Described is a cognitive signal processor (CSP) for signal denoising. In operation, the CSP receives a noisy signal as a time-series of data points from a mixture of both noise and one or more desired waveform signals. The noisy signal is linearly mapped to reservoir states of a dynamical reservoir. A high-dimensional state-space representation is then generated of the noisy signal by combining the noisy signal with the reservoir states. A delay-embedded state signal is generated from the reservoir states. The reservoir states are denoised by removing noise from each reservoir state signal, resulting in a real-time denoised spectrogram of the noisy signal. A denoised waveform signal is generated combining the denoised reservoir states. Additionally, the signal denoising process is implemented in software or digital hardware by converting the state-space representation of the dynamical reservoir to a system of delay difference equations and then applying a linear basis approximation.