"Eric C. Weaver" wrote in message ...
This discussion happens all the time on comp.dsp, between primarily
computer-science folks approaching DSP and EE types approaching it.

EE folks' definition of "linear" implicitly includes time invariance; DSP
people have to see it stated explicitly (as "LTI": Linear Time Invariant) lest
they think "linear" just means having no second-or-higher-order terms.

It is not a deficiency on either party's part, just a difference of definition
in each's respective discipline (is that enough alliteration?).

Therefore, I advise each to bend this much: Use the full phrase "Linear
Time-Invariant" when this miscommunication is suspected, so both know what the
hell the other is talking about. Now go and sin no more.

Eric,

The really efficient dsp / digital algorithms come about with
time-varying processes. Another good bit of science is the use of
recursive filters to produce a finite impulse response ... That's one
nice way to squeeze a lot of functionality in a medium-sized IC / FPGA
/ ASIC ... or whatever.

Radio receiver (demodulation) and bandpass algorithm / code get a lot
smaller.

Frank Raffaeli
http://www.aomwireless.com/

"Eric C. Weaver" wrote in message ...
This discussion happens all the time on comp.dsp, between primarily
computer-science folks approaching DSP and EE types approaching it.

EE folks' definition of "linear" implicitly includes time invariance; DSP
people have to see it stated explicitly (as "LTI": Linear Time Invariant) lest
they think "linear" just means having no second-or-higher-order terms.

It is not a deficiency on either party's part, just a difference of definition
in each's respective discipline (is that enough alliteration?).

Therefore, I advise each to bend this much: Use the full phrase "Linear
Time-Invariant" when this miscommunication is suspected, so both know what the
hell the other is talking about. Now go and sin no more.

Eric,

The really efficient dsp / digital algorithms come about with
time-varying processes. Another good bit of science is the use of
recursive filters to produce a finite impulse response ... That's one
nice way to squeeze a lot of functionality in a medium-sized IC / FPGA
/ ASIC ... or whatever.

Radio receiver (demodulation) and bandpass algorithm / code get a lot
smaller.

Frank Raffaeli
http://www.aomwireless.com/

"Kevin Aylward" wrote in message ...

[snipped much voluminous banter]

Whilst, I do agree that Win is very knowledgeable and an expert, I am
also an expert. I have been doing this rather a long time as well you
know. The fact that I am not an academic is not relevant. In all
honesty, there is not much I don't know about general analogue design,
although, obviously, I don't claim to know it all. Does Win know more
than me? Unlikely. Or do I know more than Win. Unlikely. However, we may
well know different things.

[snipped more banter]

Does the above pose a question, or is it mere rhetoric? Could the
scientific method be applied with gusto? Are Win and Kev evenly
matched? The surname of this forum is *design*. I, for one, would
prefer to see this hypothesis tested by deeds rather than by words. On
this forum, I don't care if its spelled analogue or analog - just make
it work and explain why. IMO, no one here needs to prove anything;
however, it would certaily be interesting to watch such a *contest* if
it were all in good fun and sport.

Best Regards,

Frank Raffaeli
http://www.aomwireless.com/

"Kevin Aylward" wrote in message ...

[snipped much voluminous banter]

Whilst, I do agree that Win is very knowledgeable and an expert, I am
also an expert. I have been doing this rather a long time as well you
know. The fact that I am not an academic is not relevant. In all
honesty, there is not much I don't know about general analogue design,
although, obviously, I don't claim to know it all. Does Win know more
than me? Unlikely. Or do I know more than Win. Unlikely. However, we may
well know different things.

[snipped more banter]

Does the above pose a question, or is it mere rhetoric? Could the
scientific method be applied with gusto? Are Win and Kev evenly
matched? The surname of this forum is *design*. I, for one, would
prefer to see this hypothesis tested by deeds rather than by words. On
this forum, I don't care if its spelled analogue or analog - just make
it work and explain why. IMO, no one here needs to prove anything;
however, it would certaily be interesting to watch such a *contest* if
it were all in good fun and sport.

Best Regards,

Frank Raffaeli
http://www.aomwireless.com/

Terry Given wrote:
Kevin Aylward wrote:

In summary, there are differing concepts of what linearity is being
understood to mean in the real world.


No again. Those who are confused about it, and can't admit they are
simply wrong about what amounts to a widely accepted definitional
matter
[snip]
You nor anyone else need take my word for it: it is in *all* the
Signals, Systems, and Communications texts I've ever opened up --
they are wholly consistant with each other; check for yourself. Your
"definition" is not in any of them (af(t) = f(at)???). So I feel
justified in simply saying you are flatly wrong. If you could at
least post a citation from a text that has your definition and a
worked mathematical problem/solution (no "Circuits" junk), then at
least we could say it was all a grand misunderstanding.

herewith a self-confessed doesnt-know-it-all's analysis:
IF
y(x) = mx+c (even KA cant argue with the linearity (and
time-invariance) of this....LOL)
THEN
y(ax) = max+c
AND
ay(x) = max+ac

Look, you picking up on a triviality that was thrown in as a side line
and as as immediate response to a justification of my claims. My claims
stand as correct. I clearly stated what was I consider an appropriate
definition of linearity, i.e. no frequencies present in the output, not
present at the input.

Elementary Sesame-Street Theory (one of these things is not like the
other) clearly shows this "definition" of linearity to be rubbish.

This was, to all intents and purposes, a typo. I was meaning to refer to
a simple constant gain transfer function. Is it really credible, given
that you are obviously aware of my GR papers, that I am to stupid to
know standard definition of linearity.

However, it would seem that you are another one of those sad people who
think

y=x^2

is a linear equation between x and y.


gwhite most certainly has it correct. KA does not.


Dream on. This is bloody absurd.

www.google.com "nonlinear differential equations" 22,000 hits.

You need to get to grips with than fact that the term "linear" is being
used with two different meanings, where *both* meanings are perfectly
valid in their own contexts. Look, I know what gwite white means, its
trivial. It is also trivial to understand that it is not applicable to
analogue design of amplifies.

Next you'll be declaring that "homogeneous" only, means the one specific
definition as used in differential equations. Or how about "canonical"


as a slight aside, I have read H&H about 8 times, and will continue
to do so - it is one of the more useful books on electronics I have
ever bought (and I have about 600 of them). If you do not have that
book - GO AND BUY IT!! I even met WINFIELD Hill at an MIT junkfest
once a few years ago, and had an interesting discussion with him
about my work on high-speed PMSM energy storage flywheels and giant
SMPS. That guy is really smart - I suggest anyone reading this forum
should pay close attention to win's postings (i sure do). As far as
being an "academic" - well, go read H&H - its beauty lies in its
practicality, unlike most texts. Just because someone works in
academia, doesnt mean they are useless (although to be fair, its
usually not a bad first guess).

I hope you not suggesting that I have any negative opinions of Win
because I claimed that I was not an academic.


Likewise I have met plenty of
blithering idiots out doing "real" engineering (its a good thing -
competent people end up being well paid to fix their screw-ups). The
worst ones tend to work in sales (I presume its because they cant get
real jobs)

Really this entire thread has done little more than allow Kevin
Aylward to appear like a pompous idiot, with a somewhat limited
understanding. A BSc and half-a-dozen MSc courses (one A - wow. I
remember those - they are what you get if you dont do well enough for
an A+) simply makes for a failed MSc. Of all the pomposities, I just
loved this one:

No this one is about gwhite being a pretentious prat trying to impress
everyone with a fancy mathematical definition of linearity that has
little or zero relevance in this context, i.e analogue design of
amplifiers. He has *yet* to show how said class A amplifier, as he
claimed, can form a modulator without relying on the fact that the
transfer function of the transistor is non-linear. He has simple
attempted to obscure the issues by making irrelevant technical points.


In all honesty, there is not much I don't know about general
analogue design, although, obviously, I don't claim to know it all.

It kind of makes one wonder just how KA knows there isnt much he
doesnt know.

why do I post on these newsboards? am I being selfish? I dont think
so.

Not consciously, but inherently, there is no other way, that is not if
you believe in evolution, i.e if you are one of those creationists.


Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

Terry Given wrote:
Kevin Aylward wrote:

In summary, there are differing concepts of what linearity is being
understood to mean in the real world.


No again. Those who are confused about it, and can't admit they are
simply wrong about what amounts to a widely accepted definitional
matter
[snip]
You nor anyone else need take my word for it: it is in *all* the
Signals, Systems, and Communications texts I've ever opened up --
they are wholly consistant with each other; check for yourself. Your
"definition" is not in any of them (af(t) = f(at)???). So I feel
justified in simply saying you are flatly wrong. If you could at
least post a citation from a text that has your definition and a
worked mathematical problem/solution (no "Circuits" junk), then at
least we could say it was all a grand misunderstanding.

herewith a self-confessed doesnt-know-it-all's analysis:
IF
y(x) = mx+c (even KA cant argue with the linearity (and
time-invariance) of this....LOL)
THEN
y(ax) = max+c
AND
ay(x) = max+ac

Look, you picking up on a triviality that was thrown in as a side line
and as as immediate response to a justification of my claims. My claims
stand as correct. I clearly stated what was I consider an appropriate
definition of linearity, i.e. no frequencies present in the output, not
present at the input.

Elementary Sesame-Street Theory (one of these things is not like the
other) clearly shows this "definition" of linearity to be rubbish.

This was, to all intents and purposes, a typo. I was meaning to refer to
a simple constant gain transfer function. Is it really credible, given
that you are obviously aware of my GR papers, that I am to stupid to
know standard definition of linearity.

However, it would seem that you are another one of those sad people who
think

y=x^2

is a linear equation between x and y.


gwhite most certainly has it correct. KA does not.


Dream on. This is bloody absurd.

www.google.com "nonlinear differential equations" 22,000 hits.

You need to get to grips with than fact that the term "linear" is being
used with two different meanings, where *both* meanings are perfectly
valid in their own contexts. Look, I know what gwite white means, its
trivial. It is also trivial to understand that it is not applicable to
analogue design of amplifies.

Next you'll be declaring that "homogeneous" only, means the one specific
definition as used in differential equations. Or how about "canonical"


as a slight aside, I have read H&H about 8 times, and will continue
to do so - it is one of the more useful books on electronics I have
ever bought (and I have about 600 of them). If you do not have that
book - GO AND BUY IT!! I even met WINFIELD Hill at an MIT junkfest
once a few years ago, and had an interesting discussion with him
about my work on high-speed PMSM energy storage flywheels and giant
SMPS. That guy is really smart - I suggest anyone reading this forum
should pay close attention to win's postings (i sure do). As far as
being an "academic" - well, go read H&H - its beauty lies in its
practicality, unlike most texts. Just because someone works in
academia, doesnt mean they are useless (although to be fair, its
usually not a bad first guess).

I hope you not suggesting that I have any negative opinions of Win
because I claimed that I was not an academic.


Likewise I have met plenty of
blithering idiots out doing "real" engineering (its a good thing -
competent people end up being well paid to fix their screw-ups). The
worst ones tend to work in sales (I presume its because they cant get
real jobs)

Really this entire thread has done little more than allow Kevin
Aylward to appear like a pompous idiot, with a somewhat limited
understanding. A BSc and half-a-dozen MSc courses (one A - wow. I
remember those - they are what you get if you dont do well enough for
an A+) simply makes for a failed MSc. Of all the pomposities, I just
loved this one:

No this one is about gwhite being a pretentious prat trying to impress
everyone with a fancy mathematical definition of linearity that has
little or zero relevance in this context, i.e analogue design of
amplifiers. He has *yet* to show how said class A amplifier, as he
claimed, can form a modulator without relying on the fact that the
transfer function of the transistor is non-linear. He has simple
attempted to obscure the issues by making irrelevant technical points.


In all honesty, there is not much I don't know about general
analogue design, although, obviously, I don't claim to know it all.

It kind of makes one wonder just how KA knows there isnt much he
doesnt know.

why do I post on these newsboards? am I being selfish? I dont think
so.

Not consciously, but inherently, there is no other way, that is not if
you believe in evolution, i.e if you are one of those creationists.


Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

gwhite wrote:
Kevin Aylward wrote:

Kevin Aylward wrote:
gwhite wrote:
Kevin Aylward wrote:

In summary, there are differing concepts of what linearity is being
understood to mean in the real world.


No again.

No right again.

Those who are confused about it, and can't admit they are
simply wrong about what amounts to a widely accepted definitional
matter, simply take refuge by obscuring
the basics with a bunch of
junk similar to:

"therefore

Vo = 40.Vc.Vi/Re."


Oh dear..oh dear...You claimed that the class A amp was a modulator an
achieved this modulation by way of linear means, you fail to present
your proof of this claim, and then spout of with mathematical waffle,
and claim that I am being obscure?

I clearly showed how the class A amp achieved modulation based on the
non-linear relation of emitter current verses base emitter voltage. The
fact that you have failed to give an alternative mathematically proof
indicates quite clearly that you ****ing in the wind.

Present you argument of exactly how your claim is correct, or retract
you claim.


The simple fact is you are wrong in thinking you can all of the sudden
make up your own definition of linearity, or carry forward without
challenge the mistaken definition of others.

Absolute crap. Show me one respectable math reference that says if
y=exp(x), that y is a linear function of x.

You were right about one
thing: this matter of linearity is pretty basic.

Indeed it is.

You missed it; you
are wrong, that is no big deal.

Indeed its not. My SuperSpice works quite nicely based on the well known
theory of the solution of non-linear differential equations.


The silly part was when you decided
to be condescending about it, for in most practical matters strict
linearity doesn't matter a lot -- most people know what they are
doing well enough such that the accepted definition of linearity is
not explicitly referred to.

I don't have time tonight to provide cited work (I have one from Lahti
that will be particularly useful for this discussion), since it takes
scanning and OCR time and then patch up -- I will do so soon though.
In short, you believe "non-linearity" is *required* for modulators;

Show me one real practical example that does not use a device with a
functional relation between input and output voltage/current that is
linear, as I defined above. As did note as an after thought, it may be
possible in principle, for example, maybe one could construct a true,
linear with voltage, voltage controlled resistor. However, I am not
aware of such magic devices.

The physical reality is that it is not possible. Produce one and I will
retract my claim.

that is incorrect. You confuse the time-invariance property with the
linearity property. You believe LTI systems are the *only* linear
systems -- they are not according to the widely accepted and published
definition of linearity.

No. Linearity is widely understood to have many definitions. I have
explained some of these already.

It is that simple.

Nope. Its not. Linearity has many definitions. In the context of
analogue design, linearity is defined based on where the is a non
straight line between input and output. The whole subject of non-linear
differential equations in spice is based on this concept.

I gave you an example
and worked the solution for you, but still you resist.

Look, I have no problem with your example of a particular definition of
linearity. I already explained how such an example is meaningless in
analogue design by giving an example.

A mathematical definition only has meaning if it is useful when it is
applied. In analogue design this definition is useless, so it is not
used.


You nor anyone else need take my word for it: it is in *all* the
Signals, Systems, and Communications texts I've ever opened up -- they
are wholly consistant with each other; check for yourself.

I don't care a toss about and communication texts. I care about
linearity as understood in the solution of the non-linear differential
equations used in Spice. I suggest that you read some of the many papers
on the solution of such equations.

Look, I don't claim that the particular definition of linearity that you
presence is "wrong" in principle. It is a very well known definition.
However, it is one of many, and is simple not applicable in this
context.

Your
"definition" is not in any of them (af(t) = f(at)???).

I did not say that this was a definition. This was just thrown in as
side line, and I said as much. This was, to all intents and purposes, a
typo. I was meaning to refer to a simple constant gain transfer
function. I clearly said that linearity, as defined in analogue design,
is essentially defined by the absence of any frequencies in the output
not present in the input.

So I feel
justified in simply saying you are flatly wrong.

No. You is you. You have singularly failed to show how your class a amp
is a modulator without using a non-linear relation between input
voltage/current to output voltage/current. If you claim that y=exp(x) is
a linear relation between x an y, further debate is pointless. You don't
the first thing about math.

If you could at
least post a citation from a text that has your definition and a
worked mathematical problem/solution (no "Circuits" junk), then at
least we could say it was all a grand misunderstanding.


www.google.com "nonlinear equations"

www.google.com "nonlinear differential equations" 22,000 hits.

You problem is that you are trying to argue a different point and simple
don't see it. You were off on a roll trying to impress people which
mathematical technicalities that are simple irrelevant in the context of
this original discussion. In short, you are a smart arse.


I must confess here I made a small error.

What wasn't small is your reaction to your "small error." All that
"pretentious drivel" wasn't so pretentious given the fact it is *basic
stuff* that most who've taken the appropriate classes already know

I know all about your definition. I dont disagree that it is a valid
definition in some contexts. However, it is not applicable to electronic
circuit design that is based on the solution of non-linear differential
equations, with the "non-linear" term having a universally accepted
meaning by the 10,000s of mathematician who actually study such
equations.


(it
was a couple definitions and an application using a couple simple trig
identities and no more really).

So basic that you can stand there and declare that:

Y=x^2

is a linear equation. Yeah...LOL. get real.

The meat:

You arnt wrong in this thread because of you particular claim of
linearity. You are wrong because the fundamental claim that you made was
that your class A amp was a modulator that did not rely on the
non-linear transfer function of the emitter current verses Vbe. You have
absolutely failed to explain any exact *details* to support your claim.
That is, show me a specific analysis of the amplifier, without the
irrelevant mathematical waffle, that shows that:

Vo = V(t)(1+ a.sin(wt))

I will accept the argument that you simply misunderstood my, very common
definition of linearity, i.e. y=x^2 is a non-linear equation relation x
to y in *any* mathematical book you care to name, with a linearity
definition more appropriate to general systems analysis.

In closing:

The real reason for this disagreement is that you are talking apples and
I am talking fish net stockings. You are applying the term linearity in
a completely different sense than the one I am using. Both are valid in
principle, and are indeed well accepted, under their appropriate
conditions. The issue however, is that I have made an effort to actually
explain in other posts, what the distinction is, but you are simple too
closed minded or too stupid to understand. In this particular case,
modulation is, in practise, universally achieved by a non-linear
transfer function. That is y=f(x) is non-linear as defined in any math
text book you care to name. Its simple not debatable. However, applying
signals to such a transfer function, can result in the condition, that
given that a certain output is required, non-linearly related to the
input in the strict sense, this output is linearly related to the input
signals. That is, if a certain input gives an output, the sum of two
inputs, give the same output as the individual output sums. In this
sense it may be said to be linear. That is the wanted summed output is
the wanted output of the individual inputs. In one case the term
linearity is being applied to the fact that the output is not a direct
linear function of the input, in the other case, the term linearity is
being applied to the fact the wanted output is is a linear function of
the input sums. That is, in one case, the term linearity is being
applied to the specifics of a system part, where as in the second case
linearity is being applied to a system wide property. What seems to
defies rational belief, is that you seem totally oblivious to the fact
that the term linearity is being applied to two completely different
aspects of a system, and cant be directly compared as to which one is
more valid then another.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

gwhite wrote:
Kevin Aylward wrote:

Kevin Aylward wrote:
gwhite wrote:
Kevin Aylward wrote:

In summary, there are differing concepts of what linearity is being
understood to mean in the real world.


No again.

No right again.

Those who are confused about it, and can't admit they are
simply wrong about what amounts to a widely accepted definitional
matter, simply take refuge by obscuring
the basics with a bunch of
junk similar to:

"therefore

Vo = 40.Vc.Vi/Re."


Oh dear..oh dear...You claimed that the class A amp was a modulator an
achieved this modulation by way of linear means, you fail to present
your proof of this claim, and then spout of with mathematical waffle,
and claim that I am being obscure?

I clearly showed how the class A amp achieved modulation based on the
non-linear relation of emitter current verses base emitter voltage. The
fact that you have failed to give an alternative mathematically proof
indicates quite clearly that you ****ing in the wind.

Present you argument of exactly how your claim is correct, or retract
you claim.


The simple fact is you are wrong in thinking you can all of the sudden
make up your own definition of linearity, or carry forward without
challenge the mistaken definition of others.

Absolute crap. Show me one respectable math reference that says if
y=exp(x), that y is a linear function of x.

You were right about one
thing: this matter of linearity is pretty basic.

Indeed it is.

You missed it; you
are wrong, that is no big deal.

Indeed its not. My SuperSpice works quite nicely based on the well known
theory of the solution of non-linear differential equations.


The silly part was when you decided
to be condescending about it, for in most practical matters strict
linearity doesn't matter a lot -- most people know what they are
doing well enough such that the accepted definition of linearity is
not explicitly referred to.

I don't have time tonight to provide cited work (I have one from Lahti
that will be particularly useful for this discussion), since it takes
scanning and OCR time and then patch up -- I will do so soon though.
In short, you believe "non-linearity" is *required* for modulators;

Show me one real practical example that does not use a device with a
functional relation between input and output voltage/current that is
linear, as I defined above. As did note as an after thought, it may be
possible in principle, for example, maybe one could construct a true,
linear with voltage, voltage controlled resistor. However, I am not
aware of such magic devices.

The physical reality is that it is not possible. Produce one and I will
retract my claim.

that is incorrect. You confuse the time-invariance property with the
linearity property. You believe LTI systems are the *only* linear
systems -- they are not according to the widely accepted and published
definition of linearity.

No. Linearity is widely understood to have many definitions. I have
explained some of these already.

It is that simple.

Nope. Its not. Linearity has many definitions. In the context of
analogue design, linearity is defined based on where the is a non
straight line between input and output. The whole subject of non-linear
differential equations in spice is based on this concept.

I gave you an example
and worked the solution for you, but still you resist.

Look, I have no problem with your example of a particular definition of
linearity. I already explained how such an example is meaningless in
analogue design by giving an example.

A mathematical definition only has meaning if it is useful when it is
applied. In analogue design this definition is useless, so it is not
used.


You nor anyone else need take my word for it: it is in *all* the
Signals, Systems, and Communications texts I've ever opened up -- they
are wholly consistant with each other; check for yourself.

I don't care a toss about and communication texts. I care about
linearity as understood in the solution of the non-linear differential
equations used in Spice. I suggest that you read some of the many papers
on the solution of such equations.

Look, I don't claim that the particular definition of linearity that you
presence is "wrong" in principle. It is a very well known definition.
However, it is one of many, and is simple not applicable in this
context.

Your
"definition" is not in any of them (af(t) = f(at)???).

I did not say that this was a definition. This was just thrown in as
side line, and I said as much. This was, to all intents and purposes, a
typo. I was meaning to refer to a simple constant gain transfer
function. I clearly said that linearity, as defined in analogue design,
is essentially defined by the absence of any frequencies in the output
not present in the input.

So I feel
justified in simply saying you are flatly wrong.

No. You is you. You have singularly failed to show how your class a amp
is a modulator without using a non-linear relation between input
voltage/current to output voltage/current. If you claim that y=exp(x) is
a linear relation between x an y, further debate is pointless. You don't
the first thing about math.

If you could at
least post a citation from a text that has your definition and a
worked mathematical problem/solution (no "Circuits" junk), then at
least we could say it was all a grand misunderstanding.


www.google.com "nonlinear equations"

www.google.com "nonlinear differential equations" 22,000 hits.

You problem is that you are trying to argue a different point and simple
don't see it. You were off on a roll trying to impress people which
mathematical technicalities that are simple irrelevant in the context of
this original discussion. In short, you are a smart arse.


I must confess here I made a small error.

What wasn't small is your reaction to your "small error." All that
"pretentious drivel" wasn't so pretentious given the fact it is *basic
stuff* that most who've taken the appropriate classes already know

I know all about your definition. I dont disagree that it is a valid
definition in some contexts. However, it is not applicable to electronic
circuit design that is based on the solution of non-linear differential
equations, with the "non-linear" term having a universally accepted
meaning by the 10,000s of mathematician who actually study such
equations.


(it
was a couple definitions and an application using a couple simple trig
identities and no more really).

So basic that you can stand there and declare that:

Y=x^2

is a linear equation. Yeah...LOL. get real.

The meat:

You arnt wrong in this thread because of you particular claim of
linearity. You are wrong because the fundamental claim that you made was
that your class A amp was a modulator that did not rely on the
non-linear transfer function of the emitter current verses Vbe. You have
absolutely failed to explain any exact *details* to support your claim.
That is, show me a specific analysis of the amplifier, without the
irrelevant mathematical waffle, that shows that:

Vo = V(t)(1+ a.sin(wt))

I will accept the argument that you simply misunderstood my, very common
definition of linearity, i.e. y=x^2 is a non-linear equation relation x
to y in *any* mathematical book you care to name, with a linearity
definition more appropriate to general systems analysis.

In closing:

The real reason for this disagreement is that you are talking apples and
I am talking fish net stockings. You are applying the term linearity in
a completely different sense than the one I am using. Both are valid in
principle, and are indeed well accepted, under their appropriate
conditions. The issue however, is that I have made an effort to actually
explain in other posts, what the distinction is, but you are simple too
closed minded or too stupid to understand. In this particular case,
modulation is, in practise, universally achieved by a non-linear
transfer function. That is y=f(x) is non-linear as defined in any math
text book you care to name. Its simple not debatable. However, applying
signals to such a transfer function, can result in the condition, that
given that a certain output is required, non-linearly related to the
input in the strict sense, this output is linearly related to the input
signals. That is, if a certain input gives an output, the sum of two
inputs, give the same output as the individual output sums. In this
sense it may be said to be linear. That is the wanted summed output is
the wanted output of the individual inputs. In one case the term
linearity is being applied to the fact that the output is not a direct
linear function of the input, in the other case, the term linearity is
being applied to the fact the wanted output is is a linear function of
the input sums. That is, in one case, the term linearity is being
applied to the specifics of a system part, where as in the second case
linearity is being applied to a system wide property. What seems to
defies rational belief, is that you seem totally oblivious to the fact
that the term linearity is being applied to two completely different
aspects of a system, and cant be directly compared as to which one is
more valid then another.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

gwhite wrote:
"Eric C. Weaver" wrote:

This discussion happens all the time on comp.dsp, between primarily
computer-science folks approaching DSP and EE types approaching it.

EE folks' definition of "linear" implicitly includes time invariance;


Interesting thought since a Signals and Systems course, or a Linear
Systems course, or a Communications course is often required to get an
EE degree. After all, these courses explicitly distinguish the
linearity property and the time-invariance property. And I've never
seen the "af(t) = f(at)" so-called "definition" until a few days ago.

Your a liar. Its that simple. I clearly stated that it was *not* a
definition. It was simply trying to illustrate the concept of constant
gain. You expanding on some trivial minor point to avoid answering the
main issue, to wit, you have failed to disprove my claim on your class A
amplifier.



DSP
people have to see it stated explicitly (as "LTI": Linear Time
Invariant) lest they think "linear" just means having no
second-or-higher-order terms.

It is not a deficiency on either party's part, just a difference of
definition in each's respective discipline (is that enough
alliteration?).

Therefore, I advise each to bend this much: Use the full phrase
"Linear Time-Invariant" when this miscommunication is suspected, so
both know what the hell the other is talking about.

Absolute crap. The notion that y=x^2 is a non-linear equation is
universally accepted by anyone who has done even the slightest bit of
theory on basic algebraic equations. It does not require any
qualification in the slightest.


Now go and sin
no more.

I've met folks before who think that linearity means freqs cumzoutas
must only equal freqs gozintas. But they don't usually put up such a
fuss when actually presented with the widely available and consistant
literature or reasonable arguments. This is more about fuss than
facts.

Indeed. So why *are* you putting up such a fuss about notions that are
widely held in the literature. Show me one, and I mean just one, that
declares y=x^2 a linear equation.


Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.

gwhite wrote:
"Eric C. Weaver" wrote:

This discussion happens all the time on comp.dsp, between primarily
computer-science folks approaching DSP and EE types approaching it.

EE folks' definition of "linear" implicitly includes time invariance;


Interesting thought since a Signals and Systems course, or a Linear
Systems course, or a Communications course is often required to get an
EE degree. After all, these courses explicitly distinguish the
linearity property and the time-invariance property. And I've never
seen the "af(t) = f(at)" so-called "definition" until a few days ago.

Your a liar. Its that simple. I clearly stated that it was *not* a
definition. It was simply trying to illustrate the concept of constant
gain. You expanding on some trivial minor point to avoid answering the
main issue, to wit, you have failed to disprove my claim on your class A
amplifier.



DSP
people have to see it stated explicitly (as "LTI": Linear Time
Invariant) lest they think "linear" just means having no
second-or-higher-order terms.

It is not a deficiency on either party's part, just a difference of
definition in each's respective discipline (is that enough
alliteration?).

Therefore, I advise each to bend this much: Use the full phrase
"Linear Time-Invariant" when this miscommunication is suspected, so
both know what the hell the other is talking about.

Absolute crap. The notion that y=x^2 is a non-linear equation is
universally accepted by anyone who has done even the slightest bit of
theory on basic algebraic equations. It does not require any
qualification in the slightest.


Now go and sin
no more.

I've met folks before who think that linearity means freqs cumzoutas
must only equal freqs gozintas. But they don't usually put up such a
fuss when actually presented with the widely available and consistant
literature or reasonable arguments. This is more about fuss than
facts.

Indeed. So why *are* you putting up such a fuss about notions that are
widely held in the literature. Show me one, and I mean just one, that
declares y=x^2 a linear equation.


Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.