Described is a Neuromorphic Adaptive Core (NeurACore) cognitive signal processor (CSP) for wide instantaneous bandwidth denoising of noisy signals. The NeurACore CSP includes a NeurACore block, a globally learning layer, and a neural combiner. The NeurACore block is operable for receiving as an input a mixture of in-phase and quadrature (I/Q) signals and mapping the I/Q signals onto a neural network to determine complex-valued output weights of neural states of the neural network. The global learning layer is operable for adapting the complex-valued output weights to predict a most likely next value of the input I/Q signal. Further, the neural combiner is operable for combining a set of delayed neural state vectors with the weights of the global learning layer to compute an output signal, the output signal being separate in-phase and quadrature signals.