This paper is a contribution to the definition of a new kind of digital signal processing chain. It is focused on Finite-Impulse-Response filtering (FIR) applied to irregularly sampled signals obtained from an asynchronous analog to digital converter. The paper first formalizes the convolution operator in the irregular sampling context. The computational complexity is deduced and compared to the one of standard synchronous FIR filters. It shows that a significant reduction of the computational complexity is achievable, hence a reduction in terms of energy. The paper then describes the architecture of the asynchronous filter. It finally reports the simulations performed on a speech application, resulting in a reduction of the processing power of about one order of magnitude.