Summary: This study concerns on some new development of unit analytic signals with nonlinear phase. It includes triangle shape filter, generalizes Sinc function based on nonlinear Fourier atoms, generalizes sampling theorem for non-bandlimited signals. Firstly, we introduce the triangle shape filter and give its impulse response. Secondly, we establish a Shannon type sampling theorem based on generalize Sinc function for this type of non-bandlimited signals.