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In this paper we generalize the Sato theory to the extended bigraded Todahierarchy (EBTH). We revise the definition of the Lax equations,give the Satoequations, wave operators, Hirota bilinear identities (HBI) and show theexistence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of itsFay-like identities and Hirota bilinear equations (HBEs) in terms of vertexoperators whose coefficients take values in the algebra of differentialoperators. In contrast with HBEs of the usual integrable system, the currentHBEs are equations of product of operators involving $e^{\partial_x}$ and$\tau(t)$.

Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy