  Active cancellation of broadband random noise requires the detection of the
incoming noise with some time advance. In an duct for example this advance must
be larger than the delays in the secondary path from the control source to the
error sensor. In this paper it is shown that, in some cases, the advance
required for perfect noise cancellation is theoretically infinite because the
inverse of the secondary path, which is required for control, can include an
infinite non-causal response. This is shown to be the result of two mechanisms:
in the single-channel case (one control source and one error sensor), this can
arise because of strong echoes in the control path. In the multi-channel case
this can arise even in free field simply because of an unfortunate placing of
sensors and actuators. In the present paper optimal feedforward control is
derived through analytical and numerical computations, in the time and
frequency domains. It is shown that, in practice, the advance required for
significant noise attenuation can be much larger than the secondary path
delays. Practical rules are also suggested in order to prevent infinite
non-causality from appearing.
