Most multimedia sources are bursty in nature, a property which can be used to trade queuing delay with the resulting average transmission power [2, 3, 4]. In this paper, we study the relation between average transmission power and strict delay constraints. Our main contributions are two-fold. First, we establish necessary and sufficient conditions on the service rates of the wireless transmitter, to meet the delay deadline of every packet in the queue. Second, the conditions are used to show that a scheduler which meets a delay guarantee Dmax for each of the packet over Gaussian channels is a time-varying low-pass filter of order no more than Dmax. This confirms the intuitive explanation for power reduction due to additional queuing delay provided in [3]. Using the relation between delay bounded scheduling and linear filtering, we construct schedulers without the knowledge of source statistics. This marks a significant departure from most information theoretic work on power efficient scheduling [2, 3]. We construct the optimal time-invariant scheduler, which does not require the knowledge of the source statistics.