On Jul 16, 11:30 pm, isw wrote:
In article .com,
Keith Dysart wrote:
No, that was indeed the claim. As a demonstration, I've
attached a variant of your original LTspice simulation.
Plot Vprod and Vsum. They are on top of each other.
Plot the FFT for each. They are indistinguishable.

-- lots o' snipping goin' on --

OK. I haven't been (had the patience to keep on) following this
discussion, so I apologize if this is totally inappropriate, but

If the statements above refer to creating that set of signals by using a
bunch of signal generators, or alternately by using some sort of actual
"modulation", the answer is, there is a very significant difference.

In the case where the set is created by modulating the "carrier" with
the low frequency, there is a very specific phase relationship between
the signals which would be essentially impossible to achieve if the
signals were to be generated independently.

All true. The simulation offered previously achieves the
required phase relationship (and more, so that the sum and
product versions can be directly compared).

In fact, the only difference
between AM and FM/PM is that the phase relationship between the carrier
and the sideband set differs by 90 degrees between the two.

I am not convinced. Can you explain? AM modulation with a single
frequency produces a single sum and difference for the sidebands
while FM has an infinite number of frequencies in the sidebands.
This does not seem like a simple phase difference.

....Keith

On Mon, 16 Jul 2007 16:00:29 -0700, Keith Dysart
wrote:

On Jul 16, 11:31 am, John Fields
wrote:
On Sun, 15 Jul 2007 14:57:17 -0700, Keith Dysart
wrote:
I thought the experiment being discussed was one where the
modulation was 1e5, the carrier 1e6 and the resulting
spectrum .9e6, 1e6 and 1.1e6.

---
That was my understanding, and is why I was surprised when you made
the claim, above:

"It does not matter how the .9e6, 1.0e6 and 1.1e6 are put into
the resulting signal. One can multiply 1e6 by 1e5 with a DC
offset, or one can add .9e6, 1.0e6 and 1.1e6. The resulting
signal is identical."

which I interpret to mean that three unrelated signals occupying
those spectral positions were identical to three signals occupying
the same spectral locations, but which were created by heterodyning.

Are you now saying that wasn't your claim?
---

No, that was indeed the claim. As a demonstration, I've
attached a variant of your original LTspice simulation.
Plot Vprod and Vsum. They are on top of each other.
Plot the FFT for each. They are indistinguishable.

Read my comments in that context, or just ignore them if
that context is not of interst.

---
What I'd prefer to do is point out that if your comments were based
on the concept that the signals obtained by mixing are identical to
those obtained by adding, then the concept is flawed.

See the simulation results.

I did not write clearly enough. The three resistors I had
in mind we one to each voltage source and one to ground.

To get there from your latest schematic, discard the op-amp
and tie the right end of R3 to ground.

That really doesn't change anything, since no real addition will be
occurring. Consider:

f1---[1000R]--+--E2
|
f2---[1000R]--+
|
f3---[1000R]--+
|
[1000R]
|
GND-----------+
snip

Note that 0.75V is not equal to 1V + 1V + 1V.

E2 = (V1+V2+V3)/4 -- a scaled sum

Except for scaling, the result is the sum of the inputs.

---
LOL... Except for scaling, Mr. President, the mirror on the Hubble
would have worked the first time out.
---

To get an AM signal that can be decoded with an envelope
detector, V5 needs to have an amplitude of at least 2 volts.

---
Ever heard of galena? Or selenium? Or a precision rectifier?

Oh, yes. And cat whiskers too.

But that was not my point. Because the carrier level was not
high enough, the envelope was no longer a replica of the signal
so an envelope detector would not be able to recover the signal
(no matter how sensitive it was).

---
That's easy enough to make happen, but that's not what this is
about; it's about the out signal from a 3 input adder being
identical to the output signal from a mixer.

It seems, you want to try to prove that multiplication is tha same
as addition, with:

Version 4
SHEET 1 980 680
WIRE -1312 -512 -1552 -512
WIRE -1200 -512 -1232 -512
WIRE -1552 -496 -1552 -512
WIRE -1312 -400 -1440 -400
WIRE -1200 -400 -1200 -512
WIRE -1200 -400 -1232 -400
WIRE -768 -384 -976 -384
WIRE -976 -368 -976 -384
WIRE -1440 -352 -1440 -400
WIRE -544 -352 -624 -352
WIRE -1200 -336 -1200 -400
WIRE -1136 -336 -1200 -336
WIRE -544 -336 -544 -352
WIRE -768 -320 -912 -320
WIRE -1312 -304 -1344 -304
WIRE -1200 -304 -1200 -336
WIRE -1200 -304 -1232 -304
WIRE -1200 -288 -1200 -304
WIRE -1344 -256 -1344 -304
WIRE -912 -256 -912 -320
WIRE -544 -240 -544 -256
WIRE -464 -240 -544 -240
WIRE -544 -224 -544 -240
WIRE -1552 -144 -1552 -416
WIRE -1440 -144 -1440 -272
WIRE -1440 -144 -1552 -144
WIRE -1344 -144 -1344 -176
WIRE -1344 -144 -1440 -144
WIRE -1200 -144 -1200 -208
WIRE -1200 -144 -1344 -144
WIRE -1552 -128 -1552 -144
WIRE -912 -128 -912 -176
WIRE -544 -128 -544 -144
FLAG -1552 -128 0
FLAG -1136 -336 Vsum
FLAG -976 -368 0
FLAG -912 -128 0
FLAG -544 -128 0
FLAG -464 -240 Vprod
SYMBOL voltage -1552 -512 R0
WINDOW 3 -216 102 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 .5 900 0 0 90)
SYMATTR InstName Vs1
SYMBOL voltage -1344 -272 R0
WINDOW 3 -228 104 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 .5 1100 0 0 -90)
SYMATTR InstName Vs3
SYMBOL res -1216 -320 R90
WINDOW 0 -26 57 VBottom 0
WINDOW 3 -25 58 VTop 0
SYMATTR InstName Rs3
SYMATTR Value 1000
SYMBOL res -1184 -192 R180
WINDOW 0 -48 76 Left 0
WINDOW 3 -52 34 Left 0
SYMATTR InstName Rs4
SYMATTR Value 1000
SYMBOL res -1216 -416 R90
WINDOW 0 -28 61 VBottom 0
WINDOW 3 -30 62 VTop 0
SYMATTR InstName Rs2
SYMATTR Value 1000
SYMBOL res -1216 -528 R90
WINDOW 0 -32 59 VBottom 0
WINDOW 3 -30 62 VTop 0
SYMATTR InstName Rs1
SYMATTR Value 1000
SYMBOL voltage -1440 -368 R0
WINDOW 3 -210 108 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR Value SINE(0 1 1000 0 0 0)
SYMATTR InstName Vs2
SYMBOL SpecialFunctions\\modulate -768 -384 R0
WINDOW 3 -66 -80 Left 0
SYMATTR InstName A1
SYMATTR Value space=1000 mark=1000
SYMBOL voltage -912 -272 R0
WINDOW 3 14 106 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName Vp1
SYMATTR Value SINE(1 1 100)
SYMBOL res -560 -240 R0
SYMATTR InstName Rp2
SYMATTR Value 1000
SYMBOL res -560 -352 R0
SYMATTR InstName Rp1
SYMATTR Value 3000
TEXT -1592 -560 Left 0 !.tran 0 .02 0 .3e-7

---
But, using the adder, if you change the amplitude and/or the
frequency of any input what happens to the output? The spectral
line corresponding to the changed input will change, but the lines
corresponding to the other inputs will not.

Use the multiplier and what happens if you change either the carrier
or the LO? The output lines will _all_ change even though only one
input has been changed.

On top of that, even if the output spectrum of the adder is made to
look like the output spectrum of the mixer, the phase relationship
between the outputs of the two will be different unless
extraordinary care is taken to make them the same and, even then, if
information is impressed on the adder's center frequency it will not
convey to the "sidebands".


--
JF

Ron Baker, Pluralitas! wrote:
"isw" wrote:

After you get done talking about modulation and sidebands, somebody
might want to take a stab at explaining why, if you tune a receiver to
the second harmonic (or any other harmonic) of a modulated carrier (AM
or FM; makes no difference), the audio comes out sounding exactly as it
does if you tune to the fundamental? That is, while the second harmonic
of the carrier is twice the frequency of the fundamental, the sidebands
of the second harmonic are *not* located at twice the frequencies of the
sidebands of the fundamental, but rather precisely as far from the
second harmonic of the carrier as they are from the fundamental.

Isaac

Whoa. I thought you were smoking something but
my curiosity is piqued.
I tried shortwave stations and heard no harmonics.
But that could be blamed on propagation.
There is an AM station here at 1.21 MHz that is s9+20dB.
Tuned to 2.42 MHz. Nothing. Generally the lowest
harmonics should be strongest. Then I remembered
that many types of non-linearity favor odd harmonics.
Tuned to 3.63 MHz. Holy harmonics, batman.
There it was and the modulation was not multiplied!
Voices sounded normal pitch. When music was
played the pitch was the same on the original and
the harmonic.

One clue is that the effect comes and goes rather
abruptly. It seems to switch in and out rather
than fade in an out. Maybe the coming and going
is from switching the audio material source?

This is strange. If a signal is multiplied then the sidebands
should be multiplied too.
Maybe the carrier generator is generating a
harmonic and the harmonic is also being modulated
with the normal audio in the modulator.
But then that signal would have to make it through
the power amp and the antenna. Possible, but
why would it come and go?
Strange.

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.

gr, Hein

isw wrote:
"Ron Baker, Pluralitas!" wrote:

Then you understand Fourier transforms and convolution.

I suppose so; I've spent over fifteen years poking around in the
entrails of MPEG...

Ever learned, unfortunately seldom used.
What can radio hobbyists do with Fourier transforms
nowadays? (Nowadays, for aids and appliances like
software and spectrum analysers take over some work.)
If somebody could provide some examples I'd be grateful.
Thanks.

gr, Hein

John Fields wrote:
Hein ten Horn wrote:
John Fields wrote:

And what does it look like, then?

Roughly like the ones in your Excel(lent) plots.

I've posted nothing like that, so if you have graphics which support
your position I'm sure we'd all be happy to see them.

Oops, I'm sorry Keith!
http://keith.dysart.googlepages.com/radio5

Mathematical terms like linear, logarithmic, etc. are familiar
to me, but the guys here use linear and nonlinear in another
sense.

Retrospectively viewed: not the term "linear".

gr, Hein

"Ron Baker, Pluralitas!" wrote in message
...

"Hein ten Horn" wrote in message
...
Ron Baker, Pluralitas! wrote:
"Hein ten Horn" wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

Nonsense. Mechanical oscillations are fully determined by
forces acting on the vibrating mass. Both mass and resulting force
determine the frequency. It's just a matter of applying the laws of
physics.

You don't know the laws of physics or how to apply them.

I'm not understood. So, back to basics.
Take a simple harmonic oscillation of a mass m, then
x(t) = A*sin(2*pi*f*t)
v(t) = d(x(t))/dt = 2*pi*f*A*cos(2*pi*f*t)
a(t) = d(v(t))/dt = -(2*pi*f)^2*A*sin(2*pi*f*t)
hence
a(t) = -(2*pi*f)^2*x(t)

Only for a single sinusoid.

and, applying Newton's second law,
Fres(t) = -m*(2*pi*f)^2*x(t)
or
f = ( -Fres(t) / m / x(t) )^0.5 / (2pi).

Only for a single sinusoid.
What if x(t) = sin(2pi f1 t) + sin(2pi f2 t)

In the following passage I wrote "a relatively
slow varying amplitude", which relates to the
4 Hz beat in the case under discussion (f1 =
220 Hz and f2 = 224 Hz) where your
expression evaluates to
x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t),
indicating the matter is vibrating at 222 Hz.

So where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

are fundamentally spoken valid.
Calling someone an idiot is a weak scientific argument.

Yes.
And so is "Nonsense." And so is your idea of
"the frequency".

Note the piquant difference: nonsense points
to content and we're not discussing idiots
(despite a passing by of some very strange
postings. ).

Hard words break no bones, yet deflate creditability.

gr, Hein




Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

gr, Hein

On Mon, 16 Jul 2007 12:28:07 -0700, Jim Kelley
wrote:

John Fields wrote:

On Fri, 06 Jul 2007 19:04:00 -0000, Jim Kelley
wrote:

In your example, with 300Hz and 400Hz as the carriers, the sidebands
would be located at:

f3 = f1 + f2 = 300Hz + 400Hz = 700Hz

and

f4 = f2 - f1 = 400Hz - 300Hz = 100Hz


both of which are clearly within the range of frequencies to which
the human ear responds.

Indeed. We would hear f3 and f4 if they were in fact there.

Your use of the term "beat frequency" is confusing since it's
usually used to describe the products of heterodyning, not the
audible warble caused by the vector addition of signals close to
unison.

The term is commonly used in describing the results of interference in
time, as well as for mixing.

Since the response of the ear is non-linear in amplitude it has no
choice _but_ to be a mixer and create sidebands.

Perhaps you're confusing log(sin(a)+sin(b)) with
log(sin(a))+log(sin(b)).

---
Perhaps, but I don't think either of those is correct, since for
mixing to occur (AIUI, for sidebands to be generated) the sine waves
themselves must be multiplied at the lowest level of the equation
instead of added.

That is, the solution of


log(sin(a)+sin(b))


will describe the numerical value of the logarithm of the vector sum
of two sine waves, and since the addition created no sidebands, the
output of the circuitry providing the logarithmic transfer function
will only be the instantaneous value of the logarithm of the vector
sum of the amplitudes of both signals.

Similarly,


log(sin(a))+log(sin(b))


describes the addition of the logarithm of the amplitude of sin(a)
to the logarithm of the amplitude of sin(b), which still produces
only a sum.

That is, no sidebands.
---

If you don't mind me asking, where did you get this notion about the
ears creating sidebands?

---
Well, whether I mind or not it seems you've asked anyway, so your
concern for my sensitivity is feigned.

That, coupled with your relegating it to being a "notion", seems to
be designed to discredit the hypothesis, offhandedly, and make me
work against a headwind in order to prove it valid, with you being
the negative authoritarian blowhard detractor.

If you're really interested in the subject I'll be happy to discuss
it with you if you can keep your end of the discussion objective and
free from pejorative comments.

Otherwise, **** off. ;^) -- Note tongue-in-cheek smiley, :-)


--
JF

Hein ten Horn wrote:

I've once listened to the first five harmonics of a
powerful medium wave transmitter (400 kW) at
a distance of some 300 m.
All harmonics gave normal audio; no strange
switching effects (Sony ICF-7600D).

What I'd like to know is if in such an 'experiment'
it can be excluded that (some of) these signals are
generated by the receiver itself.


That much power that close to the receiver? Its a wonder you didn't
destroy the receiver's frontend.


--
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

"John Fields" wrote in message
...
On Fri, 06 Jul 2007 19:04:00 -0000, Jim Kelley
wrote:

snip


---
Well, I'm just back from the Panama Canal Society's 75th reunion and
I haven't read through the rest of the thread, but it case someone
else hasn't already pointed it out to you, it seems you've missed
the point that a non-linear detector, (the human ear, for example)
when presented with two sinusoidal carriers, will pass the two
carrier frequencies through, as outputs, as well as two frequencies
(sidebands) which are the sum and difference of the carriers.

The human auditory system has many components,
some linear and some not. One must consider which
component is in play when considering whether there
is mixing.
As a first order approximation: the cochlea is a continous
array of resonators that separates the frequency components
the incoming signal. That is pretty linear.
Then the system assesses the amplitudes of the
various separated components. Assessing amplitude
is a nonlinear process.

The cochlea's ability to separate frequencies is not perfect.
If two frequency components are too close the
cochlea is not able to separate them before determining
amplitude. In which case intermodulation occurs in
detecting amplitude and thus there is a 'beat'.

If a 300 Hz tone and a 400 Hz tone are coming in then
the cochlea can separate them into independent areas
and assess their amplitudes independently. No beat.
If the two tones are too close, say 400 Hz and 410
Hz the cochlea can't separate them into separate
areas and assesses the amplitude of the sum of the
two tones. Since amplitude detection is nonlinear
there is intermodulation in that case and thus a beat.

To do amplitude detection the ear does something
like take only the positive half of the
signal, or take the positive absolute value of the
signal or square the signal. Then it
averages it (or otherwise lowpass it).
The first step is nonlinear. It produces intermodulation
if there is more than one frequency component
present in the band of interest.

With a single sine wave input the nonlinear
part of the amplitude detection gives a DC term and
various harmonics of the sine wave. The averaging
filter filters out all the harmonics and leaves
the DC 'amplitude' value.

If there are two frequencies close enough that they
both get into the same amplitude detector
then the nonlinearity of amplitude detection
results in intermodulation.
That gives a DC and a sum and a difference
frequency and harmonics. The averaging lets only
the DC and the difference frequency through. The
difference frequency is the beat.

Thus two tones separated sufficiently in frequency
produce no beat. Two tones within 20 Hz or
so produce a difference frequency beat but no
sum frequency tone.

snip


---
No, it doesn't.

Since the response of the ear is non-linear in amplitude it has no
choice _but_ to be a mixer and create sidebands.

Only if the tones are not separated in frequency
by the cochlea first.


What you see on an oscilloscope are the time-varying amplitude
variations caused by the linear vector summation of two signals
walking through each other in time, and what you see on a spectrum
analyzer is the two spectral lines caused by two signals adding, not
mixing. If you want to see what happens when the two signals hit
the ear, run them through a non-linear amp before they get to the
spectrum analyzer and you'll see at least the two original signals
plus their two sidebands.

Actually the nonlinear part is in the amplitude detection
which is present toward the end of the chain in both human
hearing and in spectrum analyzers.

snip

"Hein ten Horn" wrote in message
...

"Ron Baker, Pluralitas!" wrote in message
...

"Hein ten Horn" wrote in message
...
Ron Baker, Pluralitas! wrote:
"Hein ten Horn" wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

Nonsense. Mechanical oscillations are fully determined by
forces acting on the vibrating mass. Both mass and resulting force
determine the frequency. It's just a matter of applying the laws of
physics.

You don't know the laws of physics or how to apply them.

I'm not understood. So, back to basics.
Take a simple harmonic oscillation of a mass m, then
x(t) = A*sin(2*pi*f*t)
v(t) = d(x(t))/dt = 2*pi*f*A*cos(2*pi*f*t)
a(t) = d(v(t))/dt = -(2*pi*f)^2*A*sin(2*pi*f*t)
hence
a(t) = -(2*pi*f)^2*x(t)

Only for a single sinusoid.

and, applying Newton's second law,
Fres(t) = -m*(2*pi*f)^2*x(t)
or
f = ( -Fres(t) / m / x(t) )^0.5 / (2pi).

Only for a single sinusoid.
What if x(t) = sin(2pi f1 t) + sin(2pi f2 t)

In the following passage I wrote "a relatively
slow varying amplitude", which relates to the
4 Hz beat in the case under discussion (f1 =
220 Hz and f2 = 224 Hz) where your
expression evaluates to
x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t),
indicating the matter is vibrating at 222 Hz.

So where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

are fundamentally spoken valid.
Calling someone an idiot is a weak scientific argument.

Yes.
And so is "Nonsense." And so is your idea of
"the frequency".

Note the piquant difference: nonsense points
to content and we're not discussing idiots
(despite a passing by of some very strange
postings. ).

Hard words break no bones, yet deflate creditability.

gr, Hein




Well, I think I've had it. A 'never' ending story.
Too much to straighten out. Too much comment
needed. Questions moving away from the subject.
No more indistinguishable close frequencies.
No audible beat, no slow changing envelopes.

Take a plot, use a high speed camera or whatever
else and see for yourself the particle is vibrating at a
period in accordance with 222 Hz. In my view I've
sufficiently underpinned the 222 Hz frequency.
If you disagree, then do the job. Show your
frequencies and elucidate them. (No hint needed,
I guess.)

gr, Hein



Bravo. Well done. What an impressive
display of applying the laws of physics.
Newton, Euler, Gauss, and Fourier have nothing
on you.