Sidebands in AM Transmission

nsaspook

Signal Decomposition, used to analyze a signal.
http://users.ece.gatech.edu/~vkm/nii/node35.html

Yes, the sideband frequencies are actually transmitted along with the carrier (the actual carrier average power does not change during AM modulation).

http://www.technology.heartland.edu/...modulation.ppt

sophiecentaur

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 ω_c with a cosine modulating signal of frequency ω_m does:
A =A₀Cos(ω_ct)(1+Bcos(ω_mt))

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(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.

Drakkith

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

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

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

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

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

Not always.

sophiecentaur

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.