An input signal that includes narrowband interference is spectrally enhanced by an adaptive circuit that supplies as output signal(s), portion(s) of NBI at one or more frequencies that change adaptively. The output signal(s) are used in one or more tone predictor(s) to generate, based on prior values of the NBI portion, one or more predicted tone signals that are subtracted from a received signal containing the NBI, and the result is used in the normal manner, e.g. decoded. The adaptive circuit and the one or more tone predictor(s), form a feed-forward NBI predictor wherein the received signal is supplied as the input signal of the adaptive circuit. The result of subtraction may be supplied to a slicer that slices the result, yielding a sliced signal which is subtracted from the received signal to generate a signal can be used as the input signal, to implement a feedback NBI predictor.