This issue was triggered off by my friend Bhavesh who asked:
why do we always want to represent any wave/ any signal in terms of sine wave?
We represent the whole spectrum in terms of sine wave frequencies.. all our modulation techniques are based on sine wave..
why sine wave is so prominent? What is its basic charactistic that helps us?
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The answer to the key question (what is the basic characteristic that helps us?) is this:
We usually model our systems as LTI (Linear Time invariant) system.
You get the general picture if you think about basic equations which arise in *mathematical representation of real life*.
Whenever we model something, we assume (or we are taught to assume) that system is linear (so that we can easily predict the output for unknown input from the output for known inputs) and time-invariant (who likes system that will work one way today and the other way tomorrow!!).
Now here comes linear algebra. Consider input and output to be signals and the system to be an operator on those signals.
Spectral theory of linear algebra says that if we express signals as linear combination of eigenfunctions of an operator; analysis, interpretation and computation of determining output for a given input becomes very simple.
(This is because eigenfunction is a signal that remains unchanged by an operator except for some scaling or pahse-shift (or equivalent effects in other domains).)
It just so happens that complex exponentials and sinusoids are eigenfunctions of LTI systems (which are our models of real situations). We want to express our signals in terms of these eignefunctions (sinusoids) to simplify analysis, interpretation and computation.
By similar argument, if you choose some other model for your system or phenomenon sine waves are not that suitable.
