I admit to being math challenged, learning by pictures is best. Is there some source on WEB that has pictures of Fourier Transform of some common time domain waveforms? Am I "squaring the circle" or "tri-secting the angle"?
Fourier Transforms compared to FFT's [ caution -- newbie at large ;]
Started by ●September 9, 2004
Reply by ●September 9, 20042004-09-09
"Richard Owlett" <rowlett@atlascomm.net> wrote in message news:10k1n5p232cuua7@corp.supernews.com...> I admit to being math challenged, learning by pictures is best. > > Is there some source on WEB that has pictures of Fourier Transform of > some common time domain waveforms? > > Am I "squaring the circle" or "tri-secting the angle"?"Doubling the cube". I was going to suggest getting Octave or Scilab and playing around a bit, but I found a web site http://www.falstad.com/fourier/ that has a Java applet that lets you display a number of common functions and also change the magnitude and phase of the transform and watch the signal change. Best wishes, --Phil Martel
Reply by ●September 9, 20042004-09-09
Phil Martel wrote:> "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:10k1n5p232cuua7@corp.supernews.com... > >>I admit to being math challenged, learning by pictures is best. >> >>Is there some source on WEB that has pictures of Fourier Transform of >>some common time domain waveforms? >> >>Am I "squaring the circle" or "tri-secting the angle"? > > > "Doubling the cube". > > I was going to suggest getting Octave or Scilab and playing around a bit,I have Scilab, that's what got me started ;]> but I found a web site > http://www.falstad.com/fourier/ that has a Java applet that lets you display > a number of common functions and also change the magnitude and phase of the > transform and watch the signal change.I think site has problem. All sounds seem same, possible volume difference.> > Best wishes, > --Phil Martel > > >
Reply by ●September 10, 20042004-09-10
On 2004-09-10 00:47:59 +0200, Richard Owlett <rowlett@atlascomm.net> said:> I admit to being math challenged, learning by pictures is best. > > Is there some source on WEB that has pictures of Fourier Transform of > some common time domain waveforms? > > Am I "squaring the circle" or "tri-secting the angle"?Try http://www.dspdimension.com/html/Lab/FftLab.html -- Stephan M. Bernsee http://www.dspdimension.com
Reply by ●September 10, 20042004-09-10
"Phil Martel" <p.martel@comcast.net> wrote in message news:<6260d.164649$mD.3014@attbi_s02>...> "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:10k1n5p232cuua7@corp.supernews.com... > > I admit to being math challenged, learning by pictures is best. > > > > Is there some source on WEB that has pictures of Fourier Transform of > > some common time domain waveforms? > > > > Am I "squaring the circle" or "tri-secting the angle"? > > "Doubling the cube". > > I was going to suggest getting Octave or Scilab and playing around a bit, > but I found a web site > http://www.falstad.com/fourier/ that has a Java applet that lets you display > a number of common functions and also change the magnitude and phase of the > transform and watch the signal change. > > Best wishes, > --Phil MartelThat applett is just brilliant! I chose the square wave and set the "number of terms" slider to 1. Then I added the terms, one at the time. It's fascinating to see how the Fourier series gradually builds up the signal. One thing is to have a mental understanding of how the Fourier series works, seeing it so clearly in practice is quite another. Rune
Reply by ●September 10, 20042004-09-10
Rune Allnor wrote: ...> That applett is just brilliant! I chose the square wave and set the > "number of terms" slider to 1. Then I added the terms, one at the time. > It's fascinating to see how the Fourier series gradually builds up > the signal. > > One thing is to have a mental understanding of how the Fourier series > works, seeing it so clearly in practice is quite another.It's also a nice example of how point-wise convergence does not imply uniform convergence (Gibb's phenomena). There is a little math's story that goes as follows: The great French mathematician Cauchy (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cauchy.html), in a work released in 1821, asserted (and proved!) a theorem that the limit of a converging series of continuous functions is also continuous. It was Abel (http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Abel.html), aged 24, who delivered a counter-example to that "theorem". His counter-example was the Fourier-series of the saw-tooth function. Fourier had developed his theory on expanding periodic functions into trigonometric series around 1807. Well after Abel's death, Cauchy modified his theorem by requiring uniform convergence (without any mention of Abel or his counter-example). Regards, Andor
Reply by ●September 10, 20042004-09-10
"Richard Owlett" <rowlett@atlascomm.net> wrote in message news:10k1vph4787bl54@corp.supernews.com...> Phil Martel wrote: > > "Richard Owlett" <rowlett@atlascomm.net> wrote in message > > news:10k1n5p232cuua7@corp.supernews.com... > > > >>I admit to being math challenged, learning by pictures is best. > >> > >>Is there some source on WEB that has pictures of Fourier Transform of > >>some common time domain waveforms? > >> > >>Am I "squaring the circle" or "tri-secting the angle"? > > > > > > "Doubling the cube". > > > > I was going to suggest getting Octave or Scilab and playing around abit,> > I have Scilab, that's what got me started ;] > > > > > but I found a web site > > http://www.falstad.com/fourier/ that has a Java applet that lets youdisplay> > a number of common functions and also change the magnitude and phase ofthe> > transform and watch the signal change. > > > I think site has problem. > All sounds seem same, possible volume difference. >Hmm, try tweaking the 'playing frequency' bar between plays. That should give you clearly different sound. If that works, you should be able to hear the difference between a sine and a full wave rectified sine. In general, the difference between the sounds is something like the difference between the sound of different instruments playing the same note. Best wishes, --Phil> > > > > Best wishes, > > --Phil Martel > > > > > >
Reply by ●September 10, 20042004-09-10
Phil Martel wrote:> "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:10k1vph4787bl54@corp.supernews.com... > >>Phil Martel wrote: >> >>>"Richard Owlett" <rowlett@atlascomm.net> wrote in message >>>news:10k1n5p232cuua7@corp.supernews.com... >>> >>> >>>>I admit to being math challenged, learning by pictures is best. >>>> >>>>Is there some source on WEB that has pictures of Fourier Transform of >>>>some common time domain waveforms? >>>> >>>>Am I "squaring the circle" or "tri-secting the angle"? >>> >>> >>>"Doubling the cube". >>> >>>I was going to suggest getting Octave or Scilab and playing around a > > bit, > >>I have Scilab, that's what got me started ;] >> >> >> >> >>>but I found a web site >>>http://www.falstad.com/fourier/ that has a Java applet that lets you > > display > >>>a number of common functions and also change the magnitude and phase of > > the > >>>transform and watch the signal change. >> >> >>I think site has problem. >>All sounds seem same, possible volume difference. >> > > Hmm, try tweaking the 'playing frequency' bar between plays. That should > give you clearly different sound. > If that works, you should be able to hear the difference between a sine and > a full wave rectified sine. In general, the difference between the sounds > is something like the difference between the sound of different instruments > playing the same note.So why does "noise" have a pitch too? It's rather like my B-flat woodpecker. Jerry
Reply by ●September 11, 20042004-09-11
Phil Martel wrote:> "Richard Owlett" <rowlett@atlascomm.net> wrote in message > news:10k1vph4787bl54@corp.supernews.com... > >>Phil Martel wrote: >>[snip] >> >>>but I found a web site >>>http://www.falstad.com/fourier/ that has a Java applet that lets you >>>display >>>a number of common functions and also change the magnitude and phase of >>>the >>>transform and watch the signal change. >> >> >>I think site has problem. >>All sounds seem same, possible volume difference. >> > > Hmm, try tweaking the 'playing frequency' bar between plays. That should > give you clearly different sound. > If that works, you should be able to hear the difference between a sine and > a full wave rectified sine. In general, the difference between the sounds > is something like the difference between the sound of different instruments > playing the same note. >Went back and all worked fine.
Reply by ●September 11, 20042004-09-11
"Jerry Avins" <jya@ieee.org> wrote in message news:41424d39$0$6912$61fed72c@news.rcn.com... <snip>> So why does "noise" have a pitch too? It's rather like my B-flat > woodpecker. > > Jerry >If you're referring to the noise function on the web page ( http://www.falstad.com/fourier/ ), then probably because the 'noise' signal repeats. If you just click 'noise' and then 'play', the basic rep rate is 220 Hz. If you move the playing frequency down, and the number of terms up, it sounds a bit more like a hiss, but still it's basically a buzzer sound. BTW, I only remember the B-flat woodpecker thread vaguely, do you have any recordings? Best wishes, -Phil Martel
