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square wave harmonic theory (time domain)

J

John Larkin

Jan 1, 1970
0
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
 
R

Rich Grise

Jan 1, 1970
0
If you have anything sensible to say, then say it. *IF*

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

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

Cheers!
Rich
 
R

Rich Grise

Jan 1, 1970
0
On Thu, 31 May 2007 16:13:49 GMT, "Thomas Magma"


Actually, it will. If you strike it gently at a rate that's an integer
fraction of a major resonance, that resonance will build up in
amplitude over multiple strikes, much more than if the ratio is not
maintained. Of course, thet's not easy to do by hand; the frequency
and phasing have to be exact.

The bell is a bandpass filter.

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!.
 
M

MooseFET

Jan 1, 1970
0
Not even wrong.

A resonant system is a resonant system.

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

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.
 
D

Don Lancaster

Jan 1, 1970
0
MooseFET said:
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.


--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
rss: http://www.tinaja.com/whtnu.xml email: [email protected]

Please visit my GURU's LAIR web site at http://www.tinaja.com
 
T

The Phantom

Jan 1, 1970
0
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!.

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!
 
P

Paul Hovnanian P.E.

Jan 1, 1970
0
Thomas said:
Hello,
I'm trying to determine if the higher harmonics of a low frequency square
wave are actually AM modulated. For instance, I can see the harmonics of a 1
KHz square wave all the way up at 100 MHz if I zoom into them on a spectrum
analyzer. Are those harmonics really there when the 1 KHz square wave has
finished it's transition and is in a steady state for half a millisecond?

Yes, with one caveat (described below).
If I was to sample this steady state with a ultra fast ADC and FFT the samples,
would I see the harmonics extending up through 100 MHz?

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.
It's a bit of a mind bender when converting between the time and frequency
domain in the case of a square wave.

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.
 
J

John Larkin

Jan 1, 1970
0
Not even wrong.

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

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

John
 
M

MooseFET

Jan 1, 1970
0
Not even wrong.

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

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.
 
M

MooseFET

Jan 1, 1970
0
On Jun 1, 11:42 am, John Larkin

[... non-F FT ...]
Works exactly like an FFT. Same windowing artifacts, same aliasing,
same math.

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.
 
J

Jim Thompson

Jan 1, 1970
0
Not if it's an oscillator, and not if it's nonlinear. A pipe organ is
both.

John

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
 
M

MooseFET

Jan 1, 1970
0
Uh? You're tip-toeing thru the tulips there, John. In an oscillator
the forcing function IS the oscillator non-linearity.

Yes but it certainly isn't the air supply to the pipe. In cases like
the organ pipe, the tuned system determines the frequency of the input
function to the tuned system.

This makes it very different from the case of the bell.
Don't get me started on Lyopanov ;-)

Awh why not?
 
T

The Phantom

Jan 1, 1970
0
Note that if a 1 kHz square wave were generated with a trillion sine wave
generators in series, on a scope it would look the same as if it had been
generated with a flip-flop. And a circuit driven with it would behave
exactly the same as if it came from a flip-flop. In this case, there would
be *actual* sine waves adding up to form the square wave.
It occurs to me that if the square wave were actually created with a
bunch of sine wave generators in a black box, with only the final waveform
available at the terminals of the box (in this case, though, we're allow to
look inside), we could be having the argument in reverse.

Some might say, "No, there isn't a actual square wave present; it's just
a mathematical abstraction."
 
M

MooseFET

Jan 1, 1970
0
It occurs to me that if the square wave were actually created with a
bunch of sine wave generators in a black box, with only the final waveform
available at the terminals of the box (in this case, though, we're allow to
look inside), we could be having the argument in reverse.

Some might say, "No, there isn't a actual square wave present; it's just
a mathematical abstraction."


They would be correct since you can never truly make a squarewave.
The rise time is never zero.
 
T

The Phantom

Jan 1, 1970
0
They would be correct since you can never truly make a squarewave.
The rise time is never zero.

And you can never truly make a sinewave; the distortion is never zero.

There's always something to quibble about, isn't there?
 
M

MooseFET

Jan 1, 1970
0
And you can never truly make a sinewave; the distortion is never zero.

There's always something to quibble about, isn't there?


No, there isn't always something to quibble about. :)
 
T

The Phantom

Jan 1, 1970
0
No, there isn't always something to quibble about. :)

You're quibbling about whether there's always something to quibble about?
Sheeesh!! (as Winfield might say)

Ok, then.

I said '"Some might say, "No, there isn't a actual square wave present; it's
just a mathematical abstraction."'

You said "They would be correct since you can never truly make a squarewave.
The rise time is never zero."

In fact it is the mathematical abstraction that is able to achieve a zero rise
time. You just have let the "bunch of sine wave generators", be an *infinity*
of sine wave generators, which you can do in the abstraction. One of the things
about Fourier's series that impressed mathematicians of the time was that it
could converge to a discontinuous function.

It would be the real world version with only a "bunch" of sine wave generators
that couldn't achieve zero rise time. The mathematical abstraction can do it
with no problem. So anybody who said "there isn't a actual square wave present;
it's just a mathematical abstraction." wouldn't be saying that because "zero
rise time" couldn't be achieved; if they did, they would be incorrect. It is
the abstraction that *can* achieve zero rise time.
 
M

MooseFET

Jan 1, 1970
0
You're quibbling about whether there's always something to quibble about?
Sheeesh!! (as Winfield might say)

Allow me to point out the smily at the end of the line. It was
intended as a joke.
 
M

Michael A. Terrell

Jan 1, 1970
0
MooseFET said:
Allow me to point out the smily at the end of the line. It was
intended as a joke.


Some people have had their sense of humor surgically removed. :(


--
Service to my country? Been there, Done that, and I've got my DD214 to
prove it.
Member of DAV #85.

Michael A. Terrell
Central Florida
 
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