Does not have any harmonics

Geez, Sloman, you're nothing but a Thompson clone, but the cloning machine reversed the polarity of your blind fanatical extremism.

Cheers! Rich

You pretty much hit the nail on the head there.

Graham

Nice to see the flakes favouring one another's nonsense.

-- Bill Sloman, Nijmegen

At the risk of wandering in and appearing ignorant in two newsgroups at once...

I think my answer to Karthik's original question would be that a sine wave only appears "perfect" because sines (and cosines) are (normally) the "units" of our analysis of periodic waveforms. Once you start down that path, that is, once you say that every waveform is "made up of" ("will be described as the combination of") some set of scaled and shifted sine waves, then your "units" will appear to be... um, "unitary".

But suppose some truly evil and sadistic mathematician decided that his classes would forever analyze periodic waveforms using some other basis, say square waves?

Suddenly a sine wave would be seen as a truly horrible combination of shifted and scaled square waves, a thing chock-full of "harmonics"... it would no longer be the pristine, pure thing it appeared when we looked at it through Fourier's eyes.

Does this make sense (even if my choice of square waves turns out to be poor)? Or did I miss something?

-- It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking about what we are doing. The precise opposite is the case. Civilization advances by extending the numbers of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in battle -- they are strictly limited in number, they require fresh horses, and must only be made at decisive moments. -- Alfred North Whitehead

-- Frank McKenney, McKenney Associates Richmond, Virginia / (804) 320-4887 Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)

It is also because of a nice property that.

d/dt cos(wt) =3D -wsin(wt) and d/dt (d/dt cos(wt) =3D -w^2 cos(wt)

We have Fourier to thank for this approach to periodic boundary problems. And the sin cos functions do have some very nice proprties like being orthogonal, complete and continuous in every derivative.

Walsh basis functions and various others that form the Hadamard matrix can do this. In some applications they are more use than Fourier analysis since with a bit of cunning the codec only needs add and subtract.

Simplest being

1 1 1 -1

Then

1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1

Left as an excercise to the reader to generate the next order. These are by construction orthogonal and complete.

If you can live with the stepwise approximation to the function then it will work just fine. It doesn't help you solve any differential equations though where Fourier methods are clearly superior. And the DCT still has the edge over Hadamard the matrix for encoding images to concentrate power in the smallest number of components.

There are lots of other decompositions of functions into orthognal basis. Tchebechev approximation is probably the next best known and most useful for a bounded approximation to a continuous function. Wavelets have gained popularity for the combination of spatially localised decompostion.

Regards, Martin Brown

Yeah, I'm a flake. ;-) (at least _I_ _admit_ it!) The thing is, being hated equally by both you and JT is pretty much prima facie evidence that I'm right. ;-)

And another thing - when you crosspost, don't leave the blank after the comma - it screws up people's newsreaders.

Cheers! Rich

Hatred is a strong word. I don't think much of Jim, but I'd be delighted if someone managed to find a treatment that arrested or reversed his cognitive decline, not least because I've got at least one relative who is also declining into Alzheimers.

I've even less reason to dislike you. You do enjoy saying silly things, presumably to be provocative, since you don't seem to take anything much seriously, but you aren't malicious.

-- Bill Sloman, Nijmegen

Interestingly, I'd be delighted if someone managed to find a treatment that arrested or reversed _YOUR_ cognitive decline as well, as I'm sure Jim would. ;-) (be delighted ...)

From outside your box(es), you both appear to be victims of the same syndrome. )-;

And you still haven't fixed your crossposter.

Good Luck! Rich

I don't think I'm showing much sign of cognitive decline. My psychological condition could be better - I need somewhile more useful to do that correcting the daft ideas of the anti-global-warming nitwits on this usergroup (of which you seem to be one) but at least I'm aware that I've got a problem in that area. As yet there aren't any signs of florid symptoms - like reporting people to the FBI.

Perhaps, but at least I'm citing external evidence, rather than relying on my inner certainies - I've still got enough insight left to realise that what I think I know may not necessarily be so, even if it is about something as basic as why the sky is blue.

It isn't "my" crossposter - Google groups just copies the cross- posting line from the post I'm replying to, which is yours in this instance, and Eeyore's when you first complained.

For the record, a newsreader that gets screwed up by spaces in a string does no credit to the programmer who wrote the relevant bit of code - I'd worked out how to sort out that kind of problem back in

1970 when coding in Fortran 4.

-- Bill Sloman, Nijmegen

--
That, of course, is one of the first symptoms in that since it isn\'t
apparent to you, you think nothing\'s wrong ergo comments made by
others must be wrong.

...

^^^^^^^^^^^^^^^^^^^^^^^^^

On the other other hand .... ;-) ;-) ;-)

But apparently not about your Anthropogenic Global Warming faith, since that's already Established Scientific Fact, right?

Feh.

"Your pulse: 98.6. Very scientific!" "Quant Suff! Quant Suff!"

Cheers! Rich

--
Sometimes I tend to be tend to be repetitious.

How about just "whether or not"? 

:-)

ted

ho

That isn't the way it has worked with those of my relatives who have suffered from Alzheimers (though most of the blood relatives managed to die before Alzheimers set in).

The first deficits are in short term memory, and that is at least as obvious to the victim as it is to everybody else.

-- Bill Sloman, Nijmegen

Established Scientific Fact is a contradiction in terms. Scientific facts are always subject to improved instrumentation and more illuminating analysis.

Unfortunately for your anti-warmingist point of view, the people who don't believe in anthropogenic global warming aren't coming forward with better data or better ideas, but are rather puffing up minor controversies and exploded hypotheses in order to sow fear, uncertainty and doubt.

It's competent propaganda - Karl Rove should be proud of the way the anti-warmingist crew have learned from him how to promote a defective case against what ought to be overwhelming odds - but its still looks terribly feeble if you know anything about the science involved.

-- Bill Sloman, Nijmegen

y

=20

Pulse is kinda rapid there (and measured to three decimal places=20 too). Does getting between Jim and Sloman get you excited?

--=20 Keith

Yep, I've noticed that about John, too. That "repetitive syndrome", or whatever it's called, is very noticeable in the newsgroups. He sees a posted problem, then posts a good solution, with a schematic and an analysis and an .ASC listing. Then he sees another posted problem, and posts another good solution. That repetitive activity continues and has gone on hundreds and hundreds of times - maybe thousands and thousands - I dunno.

It's a shame, really. That syndrome does not appear to be infectious - apparently you have to be born with it.

Ed

Yes, this was what I was trying to explain in my post.

Essentially sine waves are the "Basis"(in fact, that is what it is called in mathematics) that we use to write signals in terms of.

Now sine waves have very special properties but you could try and decompose a sine wave in terms of other functions.

Again, this happens all the time. Polynomial expansion, Exponential expansion, Gabor expansion, Wavelet decomposition, etc are all ways to decompose signals(functions) in terms of some units.

Sine waves are just special in that they have very simple ways to decompose and nice properties. They are not necessarily the best for all types of signals or for all types of analysis but they work very well and lots of theoretical research has been done.

Its kinda like if your "units" are nickels and you ask why a quarter can be "decomposed" into nickels but a nickel cannot be decomposed in terms of a nickel(in fact it can, its just "special" in this case). Now if we use pennies then we can decompose both but again a penny is "special" because it is now our "basis".

A side note: "Square waves" are essentially whats call a haar wavelet(sorta) and one can decompose any "normal" signal in terms of them. The decomposition it a bit different than fourier analysis but in some sense its also very similar.

Basically the idea is to try to explain some phenomena(functions, signals, etc) in terms of things we understand very well. We understand sinusodial functions very well.

--
:-)