# Fourier Analysis For Dummies

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This should be helpful to those who have difficulty visualizing Fourier
Transforms:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Background to Fourier Techniques

The fundamental principle surrounding Fourier techniques is that all
sounds can be reconstructed from a series of sine waves.

Superposition (the  adding of waves) permits sine  waves  of varying
frequency, amplitude  and  phase  to be  conglomerated  to  form any
waveform. Figure 1 illustrates this principle with the creation of a
square wave.

http://rnowik.com/dyn/fourier4.10.gif

Figure 1 Creation of a square wave from sine waves

http://rnowik.com/document/7 /

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now all I need is an explanation on how to conglomerate sine waves:)

Regards,

Mike Monett

Antiviral, Antibacterial Silver Solution:
http://silversol.freewebpage.org/index.htm
SPICE Analysis of Crystal Oscillators:
http://silversol.freewebpage.org/spice/xtal/clapp.htm
Noise-Rejecting Wideband Sampler:

Re: Fourier Analysis For Dummies

Except that this image conveys nothing useful about Fourier
transforms or superposition of harmonics to form a square wave.

Re: Fourier Analysis For Dummies

John Popelish wrote:

I'd hope that you understand that Mike knows this.  I just dropped a
note to Rob Nowik, letting him know that if I was new to Fourier
analysis, it wouldn't take me long to figure out that that figure was
dead wrong, and as a result I wouldn't trust anything else on his
pages.

Cheers,
Tom

Re: Fourier Analysis For Dummies

One can only be glad it wasn't posted to s.e.b., although posting it
there and asking what the real result of the sinusiods would be might be
fun :)

Cheers

PeteS

Re: Fourier Analysis For Dummies

[...]

Hi Tom,

Thanks for the unexpected and very nice compliment:)

Did you see Fig. 3, where he multiplies two 1KHz signals together?

"Figure 3 illustrates the measuring of the 1000Hz component of a test
signal. The test signal happens to also be 1000 Hz, thus the product of the
two gives an entirely positive result."

It's not clear that Rob would even understand your note:)

Regards,

Mike Monett

Antiviral, Antibacterial Silver Solution:
http://silversol.freewebpage.org/index.htm
SPICE Analysis of Crystal Oscillators:
http://silversol.freewebpage.org/spice/xtal/clapp.htm
Noise-Rejecting Wideband Sampler:

Re: Fourier Analysis For Dummies

For a *product*:

(sin x) * (sin x) = (sin x)**2. The square of a sine wave would always be
positive.

The big question to be answered here is: how do you get the *product* of two
1000hz sine waves in order to look at it? Adding and multiplying are two
different things.

tim

Re: Fourier Analysis For Dummies

From the article, it's pretty clear we have been doing this wrong all
along. Rob's method is a lot more flexible, and it has the potential of
explaining everything, no matter what the question is.

All we need is to find a better conglomerator.

Regards,

Mike Monett

Antiviral, Antibacterial Silver Solution:
http://silversol.freewebpage.org/index.htm
SPICE Analysis of Crystal Oscillators:
http://silversol.freewebpage.org/spice/xtal/clapp.htm
Noise-Rejecting Wideband Sampler:

Re: Fourier Analysis For Dummies

On 09/10/2006 the venerable Mike Monett etched in runes:

.
.
.

Then the answer has the infinite improbability of being 42 ;-)

--
John B

Re: Fourier Analysis For Dummies

Mike Monett wrote:

Actually, the integration of the pointwise multiplication is a
legitimate viewpoint that considers the DFT coefficients to be
correlation coefficients of the original signal with the basis signals.
So he is halfway there, by accident or otherwise. The author is a C#
developer, which means he is not worth reading or listening to. He is
barely advanced of animal life, at best trained to mimic, hopefully
without error, and the only constant to be associated with his type is a
cogency expectation of zero. The web page is nothing more than a failed
attempt by various components of a weakly endowed schizoid to
communicate with one another, sad really.

Re: Fourier Analysis For Dummies

On 09/10/2006 the venerable Tom Bruhns etched in runes:

Perhaps you also should tell him about the plethora of spelling
mistakes on his site. On the other hand someone who takes pride in
sharing pictures of the inside of a hotel room in Seattle may not care
too much.

--
John B

Re: Fourier Analysis For Dummies

@Tom: Thanks for pointing out my mistakes. I have taken down the
relevant stuff and will amend / take down the full article when I get
time. As per the email, the article was written a long time ago, whilst
I was in the process of learning Fourier. I unfortunately hadn't
reviewed it since. Thanks.

@John B: So, because I had misunderstood some concepts, you find in
necessary to trawl my website trying to find other bits of unrelated
information to make cheap sarcastic comments with. What a nice guy you
are.

@Fred Bloggs: Sure, whatever.

Re: Fourier Analysis For Dummies

Em, not to sound too elitist, but "Fourier for Dummies" is much like
"Hippocampal retrodermal laparascopic infundibular demographic
defenestrationed Angioplasty with a sharp dole pinapple can lid".

There's very little simple, obvious, foolproof about the subject.  One
of the classic books in the field mentions in the preface "we're going
to take a simplified look at this".  You turn the page and the first
sentence of the first chapter is very much like:

"And as well known, the 44th-degree Peano convolution has eigenvalues
quasi-orthogonal to the Su-6 group, which everybody can see has direct
application to Fourier analysis"

... i put the book back on the shelf at that point.

Re: Fourier Analysis For Dummies

Ancient_Hacker wrote:

Aw man... and here I was hoping to get my hands on "Partial
Differential Equations for Dummies".

Maybe that 44th-degree Peano convolution was a joke - you'd have to
read to the second page to get the joke?

Well, this is pretty... http://en.wikipedia.org/wiki/Fourier_transform

Michael

Re: Fourier Analysis For Dummies

I was actually getting it, right up to:
"Suppose x\, is a complex-valued Lebesgue integrable function."

Wha...??

Thanks,
Rich

Re: Fourier Analysis For Dummies

Am i confused, or do i see a bunch of Engineers scared of a little medium

--
JosephKK
Gegen dummheit kampfen die Gotter Selbst, vergebens.
We've slightly trimmed the long signature. Click to see the full one.
Re: Fourier Analysis For Dummies

Do you do the surgery before or after the patient exits the window?

;-)
Rich

Re: Fourier Analysis For Dummies

Hi,

Yes, there were some pretty big (and embarrassing) mistakes in that
article (and with my understanding of fourier at the time I began
writing it). The document was mearly written from a non-mathematical
"programmers" viewpoint, and was put online so I could refer to it in
future if I got back into playing around with audio programming.

I have revisited the article, removing the inaccuracies that I am aware
of, as well a more clearly setting out the intention of the article. It
was not my intention to put up inaccurate or misleading information -
at the time I clearly just misunderstood.

If you do decide to read it again, and you have any constructive
criticism, please can you let me know via my contact form at
http://rnowik.com/contact .

Thanks and regards

Mike Monett wrote: