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**posted on**

- Mike Monett

October 9, 2006, 12:57 pm

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:

http://www3.sympatico.ca/add.automation/sampler/intro.htm

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

[...]

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:

http://www3.sympatico.ca/add.automation/sampler/intro.htm

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:

http://www3.sympatico.ca/add.automation/sampler/intro.htm

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

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

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:

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