square wave harmonic theory (time domain)

Yes you might say that. In fact the xform from continuous data to sampled data is a projection from a "vector space" (actually an extension of one) of functions to a subspace. In your case a finite dimensional subspace (you took a finite number of readings). In any case you can exactly analyze your experiment by replacing the edges by dirac delta functions of a +1 order and manipulating them; then you apply your sampling function to the result to see what the result is. You can also experiment with truncating the waveform or changing the sampling times. There should be formal method of doing this but I have only seen (and been able to use) block diagrams of the signal flow that are then converted to equations. My point is that you don't have to imagine a lot or take other people's opinion; you can do your own analysis. It's good for your abilities and while it takes some thought and study, the result is quite useful.

RayRogers

No, the Organ pipe is a nonlinear system. The fipple is a gain element connected to the tuned system. The bell is a linear system for the sizes of inputs we are considering.

Agreed, if the system is linear. In the case of striking the bell at a constant rate the frequency content of the input consists only of harmonics of the rate of striking. Since the bell can't create new frequencies, its output must also only contain those frequencies.

I did.

I find it easier to just ignore fatheads that I know are fatheads, rather than killfiling them; Eeyore and Sloman come to mind. DampMatter keeps changing names, so I have to catch onto that (it takes a post or two) and you have to update your kill list.

John

We have found that the plain old conventional Fourier analysis is more than fast enough with modern computers for many uses.

And that it eliminates all of the FFT happy horseshit over windowing, aliasing, Hanning, and general lying about what you think you are looking at.

Not even wrong.

A resonant system is a resonant system.

Response depends on both the forcing function (transient) and the natural function (steady state).

How do you avoid windowing artifacts, or aliasing, simply by using a classic Fourier transform? They are inherent in taking a finite time slice out of an infinite waveform, and sampling at a finite rate, not in the details of the transform.

An FFT does the same math as a discrete Fourier transform; it just reorganizes it to avoid a lot of inefficiency.

John

You use the plain old sines and cosines. Works like a champ.

Works exactly like an FFT. Same windowing artifacts, same aliasing, same math.

John

Wow, you're _really_ not a programmer, are you? ;-)

That should be "if and only if", or sometimes 'IFF'. ;-)

Cheers! Rich

On the 3-pedal pianos I've seen, the middle one is called the "sostenuto", which means "sustain". What it does is lift the dampers off the bass strings (I don't know where they draw the line, maybe a couple of octaves below middle C), so that when you play the ordinary way on the higher range, the strings will induce vibrations in the bass strings at their overtones that match the higher string.

To see this effect: gently press the C below middle C, so that it doesn't strike, but lifts the damper; then strike a middle C and release it, the lower string will continue to resonate at whichever "overtone" corresponds to its second harmonic.

Cheers! Rich

Best answer yet. It makes good sense. It's now buggered me all up philosophically when thinking of a 1nS, 0 to 5V pulse, occuring once a week and the physical nature of some kind of 'continuum' where the harmonics are spending their time oscillating and cancelling each other out. ( from Monday through to Saturday ;-) Electronics is amazing!.

You have no clue about what an organ pipe is if you say that. Air goes into the system as a source of energy. The reed or fipple is a gain element. The tube is a resonator.

What you are claiming is very like trying to say that a transistor oscillator can only make frequencies that are in its power supply connection. It is obviously nonsense.

The organ pipe isn't a linear system. The reason I used the bell in my explanation is because, at the levels we are talking, it is a linear resonator that does work as just a filter.

In the case of the bell, the bell selects the frequencies near its resonance from the input. If the input is a repeated waveform such as striking at a constant rate, this input only has harmonics of the stike rate in it. Since the bell can't create new frequencies, it must select from those harmonics.

Not even wrong.

The response is the convolution of the forcing function against the natural one.

Well, let's see. There are 6.048E14 nanoseconds in a week. You'd need substantially more than a trillion oscillators to make that work out!

Yes, with one caveat (described below).

If you are sampling a continous square wave, then this is what you would see.

What you actually have is the product of a square wave and a step function. After all, you have to turn on the square wave generator at some point.

What you will see after a few milliseconds approaches the theoretical Fourier series of a continuous signal extenting from T = minus infinity.

As far as being 'amplitude modulated', the ideal (infinite time series) square wave frequency domain products are not amplitude modulated. Their amplitude and phase remains constant. In reality, turning on the square wave generator (or turning it off) would be a sort of amplitude modulation.

Good luck with your final exam. I didn't know they had WiFi and internet access in the exam room. I hope our answers arrived in time.

Not if it's an oscillator, and not if it's nonlinear. A pipe organ is both.

John

No, in the case of the pipe organ this is simply not the case. You are attempting to apply something that is true for linear situations to a very non-linear situation.

Like I said, by your logic, this would mean that the pipes of a pipe organ can only select frequencies from its air supply. This is so far from the mark that I am truly surprised that you can't straight away see that you are wrong. What do you think the fipple or reed does? It sure isn't there as a decoration.

On Jun 1, 11:42 am, John Larkin

You can fit to sine and cosine functions that do not complete an integer number of cycles and thus get rid of the skirts on the peaks. This is more than just doing the old school FT however since it takes a fair bit of processes to do each fit.

On things that are aliased, the egg is already scrambled. You can't do anything about that.

Uh? You're tip-toeing thru the tulips there, John. In an oscillator the forcing function IS the oscillator non-linearity.

Don't get me started on Lyopanov ;-)

...Jim Thompson