

Mr. Fourier,
are you there...?  Mr. Fourier..? 
Fourier
:


"Yes,
I am here" 
Me
:


"
Where ? " 
Fourier
:


"Right here young
man",  tapping my back..... 
Me:


"Oh,
you frightened me, Sir....Hmm....Cool clothes... " :)
"Mr. Fourier, all this talk about sine waves, and squares built of sine waves,
is that not just something you said many years ago, in order to gain a name ? " 
Fourier:


" Listen, young man..
A little respect, would not be misplaced. A square is composed of an eternal amount
of sine waves.That is the truth" 
Me:


"Can
you prove that ? " 
Fourier:


"Certainly. Square
= 4/Pi ( eternal ) Epsilon times sine times 2n  1 x 2 Pi frequency t divided with
2n1." 
Me:


 not
really understanding the formula: " ehhh.. well , yes, I see. But wouldn't an
f_{2} round the flat top ? " 
Fourier:


" Hmm. Not if they
are not there. I mean it is composed of entire infinite ODD frequencies" 
Me:


"
Oh, yes, that makes more sence. But as the phase changes , wouldn't some of these
compare to a second related frequency ? " 
Fourier:


 a little irritated by
now  "No, I most certainly assume that they are all in phase, from the same
starting point" 
Me:


"I
see, Sir. Yes, I understand it now, but can you PROVE that...."  blink  blink
:) 
Fourier:


"Of course, I can
young man. 1f + 1/3 ( 3f) + 1/5 ( 5f) + ..... and so on in eternity 
Me:


That seems
right, Sir, I believe you. But please, come over here and see my tone generator.
I have removed the top. It is an old Trio, but it is real good" 
Fourier:


"Trio ? ", takes
a good and long look in to the PCB.. "What are all these small black things
?" 
Me:


"Oh,
that would be transistors, Sir, and ICs" 
Fourier:


"Hmm...Where are
all the transformers ? " 
Me:


"
That will be a long tale, Sir ... Lets just get down to the basic. We do not have
all time". 
Fourier:


" I'm in no hurry.
I kind of like being here. You have so many interesting things , and you talk funny" 
Me:


"
 Funny..?... Hmm.. yes...Well, this is a generator , as you know, and it produces
sine waves and square waves" 
Fourier:


"Yes, yes, I know
that. I just could not spot the spark gap relay" 
Me:


"
Spark..?...No,  but what I mean, is I do not have an eternal amount of sine wave
generators in here, I only have one. And yet it is capable of producing perfect square
waves"? 
Fourier:


"Ha, ha.. You are
so funny young man. You only need two batteries, and a shift relay to produce a square
wave. It is a DC value, don't you get it ? "  Smiling from his head to his
knees... 
Me:


"Ahem,
yes, I hope I do.... At least to some degree , but what about your statement before,
with all the formulas ? " 
Fourier:


"Oh, I see what you
mean, silly young man. Do you actually imply that I claim we need a infinite amount
of odd signals to produce a single square ? Of course, not, we can make it SO many
other ways. Ha . ha. ha.... I really like being here" :) 
Me:


"But,
Sir, I am only to...." 
Fourier:


"Now, hush, young
man, and I will explain it to you.. Ha, ha....This is SO funny..  What I am proving
with the square is that my analysis about the mathematical relation of sine waves
signals, holds water. ANY signal can be composed and resolved in to sinewaves..Well,
at least it goes for PERIODIC signals. The discrete sine wave is the fundamental
signal, that can not be parted further.  According to the math that is..." 
Me:


"Periodic
signals ? " 
Fourier:


"Yes, you know something
that is repeated again and again.  A rotation, like a sine wave" 
Me:


"Ah,
I see. So it does not covers for music signals, like an orchestra ?" 
Fourier:


"No, of course not.
I never said that.The definition of a sine wave is 2 pi at constant seconds, that
is electronically constant amplitude Vpeak sinus times 2 Pi. f seconds + constant
phase angle. Certainly no music instrument signal at all is composed of such, young
man. Musical instruments, as well as any other natural sound, may not even complete
the entire cycle ( = sine wave ), and the fundamental is always gradually falling
in amplitude.  Think of all the harmonics coming from say a violin string, the wood
mechanics and reflections ? They bend and move in and out of phase, frequency and
amplitude... Not to speak of all the reflections and intermodulation and tone difference
that takes place... No, you would be very lucky indeed, if you as much as found one
single entire pure sine wave, or even two periods repeating to become a cycle, son.
 And do remember, that it takes at least two 100% identical periods to define/identify
a cycle." 
Me:


"Thank
you very much Mr. Fourier. I am glad you would attend here to night and help us all
with the questions we have discussed. I am sure we are all better informed now. At
least I understand the matters better now"
 Goodnight, Mr. Fourier" 