, none of the sine waves that you compare it to with the Fourier integral average out, so they all have some non-zero value coming out of the integral. Only because the impulse has infinite energy does it have energy at each of the frequencies you try. To draw this into the physical world, think of the impulse as an approximation. Real infinite-energy events don't exist, nor do real infinitesimal time events. What you simulate with the impulse is a really short, really strong event compared to what you're working with (like -- a lightning strike near a radio receiver). So your real signal has some extent in time, and some finite energy. But if you tried to do your integrals with it it'd be a pain in the behind. So you just take the area of your real signal, and say that it's a Dirac delta functional and proceed. One way to gain some intuition on this is to consider a signal whose time-domain representation is a rectangular signal, so it has width T and height 1/T. Take it's Fourier transform -- you get that familiar sinc function. Now take the limit of the sinc function as T goes to zero -- starting to look familiar? -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
jnarino wrote:
> Dear list > I would like to ask the group, about a certain doubt I have. In an > examination, the professor asked 'why lighting causes disruptions to > TV and Radio signals?'. The answer supposedly is, since a lighting can > be seen as an electric 'impulse' signal (on the time domain), then in > the frequency domain we have white noise, thus, generating noise in > all frequencies. For the time being, let's ignore the electromagnetics > involved, and let only focus on the Fourier transform part. > > The following explanation may be wrong, but the fact that the Fourier > transform(FT) of an impulse is white noise is due to the fact that for > FT 'localizing' a very short and abrupt event in time is very > difficult (we can see this in the Gibbs phenomenon), so all bases > (sines and cosines) are summed up and we end with the continuous > frequency representation, or 'white noise'. > > However, a more advanced transform (like a Gabor transform), shows in > a Time frequency plane that the impulse is localized in time and > frequency. > > I am highly confused of how to see on a real physical sense the > Fourier transform of an impulse function . Any insights?
First of a all, you mean "lightning", the electrical flash that produces thunder. Second, you don't need to think about Fourier transforms, but if you do, recognize the while white noise and an impulse have the same power spectrum, they do not have the same spectrum. (The inverse transform of white noise's spectrum is white noise, but the inverse transform of an impulse's spectrum is an impulse. Each to its own kind.) The spectrum of a lightning strike is very broad because, as you recognized, it is quite impulsive. A receiver is affected by any signal at the frequency it is tuned to, including any external sources. Lightning is one such. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Hi Juan,
Consider a pulse with a finite width.  The shape doesn't matter-- it might
be rectangular, Gaussian, etc.  The frequency spectrum of this pulse will
have a value of 1 at DC, and fall off at higher frequencies.  (There are
more details, but this is a 6 sentence explanation).  

Now, squeeze the pulse and make it narrower. This makes the frequency
spectrum broader.  Here's a reference:  

http://www.dspguide.com/ch10/4.htm

When you have squeezed the pulse into an impulse, the frequency spectrum
has been broadened so much that all is left is a contant value of one.  
Regards,
Steve




But the frequency spectrum exists over all time, not just during the
impulse.

So I don't think this can be used to explain why the lightning
disrupts radio for a short time.

Chris
======================
Chris Bore
BORES Signal Processing
www.bores.com


On Aug 5, 9:39&#2013266080;am, jnarino <jnar...@gmail.com> wrote:
> Dear list > I would like to ask the group, about a certain doubt I have. In an > examination, the professor asked 'why lighting causes disruptions to > TV and Radio signals?'. The answer supposedly is, since a lighting can > be seen as an electric 'impulse' signal (on the time domain), then in > the frequency domain we have white noise, thus, generating noise in > all frequencies. For the time being, let's ignore the electromagnetics > involved, and let only focus on the Fourier transform part. > > The following explanation may be wrong, but the fact that the Fourier > transform(FT) of an impulse is white noise is due to the fact that for > FT 'localizing' a very short and abrupt event in time is very > difficult (we can see this in the Gibbs phenomenon), so all bases > (sines and cosines) are summed up and we end with the continuous > frequency representation, or 'white noise'. > > However, a more advanced transform (like a Gabor transform), shows in > a Time frequency plane that the impulse is localized in time and > frequency. > > I am highly confused of how to see on a real physical sense the > Fourier transform of an impulse function . Any insights? > > regards > > Juan Pablo
> On Aug 5, 9:39 am, jnarino <jnar...@gmail.com> wrote:
>>I would like to ask the group, about a certain doubt I have. In an >>examination, the professor asked 'why lighting causes disruptions to >>TV and Radio signals?'. The answer supposedly is, since a lighting can >>be seen as an electric 'impulse' signal (on the time domain), then in >>the frequency domain we have white noise, thus, generating noise in >>all frequencies. For the time being, let's ignore the electromagnetics >>involved, and let only focus on the Fourier transform part.
(snip)
>>I am highly confused of how to see on a real physical sense the >>Fourier transform of an impulse function . Any insights?
Chris Bore wrote: > But the frequency spectrum exists over all time, not just during the > impulse. > So I don't think this can be used to explain why the lightning > disrupts radio for a short time. It is even worse than that. Note that the Fourier transform of an impulse function includes both positive and negative time. But in reality there are no impulse functions, only approximations to them. The frequency range of the Fourier transform depends on how sharp the edge of the approximate impulse function is. That is one reason that lightning affects AM radio much more than FM radio. -- glen
Chris Bore wrote:
> But the frequency spectrum exists over all time, not just during the > impulse. > > So I don't think this can be used to explain why the lightning > disrupts radio for a short time.
Chris, The lightning isn't really an impulse. Some have durations of milliseconds, few less than tens of microseconds. That's more than enough to localize the interference in time. ... Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Chris Bore wrote:
> But the frequency spectrum exists over all time, not just during the > impulse. > > So I don't think this can be used to explain why the lightning > disrupts radio for a short time.
Chris, The lightning isn't really an impulse. Some have durations of milliseconds, few less than tens of microseconds. That's more than enough to localize the interference in time. ... Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Tue, 5 Aug 2008 01:39:47 -0700 (PDT), jnarino <jnarino@gmail.com>
wrote:

>Dear list >I would like to ask the group, about a certain doubt I have. In an >examination, the professor asked 'why lighting causes disruptions to >TV and Radio signals?'. The answer supposedly is, since a lighting can >be seen as an electric 'impulse' signal (on the time domain), then in >the frequency domain we have white noise, thus, generating noise in >all frequencies. For the time being, let's ignore the electromagnetics >involved, and let only focus on the Fourier transform part. > >The following explanation may be wrong, but the fact that the Fourier >transform(FT) of an impulse is white noise is due to the fact that for >FT 'localizing' a very short and abrupt event in time is very >difficult (we can see this in the Gibbs phenomenon), so all bases >(sines and cosines) are summed up and we end with the continuous >frequency representation, or 'white noise'. > >However, a more advanced transform (like a Gabor transform), shows in >a Time frequency plane that the impulse is localized in time and >frequency. > >I am highly confused of how to see on a real physical sense the >Fourier transform of an impulse function . Any insights? > >regards > >Juan Pablo
I wish I'd seen this yesterday when you posted, but I'll try to catch up. As others have pointed out, the FT of an impulsive function isn't noise, but it generally does have energy spread out over a wide range of frequencies. In the case of lightning the power levels involved are quite high, so it stands to reason that systems sensing spectrum in the region affected by the lightning would respond to it. So there are, IMHO, two major things at work 1) Impulsive waveforms have broad power spectra, 2) There's a LOT of energy in a lightning strike. ;) Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php
Eric Jacobsen <eric.jacobsen@ieee.org> writes:
> [...] > So there are, IMHO, two major things at work 1) Impulsive waveforms > have broad power spectra, 2) There's a LOT of energy in a lightning > strike.
God's impulse radio??? :) -- % Randy Yates % "Watching all the days go by... %% Fuquay-Varina, NC % Who are you and who am I?" %%% 919-577-9882 % 'Mission (A World Record)', %%%% <yates@ieee.org> % *A New World Record*, ELO http://www.digitalsignallabs.com