
#19
Feb113, 04:32 PM

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PF Gold
P: 11,370

But the easiest way to show how AM produces sidebands is to start with a formula which describes Amplitude Modulating a carrier wave with angular frequency ω_{c} with a cosine modulating signal of frequency ω_{m} does: A =A_{0}Cos(ω_{c}t)(1+Bcos(ω_{m}t)) A_{0} is the mean amplitude of the carrier and B is the Modulation Index  the depth of modulation. This will give you the familiar picture of a carrier amplitude varying in level, as the modulation varies, and around its unmodulated amplitude. (The envelope picture). That expression can be transformed, using the basic multiple angle trig identities into A = A(cos(ω_{c}) + Bcos((ω_{m}+ω_{c})/2 + B((ω_{m}ω_{c})/2) which shows you that the AM signal can be described as a carrier and a pair of sidebands that have up to half the amplitude of the carrier. You don't need to do any Fourier analysis for this  in the simple case, it's just a bit of simple trig. And, if you don't like trig, then steer clear of Fourier  it's harder still. 



#20
Feb113, 05:45 PM

PF Gold
P: 11,047

My god what have I gotten myself into!? This is why I don't ask questions! I get amazing answers that show me how ignorant I really am! I think I'll take some of the advice I see you give around the forum Sophie. I'll hold off on running until I can walk in this area. (Or in my case, roll over and crawl first)
Thanks guys! I don't quite understand, but I'm definitely better off than I was before. Nsaspook, thanks for the links, they were pretty helpful! 



#21
Feb113, 07:35 PM

P: 494





#22
Feb213, 07:48 AM

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PF Gold
P: 11,370

It's a bit simplistic to say that our hearing receives the FT. The cochlea does a time varying frequency analysis. Both time and frequency domains are perceived. FT is just a mathematical process relating the two domains yet is often quoted in cases where it just isn't that straightforward. Windowing is very relevant in practice.




#23
Feb213, 10:20 AM

P: 494

http://clas.mq.edu.au/perception/psy...ng_theory.html 



#24
Feb213, 04:55 PM

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PF Gold
P: 11,370

I think the big problem arises when we attempt to describe what the brain / sensor combination 'actually does' with its input, using the same terms that we use to describe how we would make a recording or perform signal analysis using technology.
The same difficulty arises when describing our visual perception, where the temptation is to think that the cameralike structure of the eye's hardware gives the remotest clue about how we make a conscious model of our surroundings in our heads. I think this thread would be better to stick to the basics of signal processing, where we do have a chance of understanding what goes on. At least the Maths is appropriate and fits the evidence. 



#25
Feb213, 06:43 PM

P: 494





#26
Feb313, 06:19 AM

Sci Advisor
PF Gold
P: 11,370

Actually, I should qualify that a bit. The Cochlea and the interconnections on the retina are examples of just those structures. 


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