We present a new technique for estimating the specular peak of the bidirectional reflectance distribution function (BRDF) based on finite rate of innovation (FRI) sampling. The specular component of the BRDF varies rapidly, so it is challenging to acquire it by pointwise sampling. Yet, the knowledge of its precise location is key to render realistically complex materials. We show how to adapt the FRI framework to accurately determine the location of a single pulse when the sampling kernel is unknown. We use this result to determine the position of the specularity, and then estimate its shape by non-linear optimization. We demonstrate the feasibility of our approach in simulations and via a practical experiment using a custom-built BRDF acquisition device.