A separate filter circuit is inserted between the D/A converter and the summing junction in the feedback path of a conventional sigma delta modulator. This additional filter allows control of the quantization noise transfer function profile independently of the forward signal transfer function. By proper tailoring of the transfer functions a third or higher order modulator can be constructed without instability developing. The modulator can also be constructed as a completely digital circuit and used as a noise shaping circuit in a digital digital-to-analog converter.