Sidebands in AM Transmission


by Drakkith
Tags: sidebands, transmission
sophiecentaur
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Feb1-13, 04:32 PM
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Quote Quote by Drakkith View Post
I understand most of that, however what exactly does "decomposed" mean? Is this something that you do when the signal gets to the receiver, or are there actually two different frequencies in addition to the carrier that are being transmitted from the antenna which interfere and cause the carrier to vary in amplitude?



Are you asking me?
There is a parallel with vectors. You can 'decompose' a vector into two components along two arbitrary axes and that may make a problem easier to solve.

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 ωc with a cosine modulating signal of frequency ωm does:
A =A0Cos(ωct)(1+Bcos(ωmt))

A0 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(ωc) + Bcos((ωmc)/2 + B((ωmc)/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.
Drakkith
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Feb1-13, 05:45 PM
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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!
nsaspook
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Feb1-13, 07:35 PM
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Quote Quote by sophiecentaur View Post
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.
Fourier analysis is complex when looked at from the viewpoint of pure mathematics but it's how our ear/brain works so it's a natural way of analyzing complex events. The inner ear is an approximation of Fourier analysis as it separates the sound energy using nerve structure filters that each only respond to a narrow range of vibrations. The brain receives the Fourier Transform of the acoustical signal, phase and intensity information and then somehow generates the patterns that we recognize as sounds.
sophiecentaur
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Feb2-13, 07:48 AM
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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.
nsaspook
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Feb2-13, 10:20 AM
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Quote Quote by sophiecentaur View Post
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.
Agreed, I did say it was an "approximation of Fourier analysis", our hearing is a blend of several methods.

http://clas.mq.edu.au/perception/psy...ng_theory.html
sophiecentaur
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Feb2-13, 04:55 PM
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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 camera-like 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.
nsaspook
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Feb2-13, 06:43 PM
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Quote Quote by sophiecentaur View Post
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.
Not always.
sophiecentaur
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Feb3-13, 06:19 AM
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Quote Quote by nsaspook View Post
Not always.
At the 'component level', perhaps and we can monitor input and output signals. I was referring to the conscious level and how that deals with what is heard and seen. I know there is some active work on brain activity, memory and 'awareness' but it isn't very far along the road yet. One day, perhaps, they will be able to identify correlators, temporal and spatial filters at work amongst the synapses but not next week.

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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