[R] plot sin wave and fft

[Randall A. Blake]

I am reading John R. Pierce's An Introduction to Information Theory and read 
that any wave can be decomposed into simple sin waves by means of a Fourier 
analysis.  I would like to play with the idea a little and want to plot a 
couple simple sin waves in R; add them together as if they were being 
transmitted simultaneously over a single wire; and then "decompose" the 
aggregate signal back into its components using a FFT (I suppose).  Can 
anyone point me to a tutorial which would get me going on this project? 

Thanks, RAB