In this study, we study the decomposition of signals, namely mono-component decomposition, in which signals are decomposed into a series of components, each of which has a non-negative instantaneous frequency. Given a real-valued 2π-periodic signal f, let Ã(f)= f+ iH(f) to be the complex-valued analytic signal associated to f such that “H(Ãf)=-iÃ(f)where H "is the circular Hilbert transform. Rewrite Ãf(t) in polar form ρ(t)e^(iθ(t)), then f is called mono-component if f'(t)> 0 almost everywhere. We know that if Ãf is starlike on unit disc, then '(t)>0, hence f is mono-component. In this thesis, we make use of starlike criteria and Fourier series to construct a mono-component decomposition, and such decomposition is adaptive respect to the signals.