Assume-guarantee reasoning is a popular and expressive paradigm for a modular and compositional specification of programs. It is in turn of becoming a fundamental concept in mainstream industrial computer-aided design tools for embedded system design. In this paper, we elaborate new foundations for contract-based embedded system design by proposing a general-purpose algebra of assume/guarantee contracts based on two simple concepts: first, the assumption or guarantee of a component is defined as a filter and, second, filters enjoy the structure of a Boolean algebra. This yields an algebraically rich structure which allows us to reason on contracts.