Also, the signal you want to represent as Fourier (using a sum of sin and cos waves) must be a
periodic signal. Periodic signals cannot carry any
information since they are of a regular pattern. Information signals are non-periodic. Thus, application of the Fourier Series is very limited.
To represent non-periodic signals as summations of sin and cos waves, one needs to use
Fourier Transform and not Fourier Series. Laplace Transforms also deal with non-periodic signals.
Hope this helps.