Derivation Of The Spectrum Due To f(t).d(t - T)?????

Stupid boy.

Don't defend me. Defend the truth.

If you believe something to be true then stand by your guns.

So you are one of the trolls that everybody has been complaining about.

It is indeed a Delta Function, being the expression of the Gaussian Normal Distribution.

Uhm, sorry! But I find this thread such a mess that I cannot find what truth I should defend. And what guns to stand by ...

Han de Bruijn

Yep. That's precisely what I expected. As a radio amateur, Mr. Bean is in his own right.

Han de Bruijn

The truths that you should defend are those that you hold to be true.

The > > Don't defend me. Defend the truth.

will you marry me beany?

dr. x

will you marry me beany?

dr. x

will you marry me beany?

dr. x

will you marry me beany?

dr. x

ITYM The opinions of others are irrelevant unless they concur with yours. ...(_!_)...

I feel kind of silly saying this, since it's becoming so clear that _nothing_ you say about any of this is ever going to make any sense, but just for the record:

That's ridiculous.

David C. Ullrich

It's _not_ ridiculous. I understand precisely what he says. And it's not that far from the "truth", as _you_ define it. And it certainly doesn't justify much of the harsh comments I've read here.

Do you ever care about what people _think_, Mr. Ullrich? Even if they don't have the mathematical eloquence that you have, to express what they think "properly" (whatever that means). People at work in the real world often don't have those specialized skills. And yet they can do things that you cannot even dream of. Like building the house that you live in.

Han de Bruijn

I wonder why you are incapable of enjoining discussion in a civilised and mature manner? Would the headmaster of the infants' school at which you teach be happy with your advertisement of his school in every vituperative posting from you?

More to the point, would that headmaster be concerned that you are also advertising your own incompetence so publicly, and would he wis to have a continuing association with you?

Far from ridiculous, the Normal Distribution as a PDF has a definite integral of 1 over the whole of the domain of the independent variable. The same curve can then be employed as a sampling function in DSP; when the width function tend to zero, then the function becomes a continuous delta function, from which the derivation int-oo^+oo f(t) d(t) gives f(0).

That's true. Otoh given that x < 0 there exists eps > 0 such that the two, Erf(x/eps) and 0, are very close together.

Thus the truth of the statement that the two are far apart oscillates in time. With DCU, the statement is true. With HdB, the statement is false. Then DCU comes in and the statement is true. Then HdB comes in and the statement is false again.

Now abstract TIME from this process, as is actually done by mainstream mathematics. Then we arrive at a _paradox_. The two are close together AND far apart at the same time (since there is no such "time" anymore). We conclude herefrom that the Law of Excluded Middle does not hold. :-O

Han de Bruijn

Yes, it's ridiculous.

Yes, those gaussians suffice as a useful approximation to the delta function in certain contexts. So if a person said "gaussian = delta" and he _meant_ "in some situations we can replace delta by a gaussian and make an acceptably small error in that calculations" then what he said might not be so ridiculous - it would be a very very bad way to express something that's true.

But that's not what's happening here. What's happening here is that we're asserting gaussian = delta, and deducing that the delta function has certain mathematical properties because a gaussian has those properties (in particular we're concluding that delta is a continuous function). That's ridiculous.

It's exactly like the following: Someone says 1/n = 0 for large values of n. If that means that if n is large enough then 1/n will be indistinguishable from 0 from a certain point of view then again it's just an unfortunate way of expressing something true. But that's not what's happening here. What's happening here is like this:

Theorem: 0 > 0. Proof: 1/n > 0 and 1/n = 0. QED.

If Airy's arguments are not ridiculous then neither is that.

If so then 0 > 0 is also not far from the truth.

What harsh comments? When someone says something ridiculous on sci.math people are supposed to say it's ridiculous - that's an aid to other readers who're interested in the truth of the matter.

What is your point here? I haven't said that the fact that someone's very confused about mathematics makes him a bad person, or a useless person. I haven't even pointed out that the fact that someone thinks he's right and all the textbooks on the planet are wrong makes him a lunatic.

David C. Ullrich

Five lines is too long for signature material.

Perhaps you could list those functions that blow up at zero dependent upon a limit with an integral of one, from which the property of int -oo^+oo f(t).d(t-T) giving f(T) derives are the equivalent of the Diracian and those which are not?

It seems that you're not arguing from the perspective of a DSP engineer pursuing the search for truth, which is the essence of these threads, but from a perspective of being seen to score a point.

You did, indeed, propose that a function f(t) = 1 if t is a rational number would serve the same purpose as the Diracian, which is patent nonsense in DSP; and yet this discussion has always centred around DSP.

It's notable that in what you say below you are starting to be selective about the targets of your discussion where previously you talked generally; a sure sign of goalposts being shifted in order to score points. Perhaps it is you who is the troll about which a number complain?

I am glad that you include yourself by saying that "we're asserting gaussian = delta, and deducing that the delta function has certain mathematical properties because a gaussian has those properties (in particular we're concluding that delta is a continuous function). That's ridiculous." and thereby declaring yourself to be ridiculous.

Despite that you name-drop the Theory Of Distributions, you seem to be remarkably ignorant (to use your term) about the nature of a whole family of functions giving rise to the distribution. The parameter "x" when tending to zero makes the Normal Distribution behave like a Diracian, but TOD holds the whole family to be so equivalent, even when not suitable as a sampling function for DSP.

Perhaps you _ARE_ The Troll?