  We present a systematic method for computing explicit approximations to
martingale representations for a large class of Brownian functionals. The
approximations are obtained by obtained by computing a directional derivative
of the weak Euler scheme and yield a consistent estimator for the integrand in
the martingale representation formula for any square-integrable functional of
the solution of an SDE with path-dependent coefficients. Explicit convergence
rates are derived for functionals which are Lipschitz-continuous in the
supremum norm. Our results require neither the Markov property, nor any
differentiability conditions on the functional or the coefficients of the
stochastic differential equations involved.
