Fourier Analysis For Dummies

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

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

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

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:

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.

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

tim

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:

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

. . .

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

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.

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.

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...

Michael

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

;-) Rich

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

Wha...??

Thanks, Rich

@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.

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

Thanks and regards

Mike M> This should be helpful to those who have difficulty visualizing Fourier

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