Difficulties in understanding e^(-jwt)

[Anonymous.]

In message <[email protected]> which was published
in these
newsgroups on 13 Dec 2003, the following is asserted.....

"The term e^(-jwt) isn't some magical time machine relating to "minus
time", e^(-jwt) is simply another way of writing 1/(e^jwt) which
is a value that decreases as t increasing. "

Surely this is quite wrong?

Surely e^(-jwt) is a cyclic phenomenon, the value, or modulus, of
which remains absolutely constant and of the value unity?

 

[Blair]

In message <[email protected]> which was
published in these
newsgroups on 13 Dec 2003, the following is asserted.....

"The term e^(-jwt) isn't some magical time machine relating to "minus
time", e^(-jwt) is simply another way of writing 1/(e^jwt) which
is a value that decreases as t increasing. "

Surely this is quite wrong?

I remember it well. I later found out that the statement was correct.

Blair

 

[Anonymous]

Please do not take this the wrong way. You need a bit more experience and
understanding in order to interpret this notation well.

You are incapable of admitting when you are in the wrong.

Your response above is that of a disruptive maladjusted child, squirming
evasively, changing the subject and lashing out.

Shame on you, Salmon Egg.

Grow up! Stupid boy!

 

[Anonymous]

I remember it well. I later found out that the statement was correct.

On a daily basis, this NG is a forum seemingly for escapees from the school
playground, with gratuitous and offensive personal remarks originating from
even those who have not been part of a conversation and who could have no
reason, other than uncontrolled infantile emotions, for interjecting as they
do.

Is such public and international demonstrations really the way forward; the
way for PR for the future of Ham Radio. I say, "No!".

I cannot see how something that is a technical pursuit with traditions of
gentlemanly behaviour could possibly give way to the childish sneering that
is typical of this NG."

Really Blair, the number of times you appear here with the intention of
flinging infantile insults says more about you than perhaps you had hoped
for.

Grow up, Blair!

 

[Sponger's Conscience]

trigonometric functions and complex notation. There is no point in moving
on
to electrical applications unless you are willing to settle for monkey
see,
monkey do.

Beanie can do that. He's the biggest monkey in this NG!

 

[Roy]

I will not get into this.,
though I am tempted.

Once you I numbers deep there is no turning back, and it usually leads
right out the door with convention

®

 

[Don Kelly]

In message <[email protected]> which was
published in these
newsgroups on 13 Dec 2003, the following is asserted.....

"The term e^(-jwt) isn't some magical time machine relating to "minus
time", e^(-jwt) is simply another way of writing 1/(e^jwt) which
is a value that decreases as t increasing. "

Surely this is quite wrong?

Surely e^(-jwt) is a cyclic phenomenon, the value, or modulus, of
which remains absolutely constant and of the value unity?

--
It is wrong in the interpretation which appears to be based on real numbers.
You have it right but in light of your reaction to Salmon Egg's comments, it
seems that you really don't know why.
He was simply pointing out that you should know that and what he said is
absolutely correct. Your reaction to his comment was rather childish.

Look up Euler's equation and the whole concept of complex numbers

e^jwt =cos(wt-jsin(wt)

e^-jwt =cos(wt)-jsin(wt) which happens to be 1/e^jwt

 

[John]

"Salmon Egg" wrote

I am sorry for you, but not what I posted.

He's acting true to form. You give him an opinion which he doesn't like and
he slags you off.

And you wonder why the OP is unemployed and unemployable.

What he doesn't realise is that most employers now do websearches to
determine the strengths, weaknesses and overall merits of a prospective
employee.

 

[Anonymous.]

Please do not take this the wrong way. You need a bit more experience and
understanding in order to interpret this notation well.

Thank-you for your extended reply. Unfortunately you have
missed the boat. The point of my posts was to draw attention
to the heinous error, "is a value that decreases as t increasing"
which was published by a teacher of mathematics in Britland.

 

[Anonymous.]

I am sorry for you, but not what I posted.

Unfortunately you have responded to one of my stalkers and not to me.

He is Nathan Hull with the CB Handle of G7KUJ and posts with the
id of "+7IiMjEePDrUlHMcutxEQw.user.aioe.org". Many of his posts
are parodies of what I post and for many months he has masqueraded
as me, and usually adopts the pseudonym that I do shortly after I change
pseudonym because of his harassment, in this case "Anonymous".

Nathan Hull is one sick, sick kiddie.

I post with the id of "Z3IpgFh83JnnDIiU15n1gQ.user.aioe.org".

However, I note that you feel sorry for him, as do I.

(I had already responded to your first post)

 

[Anonymous.]

On a daily basis, this NG is a forum seemingly for escapees from the
school playground, with gratuitous and offensive personal remarks
originating from even those who have not been part of a conversation and
who could have no reason, other than uncontrolled infantile emotions, for
interjecting as they do.
Is such public and international demonstrations really the way forward;
the way for PR for the future of Ham Radio. I say, "No!".
I cannot see how something that is a technical pursuit with traditions of
gentlemanly behaviour could possibly give way to the childish sneering
that is typical of this NG."
Really Blair, the number of times you appear here with the intention of
flinging infantile insults says more about you than perhaps you had hoped
for.
Grow up, Blair!

Unfortunately, another obsessive post from my stalker, Nathan Hull, G7KUJ.

 

[Anonymous.]

It is wrong in the interpretation which appears to be based on real
numbers. You have it right but in light of your reaction to Salmon Egg's
comments, it seems that you really don't know why.

Thank-you for your input, Don, but unfortunately you also have fallen from
the reaction
of my stalker, Nathan Hull, G7KUJ who posts as
"+7IiMjEePDrUlHMcutxEQw.user.aioe.org", and who adopted the pseudonym
of "Anonymous" immediately after I changed to Anonymous.

He has also posted recently as...

Ne Plus Ultra, (Adopted immediately after me)
ne plus givre,
Lazy-Arsed Class A,
Gareth Tesla Evans, nee G8DXY,
pope benedict,
fr neil evans,
WPC Pullman,
Cool For Twats,
Beanie Simon,
Hypocrite,
Evans is a Lying Useless Sack of Shit,
Big K,
"Gugliemo Sponger Evans",
The G3VKI4KFK7KUJ Triumvirate of Mediocrity,
Counsellor for Comportment,
Dictator of Dogma,
Anonymous (Adopted immediately after me)


(Despite that I am gareth evans and my brother Fr. Neil Evans, but from
those two pseudonyms alone plus the abusive references to me you can
see that he is one sick, sick kiddie)

I post as "Z3IpgFh83JnnDIiU15n1gQ.user.aioe.org"

 

[Anonymous.]

--
It is wrong in the interpretation which appears to be based on real
numbers. Look up Euler's equation and the whole concept of complex numbers
e^jwt =cos(wt-jsin(wt)
e^-jwt =cos(wt)-jsin(wt) which happens to be 1/e^jwt

Indeed. However it was the blatant misunderstanding, "a value that
decreases as t increasing" that I was discussing.

 

[Anonymous.]

numbers.

Anonymous (under one of his many aliases) had been posting of negative
frequency and the context was clear to all but him. His confusion is
clear enough, especially as he recently added the word "size" into his
argument (as in "his case", not angle).
Well, that is normal of for him. Over the years, I've tried to educate
this fellow (as have many others) and he always reacts like this.
Sometimes I just leave him to rant on, he seems happier that way.
Oh, I remember showing the sock puppeteer that on one of the newsgroups.
He has previously claimed that division isn't valid in complex numbers.
Unless you want him stomping all over alt.engineering.electrical, I
suggest you let him stew.

Brian Reay is unfortunately another person who has been stalking me
for several years and is well aware that the person who posts under
"+7IiMjEePDrUlHMcutxEQw.user.aioe.org" is not I.

 

[Anonymous.]

numbers.
No, it is based on looking at the direction of rotation- CCW or CW.
Taking CCW as +ve (the normal convention), CW is -ve. So a CCW rotation
increases the argument whereas a CW rotation decreases it.

I think I can see where your misunderstanding arises. (In Britland, this
is easily covered by KS2, so see if you can sit it on a class given
by a competent maths teacher)

If there had been previously some rotation CCW, then a rotation CW
would represent a decrease BUT ONLY UNTIL THE ANGLE
CAME BACK TO ZERO, at which point the angle would then
grow in a negative direction, INCREASING.

However, this is all by the way. In the function e^(-jwt) there
NEVER WAS ANY CCW ROTATION, so that a statement to
the effect, " 1/(e^jwt) which is a value that decreases as t increasing"
is just plain hogwash and pig-ignorance and would be dangerous if
made by a schoolteacher.

 

[Anonymous.]

Oh, I remember showing the sock puppeteer that on one of the newsgroups.
He has previously claimed that division isn't valid in complex numbers.

As indeed it is not.

You can certainly evaluate a quotient by multiplying by unity
(a unity that is the quotient of the original denominator over
itself), but evaluating the quotient by the action of multiplication is not
the
action of division.

How would you evaluate (253 + 16j) / (4 +3j) by a dividing
process? Would you divide the 253 by the 4 in the first instance
or the 16j by the 3j?

Division is only valid for vector quantities when those vectors
are related by simple colinearity.

 

[Anonymous.]

You can certainly evaluate a quotient by multiplying by unity
(a unity that is the quotient of the original denominator over
itself), but evaluating the quotient by the action of multiplication is
not the
action of division.

Oops!

The _COMPLEX CONJUGATE_ of the original denominator over itself!

 

[Blair]

I think I can see where your misunderstanding arises. (In Britland, this
is easily covered by KS2, so see if you can sit it on a class given
by a competent maths teacher)

If there had been previously some rotation CCW, then a rotation CW
would represent a decrease BUT ONLY UNTIL THE ANGLE
CAME BACK TO ZERO, at which point the angle would then
grow in a negative direction, INCREASING.

However, this is all by the way. In the function e^(-jwt) there
NEVER WAS ANY CCW ROTATION, so that a statement to
the effect, " 1/(e^jwt) which is a value that decreases as t increasing"
is just plain hogwash and pig-ignorance and would be dangerous if
made by a schoolteacher.

It is you that is posting hogwash AND being very rude about it you jerk off.


Blair

 

[Anonymous]

It is you that is posting hogwash AND being very rude about it you jerk
off.

I an never rude, nor have I ever used these International Fora to broadcast
hogwash.

It seems almost inconceivable that the contributors to the gangrenous
degeneration that is alt.electrical.engineering would have such a primitive
understanding of the level of arithmatic required to pass an examination
written for 6 year olds!

I append some text to disambiguate.

-----ooooo-----

Copyright 1999 G.A.Evans. All Rights Reserved.

OK, you're still with me - good! I am pleased that you are determined to
make the effort to improve yourselves. I was a bit worried that my audience
would consist of only negative CB whingers, who never get anywhere, and who
gripe persistently that we Radio Hams never do anything to encourage
newcomers. In fact, such is the bigotry of such whingers in this NG, that I
half expected them to interpret my opening comments in Lesson 1 as a polemic
against CBers. How wrong can you be!

Where do we go from here? OK. I'm going to take you through some essential
ideas in maths, and then I'm going to leave the maths behind for a while and
start
talking about electrical matters. (It's electricity that matters for Radio
Hams!) My first topic on electrical matters will be "Energy"; this should
give you advanced notice to enable you to think about what energy means to
you.

For the moment, though, let's get back to the maths.

Some of the topics I am going to cover may seem to you to be far too simple,
but let's get the foundations secure before we build the walls. The topics I
have
selected come from my experience as a part-time tutor in adult education,
dealing with the common problems that my students come up with.

Here's the road map :- Addition, Multiplication, Finish Off Addition,
Subtraction, Negative Numbers, Division, Fractions And Decimals, Brackets.
Algebraic Puzzles.

At this point, you will have enough under your belt to solve electrical
formulae, I will stress time and time again that THERE IS NOTHING NEW IN
MATHS - most of what you will come across will be a different way of writing
down something that you already know. The different way is a shorthand to
make life easy. But remember! If at any time you are confused by the new
short-hands, you can always go back and work in the older, simpler ways,
(although it might take you longer, you'll still get the correct answer!)

ADDITION

Suppose that you've got three eggs (and continuing my pun of "X's" for eggs,
you will have XXX.) Someone now gives you another five XXXXX. How many have
you got? Well, you put your three, XXX, next to the new five, XXXXX giving
you XXXXXXXX, and you count them again. This is the simple rule for
addition. You had three, you add another five, giving you eight. You don't
need to understand how to do adding, because after putting them together,
you can count them again from scratch.

OK. Suppose that your weekly income is £200, and you get a raise of £37
pounds per week, the same principle applies - put down 200 ticks, then write
down a further 37, and count them all from scratch - you're doing
addition.....

XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXX

This soon gets tedious, so let's devise a shorthand to make life easier -
but remember! You don't HAVE to use the shorthand, because it's just another
way of writing down something that you already know - you can carry on
putting down two lots of ticks next to each other, and count them all again
from scratch.

The short-hand is "5 + 3", where the "+" is known as a "Plus Sign". When you
see this Plus Sign ("+"), it means take the number on the left side, and
write down that many ticks. Then take the number on the right side, and
write down THAT many ticks, right next to the original group of ticks. Then
count how many ticks you've got altogether.

So, let's recap... you can see in the example TWO short hands, firstly the
use of "5" instead of "XXXXX", and then the use of "+" to read as the
instruction to do an addition. OK. I bet you've never seen that presented
like that before, but you see, even addition, which you did right in the
early days at school, is a convenient way OF WRITING DOWN SOMETHING ELSE
WHICH YOU ALREADY KNEW ABOUT.

Now, whether you do 5 + 3 :- XXXXX then XXX to give XXXXXXXX or 3 + 5 :- XXX
then XXXXX to give XXXXXXXX you get the same result. This effect is known in
the trade as "Commutativeness", which means "switching around". The word has
the same origin as the "commutator" in an electric motor which "switches
around" the coils in the armature.

OK, in the early days, one concept per lesson is more than enough. I need to
digress into multiplication in the next lesson, before I can finish with
addition.

 

[Sponger's Conscience]

8 years later and hes still working on lesson 2...