We consider the problem of designing a pulse shaping filter for a digital communication system where some spectral mask constraints must be satisfied. Since the constraints are nonconvex in the filter tap weights and are semi-infinite (each corresponding to a frequency point), the pulse shaping design problem has long been considered a difficult task. In this work, we provide a convex reformulation of the spectral mask constraints using linear matrix inequalities. This reformulation allows the pulse shaping filter design problem to be efficiently solved using the recently developed interior point methods for semidefinite programming. Our reformulation can be considered as an extension of the well known positive real lemma in the area of systems and control. Some computational results will be given.