Fourier Series (in reverse) In electronics (and in other fields of engineering), we study that every periodic signal (whatever its shape) may be decomposed in a series of sine waves with frequency $f, 2f, 3f, \ldots, nf$ with decreasing amplitudes. This is the basics of Fourier Series.  
I've carried with me one question that I never have seen any answer: can we prove the opposite of this?  
Let me explain in more detail: if I have a sine wave of amplitude $A$ and frequency $f$, can I decompose the sine wave in a series of square waves (or triangular, or whatever) with frequencies $f, 2f, 3f, \ldots, nf$ with decreasing amplitudes? 
If the answeer is yes, please indicate me bibliography where can I find such math demonstration. 
Thank you 
Carlos
Lisbon, Portugal
 A: The paper DN Green, SC Bass, Signal representation with triangular
basis functions, IEE Journal on Electronic Circuits and Systems, vol. 3, Mar. 1979, p. 58-68 states the following result: A signal possesses a trigonometric series representation if and only if it has a "triangular series" representation.
However, as Robert points out in the comment, there is no reason to believe that the amplitudes of the triangular wave components are decreasing.
A: 
Let me explain in more detail: if I have a sine wave of amplitude  and frequency , can I decompose the sine wave in a series of square waves (or triangular, or whatever) with frequencies ,2,3,…, with decreasing amplitudes?

Roughly, Yes

*

*The sine wave is just another function

*You can de-compose any function onto an orthonormal basis of functions

Basically this is linear algebra, and you are doing a "projection" onto each of the axes (functions) to get your coefficients.
You may have to "normalize" your functions so that they have "unit length".
I'm being sketchy here, get a good linear algebra book for all the details.
