In recent years, the capacity and charging speed of batteries have become the bottleneck of mobile communications systems. With the development of wireless power transfer technologies, simultaneous wireless information and power transfer (SWIPT) becomes a possible alternative. Due to the limitations of practical circuit implementation, the energy harvesting circuit cannot directly decode the information carried by the same signal. Hence, the problem of optimal power splitting at the receiver arises in addition to the conventional problem of power allocation in communication systems. In this paper, the joint power allocation and splitting (JoPAS) for SWIPT over a timevariant channel is proposed with the objective of maximizing the achievable data rate with constraints on the delivered power. Simulations show significantly improved performance compared with the existing dynamic power splitting scheme. A suboptimal algorithm, named decoupled power allocation and splitting (DePAS), is also proposed with dramatically reduced computational complexity and simulations demonstrate its near optimum performance.