Investigation of combustion instabilities in gas turbine combustors require the knowledge of flame transfer functions. Those can be obtained by experimental measurement or by-Large Eddy Simulations (LES). Because calculations are usually limited to a portion of the whole combustor, boundary conditions are of crucial importance. It is common practice to inject acoustic perturbations for the flame transfer function measurement in form of velocity perturbations (u'(t)). We present an alternative method based on a characteristic treatment of the Euler Equations. It consists of injecting sound waves traveling into the computational inlet while letting outgoing waves leave the domain without reflection. This method has several advantages concerning the study of flame transfer functions compared to injecting velocity perturbations. Both techniques are compared for cases where analytical solutions may be derived (a duct without flame and a planar laminar flame) and for one case where a CFD code is necessary (a laminar Bunsen-type flame).