This paper presents an identification scheme for sparse FIR systems with quantised data. We consider a general quantisation scheme, which includes the commonly deployed static quantiser as a special case. To tackle the sparsity issue, we utilise a Bayesian approach, where an l(1) a priori distribution for the parameters is used as a mechanism to promote sparsity. The general framework used to solve the problem is maximum likelihood (ML). The ML problem is solved by using a generalised expectation maximisation algorithm.