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post #91 of 514 Old 01-12-2007, 06:43 AM
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Before I believe that a crossover can separate the "harmonics generated by clipping" I will need a detailed, non-BS, well-supported explaination of the phenomenon that causes the tweeter to move when there are no high frequency voltage fluctuations. I am looking for something above just saying that sharp edges in the wave cause clipping. I want to know what exactly is causing a voltage fluctuation after the crossover does not exist before the crossover.

psgcdn has it right. And several people have been saying the same thing over and over. There has been no BS in any of my technical comments. No hand waving or supposing. So I'll try again, and I'll try not to repeat exactly the same thing I've said in the past.

Let's forget about the Fourier transform for a bit. Let's just think about a spectrum analyzer. If you're not familiar with it, check it out here http://en.wikipedia.org/wiki/Spectrum_analyzer. A spectrum analyzer may use the FFT, but that doesn't really matter. In theory, it could also use a bunch of bandpass filters. All we care is that the spectrum analyzer will show us the frequency content of an input signal.

The thing you have to give up is the rationalization that just because you can't see these "high frequency fluctuations" on a scope, they aren't there. This is a logical flaw, and it's stopping you from really understanding what's going on. Can you see 18kHz fluctuations on a scope when playing a music track? No, you just assume they are there because the signal's a jumbled mess. And it's a jumbled mess because the signal is a sum total of a bunch of other signals of varying frequencies. The same goes for a square wave, and I think we've all agreed that the square wave is indeed the sum total of a bunch of other pure tones.

If you look at a music signal on a scope, it can sometimes seem to be primarily a sine wave. How can that contain HF? It just does, and again the time based signal isn't telling you everything. Because our human eyes aren't good at picking out frequency from continuous time based signals, we invented the spectrum analyzer. And that's really the tool that we need to talk about here. That's the only way that you are going to get a true representation of the frequency content of a signal.

When you run a square wave through a spectrum analyzer, you get HF content, of course. So you know it's there even though you can't see it on the scope. Don't try to simplify it to a capacitor allowing voltage through or not based on the signal you can see using a scope. Think of a general filter (digital or analog, doesn't matter). What does a filter do? It passes some of the spectrum and cuts some of the spectrum, based on its designed crossover frequency (we can even thing outside the audio spectrum to GHz and above). Just think general filtering and spectral content and you will see it. Forget about the cap, forget about the time based voltage signal. Filter and spectral content is the key.

So, to recap:

1. A filter, in general, acts on signals of arbitrary frequency.
2. A high pass filter, for example, kills all frequencies below frequency x.
3. A spectrum analyzer is the tool to determine which frequencies are in any given signal.
4. A square wave will generate odd harmonics of the fundamental signal, per the Fourier transform.
5. A square wave will have measurable high frequency content when viewed with a spectrum analyzer.
6. If the square wave is fed to the crossover with a fundamental slightly below crossover frequency x, the crossover will filter the fundamental and pass the harmonics.

That's it. Just remember that the spectrum analyzer is the key, forget about the simplified capacitor example. You don't even need to know about the Fourier transform exists if you believe that the spectrum analyzer works.

Again, if you have a stereo system that has variable crossovers, I suggest that you re-read through the experiment that I did, and try it for yourself. You can at least then prove to yourself that it's possible, and work out the "why" going forward. I promise -- it's there, and it happens.

Here's another practical example. Have you ever played with a "graphic equalizer"? You know, the one with all the sliders on it? You also have one in WindowsMediaPlayer or Winamp. Now, if you had one of those in your system, and you played a square wave through it, you would see the little lights light up at frequencies above the fundamental of the square wave. And you could hear them. And you could affect them by playing with the little sliders on the graphic EQ. In this case, the graphic EQ light panel display is working as the spectrum analyzer, and each slider is a filter. You can find on the web a square wave mp3 somewhere, and run this through winamp for yourself. Again, empirical evidence that it's possible to separate HF using filters.

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Maybe the source of the high frequencies is the amplifier, not the crossover.

The source of the high frequency content is sharp edge of the clipped wave. In most of my cases, I've used "square wave" to keep it simple, as a theoretical case. And I know you don't like this, but it's just true -- the source of the HF content is the sharp edges. Why? Because to get a square wave, you start with a sine wave, and then you add in a bunch of other sine waves that combine with the original to create a sine wave. Just think of all the subtraction from the original sine wave that must be done to get those edges so sharp. And then you have to add in a little here and a little there to get it just right. That's the Fourier series, of course, and that's why there's HF content in square waves (or clipped waves, to a lesser degree), and that's exactly why the sharp edges cause it. The amplifier can be the source of the HF if it's clipping. In the case of the experiment I did here, the square wave itself was the source of the HF. My amp wasn't clipping, the HF was just there from the start. The crossover is definitely not the cause of the HF. It's just filtering the signal that's coming in.

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Strange, I started reading about THD, and it seems to be in reference only to pure sine waves.

I'm not up on THD enough to say that it's not the cause of some blown speakers. Usually, THD increases at the limits of the amp. They are probably talking about sine waves because that's the easiest way to measure THD. Many amps are spec'd at whatever THD level at 1kHz or whatever. I don't know the standards, if there are any, but I think that's probably why you're seeing references to pure tones and THD. Nonetheless, all my discussion about square waves, spectrum analyzers, filters and HF content still stands. THD is a different animal.

--Otto
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post #92 of 514 Old 01-12-2007, 09:00 AM
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Also, since the high frequencies are there, you will hear them A clipped signal sounds different because of the HF content.

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post #93 of 514 Old 01-12-2007, 09:04 AM
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That's absolutely right, and exactly what I did when playing the sine wave vs. square wave in my system. You can hear it. Download REW from the HomeTheaterShack and try it yourself. It should be pretty enlightening.

--Otto
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post #94 of 514 Old 01-12-2007, 12:24 PM
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I downloaded the first square wave sound file I could find here: http://www.sfu.ca/sonic-studio/handb...uare_Wave.html

There were harmonics as you described when I playing it in Winamp. When I was trying to see if it was possible to make the spectrum analyzer larger, I accidentally switched it to oscilloscope mode. I was surprised (well not really) to see this:

Strange, this doesn't look like a square wave! Since parts of the line are two pixels thick, it also hints of high frequencies, something you would not see in the square wave itself.

The question is, is this file actually a square wave, or is Winamp screwing up somewhere? One way, it makes me doubt the audio analysis capabilities of Winamp. The other way, it makes me doubt if the square wave generators actually generate a square wave.

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post #95 of 514 Old 01-12-2007, 12:43 PM
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You're right to doubt either or both. It's pretty close, but kinda sloppy. Keep in mind that we don't really know the origin of the file, or its actual content. Also, to create a perfect square wave, we need an infinite series of sine waves (impossible). In this audio file, I assume we're limited to 20kHz or so, so we're not even close to an infinite series. I don't know how much this will affect this particular signal, though. There's also something called the Gibbs Effect that describes overshoot in square waves. That may be contributing to what you are seeing (I'm ony tangentially familiar with it, but I'm sure it's on Wikipedia) Finally, I wouldn't really consider Winamp a real analysis tool, but something that will start us down the right path. If you have access to these types of tools, try a similar test with a function generator, an oscilloscope and a spectrum analyzer.

Again, forget about looking for voltage transients. If we had a perfect square wave with no overshoot, perfect corners, etc., there will still be high frequency content, and that HF content is simply part of the square wave, and fully described mathematically by the FT.

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post #96 of 514 Old 01-12-2007, 01:20 PM
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You guys have finally stumbled across the answer.

hint- a clipping amp doesn't produce a text book perfect square wave, shhh...


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post #97 of 514 Old 01-12-2007, 01:25 PM
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Originally Posted by OttoSpiral View Post

Again, forget about looking for voltage transients. If we had a perfect square wave with no overshoot, perfect corners, etc., there will still be high frequency content, and that HF content is simply part of the square wave, and fully described mathematically by the FT.

This is all with the frame of mind that everything is based from sine waves. I feel like I am trying to talk about triangles and everyone else is talking about circles. "Yes, but a triangle is composed of smaller circles." "Circles are just part of a triangle" See what I am saying? A square wave is a function by itself. You don't need to talk about sine waves to talk about square waves. From the frame of mind that everything is composed of square waves, a square wave has one frequency and a sine wave has many harmonics in it.

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post #98 of 514 Old 01-12-2007, 01:30 PM
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Originally Posted by soho54 View Post

You guys have finally stumbled across the answer.

hint- a clipping amp doesn't produce a text book perfect square wave, shhh...

The answer to which question?

I noted that I was using square waves as a theoretical example. It doesn't have to be a perfect square wave to introduce HF content.

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post #99 of 514 Old 01-12-2007, 01:30 PM
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Originally Posted by soho54 View Post

You guys have finally stumbled across the answer.

hint- a clipping amp doesn't produce a text book perfect square wave, shhh...

We are only talking about square waves because it is easier to deal with. Our actual tests have been with what *should* be pure square waves, so it is a mystery why is appears to not be a square wave.

I did suggest earlier that the amp might actually be the cause of the high frequencies (not the clipping) because of the weird things that happen when an amp is turned up to loud. I don't know, though.

Unrelated, but I found something interesting when I took the antiderivative of a square wave. I got a triangle wave!
-cos(x) - (1/9)*cos(3x) - (1/25)*cos(5x) - (1/49)*cos(7x) - (1/81)*cos(9x) - (1/121)*cos(11x)

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post #100 of 514 Old 01-12-2007, 01:34 PM
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Originally Posted by greeniguana00 View Post

This is all with the frame of mind that everything is based from sine waves. I feel like I am trying to talk about triangles and everyone else is talking about circles. "Yes, but a triangle is composed of smaller circles." "Circles are just part of a triangle" See what I am saying? A square wave is a function by itself. You don't need to talk about sine waves to talk about square waves. From the frame of mind that everything is composed of square waves, a square wave has one frequency and a sine wave has many harmonics in it.

How about forget about time-based signals at all and just talk about the frequency domain? And how crossovers behave on the frequency spectrum?

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post #101 of 514 Old 01-12-2007, 01:36 PM
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Originally Posted by OttoSpiral View Post

How about forget about time-based signals at all and just talk about the frequency domain? And how crossovers behave on the frequency spectrum?

This would be a bad idea because frequency is based on time!

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post #102 of 514 Old 01-12-2007, 02:06 PM
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Originally Posted by greeniguana00 View Post

This would be a bad idea because frequency is based on time!

OK. I'd love to keep this thread going (seriously), but I don't know what else there is to say. Lemme know if you get it sorted out.

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From the frame of mind that everything is composed of square waves, a square wave has one frequency and a sine wave has many harmonics in it.

I disagree...and so does physics.
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post #104 of 514 Old 01-12-2007, 07:00 PM
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Originally Posted by greeniguana00 View Post

This would be a bad idea because frequency is based on time!

Yes, but a time-based signal (in a steady-state, e.g. always the same sum of harmonics) can be represented perfectly in the frequency domain. They are interchangeable.

(Not that attempting to invoke any academic credibility will convince you, but I have a B.Sc. in engeneering physics and a Ph.D. in a physical science if that helps.)

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post #105 of 514 Old 01-12-2007, 07:32 PM
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Originally Posted by Targus View Post

I disagree...and so does physics.

Well go tell physics he is wrong.

Seriously, what are you talking about?

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post #106 of 514 Old 01-13-2007, 05:21 AM
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Originally Posted by greeniguana00 View Post

Well go tell physics he is wrong.

Seriously, what are you talking about?

He's saying that your assertion:

Quote:
From the frame of mind that everything is composed of square waves, a square wave has one frequency and a sine wave has many harmonics in it.

is wrong. You can't consider everything to be made up of square waves, and then consider a sine wave to be some type of Fourier series of square waves. I think that's what you were saying, anyway. Unless you have some other information that you could point us to that would support that idea, I don't think it works that way. The point of the Fourier transform is to decompose signals in general to their canonical representation so that we can talk about them in the frequency domain. Considering everything to be made of square waves (which theoretically requires infinite bandwidth) as a starting point doesn't make sense. Sine waves, from a frequency point of view, cannot be further decomposed. How did you come up with this idea?

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post #107 of 514 Old 01-13-2007, 06:56 AM
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greeniguana00, I think you mean well. You have thought about this stuff and have come up with your own rational of how things work, and what clipping is made up of. But unfortunately there's a gap between what you think should be correct and what some of us have learned to be correct from reliable source (like university classes in electrical engineering). At some point, you should stop arguing for the sake of arguing, listen to what the rest of us are saying, and read references on what we are saying if you want to learn more on your own.

I appreciate that everyone has avoided name-calling through this thread (as I recall).

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post #108 of 514 Old 01-13-2007, 07:12 AM
 
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Seriously, what are you talking about?

Never mind, I thought you'd be able to keep up....
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post #109 of 514 Old 01-13-2007, 07:21 AM
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I'm not done yet...

edit: I have managed to make something that resembles a sine wave pretty closely with just subtracting the odd harmonics of a square wave from itself, but when trying to get the actual sine value of a point on the wave, the values are not what they should be. There is no singe number to scale everything to the right value. I need to spend some more time with this.

You can graph this if you want to see an approximation of sine waves using approximations of square waves: sin(x) + (1/3)*sin(3x) + (1/5)*sin(5x) + (1/7)*sin(7x) + (1/9)*sin(9x)+(1/11)sin(11x)+(1/13)*sin(13x) - ((1/3)*(sin(3x) + (1/3)*sin(9x) + (1/5)*sin(15x) + (1/7)*sin(21x) + (1/9)*sin(27x)+(1/11)sin(33x)+(1/13)*sin(39x))) - ((1/5)*(sin(5x) + (1/3)*sin(15x) + (1/5)*sin(25x) + (1/7)*sin(35x) + (1/9)*sin(45x)+(1/11)sin(55x)+(1/13)*sin(65x))) - ((1/7)*(sin(7x) + (1/3)*sin(21x) + (1/5)*sin(35x) + (1/7)*sin(49x) + (1/9)*sin(63x)+(1/11)sin(77x)+(1/13)*sin(91x)))

It is very long because each of the square waves is actually written as a sum of sine waves.

Here are two places youcan graph it online:
http://gcalc.net/
http://www.coolmath.com/graphit/index.html

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post #110 of 514 Old 01-13-2007, 05:04 PM
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Here are some pictures of the graph:



Here is the program I made to estimate the sine of a value using the weighted sum of square waves: http://www.wikiupload.com/download_page.php?id=52349
I can't get it to give the correct sine values yet, but you guys can test it out. It can also serve as a computer benchmarking utility.

As you can see, the value that it determines is not the correct value.

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post #111 of 514 Old 01-13-2007, 05:29 PM
 
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Originally Posted by greeniguana00 View Post

A square wave is a function by itself. You don't need to talk about sine waves to talk about square waves. From the frame of mind that everything is composed of square waves, a square wave has one frequency and a sine wave has many harmonics in it.

Wow. Just, wow. Please take an introductory physics class or go to your local library and find a basic physics textbook and examine the appropriate sections on waves.

If there is any quote that sums up this thread, it is the following:

Quote:
Originally Posted by greeniguana00 View Post

I will admit I was completely wrong about high frequency peaks still getting thorugh during the plateau. I don't know what I was thinking then, but I know I am right about this.

Well, others are free to make their own decision, I personally find hundreds of years of basic physics understanding fairly convincing. You are free to believe that the sun goes around the earth if you choose, but don't expect to convince physicists of this "fact" despite how "right" you think you are. You're just wasting your time. And I can see that it would be a waste of my time to try to explain how waves work.
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post #112 of 514 Old 01-13-2007, 05:36 PM
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I have managed to make something that resembles a sine wave pretty closely with just subtracting the odd harmonics of a square wave from itself

But what's the point?

Quote:


As you can see, the value that it determines is not the correct value.

I'm gambling on code bugs and a basic misunderstanding of what we've been talking about all along. It should be some good experience for C Programming 111, though.

--Otto
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post #113 of 514 Old 01-13-2007, 05:44 PM
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Originally Posted by ChrisWiggles View Post

Wow. Just, wow. Please take an introductory physics class or go to your local library and find a basic physics textbook and examine the appropriate sections on waves.

So are you implying that all waves are defined by the sine function?

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Well, others are free to make their own decision, I personally find hundreds of years of basic physics understanding fairly convincing. You are free to believe that the sun goes around the earth if you choose, but don't expect to convince physicists of this "fact" despite how "right" you think you are. You're just wasting your time. And I can see that it would be a waste of my time to try to explain how waves work.

Funny that you mention that. Saying the earth revolves around the sun isn't quite right. There was this scientist named Isaac Newton who came up with a widely accepted theory that two bodies revolve around their center of gravity, not the center of the larger object. Another common misconception is that the acceleration of an object towards the center of Earth is the same for objects of all masses. In fact, the larger the mass, the faster it will accelerate towards the center of the Earth.

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post #114 of 514 Old 01-13-2007, 05:50 PM
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Originally Posted by OttoSpiral View Post

But what's the point?

To show that sine waves can be shown as a composition of square waves, which you think is incorrect.

Quote:
Originally Posted by OttoSpiral View Post

I'm gambling on code bugs and a basic misunderstanding of what we've been talking about all along. It should be some good experience for C Programming 111, though.

It's not code bugs. I think I just don't have the transformation from square to sine quite right yet. I tried scaling, and it didn't work.

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So are you implying that all waves are defined by the sine function?

Absolutely. I'm not just implying it, I'm stating it as objective fact. Every waveform consists of and is defined by individual pure sine waves.

But as I said before, you don't have to believe physics...
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post #116 of 514 Old 01-13-2007, 06:04 PM
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Originally Posted by Webster's Dictionary View Post

a disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure, electric or magnetic intensity, electric potential, or temperature

and what about these? http://en.wikipedia.org/wiki/Transverse_wave

http://en.wikipedia.org/wiki/Wave_equation

Notics how the sine function doesn't seem to be in these descriptions?

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post #117 of 514 Old 01-13-2007, 06:17 PM
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I see them talking about "sound waves" and "electromagnetic" waves, among others. I don't know much about hydraulics and light waves, but be sure that "sound waves" and "electromagnetics" depend on definitions of sine waves.

What's your background?

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post #118 of 514 Old 01-13-2007, 06:28 PM
 
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Quote:
Originally Posted by greeniguana00 View Post

and what about these? http://en.wikipedia.org/wiki/Transverse_wave

Yup. Transverse waves are waves.

Transverse waves are like string, where the disturbance moves perpendicular to the transmission of the wave. I.e. with a string, the wave moves down the string, but the displacement of the medium is perpendicular to the propagation.

In comparison, compression waves (or longitundinal waves) are like sound waves, where the displacement of the medium (air) is not perpendicular to the direction of the wave, i.e. the air molecules move back and forth along the same direction as the propagation of the wave.

That is all they are saying. It is clear to me that you really have a very rudimentary understanding of waves, if it is to be characerized as an understanding at all. You really should read up on what waves are and how they work before you try to come on here and make statements as if you know what you're talking about. If you don't even understand what a "transverse wave" is, how can you expect to engage with these issues?

Quote:


http://en.wikipedia.org/wiki/Wave_equation

Notics how the sine function doesn't seem to be in these descriptions?

All complex waves are constructed by various sine waves.

See: http://en.wikipedia.org/wiki/Harmonic_analysis
Or:
http://en.wikipedia.org/wiki/Fourier_series

Or see any basic physics textbook that deals with waves

I mean, if you don't even understand what a wave is, how do you expect to participate in this kind of discussion? Why do you think everyone dismisses what you are saying as silly nonsense? Perhaps you should just stop trying to protect your ego and recognize that your understanding in this area is basically zero, and maybe you should go read about waves and see how they work and what they are. Then we can actually have an interesting and useful discussion. Otherwise, I mean, I'm not really interested in debating a stubborn person who doesn't even understand what a wave is.
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post #119 of 514 Old 01-13-2007, 06:32 PM
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They depend on sine waves only because there needs to be a universal standard to compare things to. It's just like saying that frequency is based on the second. Just because frequency is based on the second doesn't mean that you can't also think of it based on another time standard. The AMU is based on carbon-12, but that doesn't mean people talking about mass in terms of grams are wrong.

While square waves aren't what most people talk about when talking about waves, they are still waves. If I can show that the sine wave can be decomposed into square waves, then I can show that the square wave is as good a wave to be used as the reference wave as the sine wave.

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post #120 of 514 Old 01-13-2007, 06:36 PM
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From Wikipedia: "Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves."

It's funny how they say basic waves instead of sine waves.

Health insurance inevitably leads to poor quality, inefficiency, inflated costs for health care, and rationing.
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