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A small doubt regarding modulation Answered

Hi guys!

I have a doubt regarding modulation process, more specifically regarding the spectrum.
I understand the spectrum of sinusoidal signals, the amplitude or energy is concentrated at a particular frequency, say Fm, and hence the delta functions. But why is the spectrum of the unmodulated message(original) signal always displayed only in the shape of triangle? I have been going nuts over this question. 
I have attached the images just in case

10 Replies

Orngrimm (author)2013-01-23

They arent normally drawn a single-line-spikes since most sources arent this "clean". And while an accurate real-world-form is much more complicated to draw as freehand, the triangles are quite close to the real deal.

And yes: as charmquark (what a name BTW! :)) posted: It is a convention.
But in my oppinion, if you draw them as squares, thats quite a distance to the "real-like" triangles which represent the expected distribution in the time-domain.
See as an example http://www.dxsatcs.com/sites/default/files/satellite/74-0east-ku/Edusat%20at%2074.0E-archived%20spectral%20analysis-6.4.2009-w.jpg where you can see the triangle-like features of the signal-analysis.

Bottom-line: Yes. It is a convention. But one that makes sense.

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charmquark (author)Orngrimm2013-01-23

Oh! Now it all seems to make sense!
As usual, thanks "orngrimm" for the useful graphs, (also for the appreciation of my name if you meant it :3) and yes Steve does deserve the credit! the other users, Steve and kelseymh, thanks for the explanation! : )

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Orngrimm (author)steveastrouk2013-01-23

Mea culpa! Mea culpa maxima!
Sorry, steveastrouk! After 14h of work i was a _bit_ tired and simply mixed up the two names...
To make it clear and give steveastrouk the flowers he deserves:
It was steveastrouk, who said (correctly by the way) that it is a convention.

Can you forgive me, steve?

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kelseymh (author)Orngrimm2013-01-23

As a further "complication", the signal peaks are not triangles, they are generally Gaussian shapes, often called "bell curves.", which sit on top of a uniform (either flat or slowly varying) background noise across all frequencies.

A Gaussian is characterized by its central position (the peak), and its width (either the full width at half maximum, FWHM, or the standard deviation "sigma"). The width, or the ratio of height to width, is sometimes referred to as the "Q value" or quality of the signal.

I have simplified my description as a physicist will, and I'm sure Steve can clarify the even more complex nature of real signals :-)

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steveastrouk (author)kelseymh2013-01-23

What we engineers call "the fuzzy bits", to use the technical term.

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steveastrouk (author)2013-01-21

Its just a convention.Its a generic source

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charmquark (author)steveastrouk2013-01-21

So it's nothing but a convention? Which means, if situation arises, or if i want to, i can replace those triangles with, say, squares?

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