Periodic spline wavelets provide an efficient tool to analyze periodic signals. Wavelet analysis gives its best performance when it is applied to detect transients or local events in the signal. However, it is not well suited to characterize stationary phenomena. To overcome this problem we propose a new family of periodic spline functions, capable of playing the role of trigonometric wave-forms. They lead us to an orthogonal decomposition of the signal into quasi-monochromatic spline waves. Further, a full collection of periodic spline wavelet packets is also proposed. These elemental functions can be organized in a large library of orthonormal bases. Thus, one can analyze any periodic signal in accordance with a well adapted strategy.