The separation of mixed auditory signals into their sources is an eminent neuroscience and engineering challenge. We reveal the principles underlying a deterministic, neural network–like solution to this problem. This approach is orthogonal to ICA/PCA that views the signal constituents as independent realizations of random processes. We demonstrate exemplarily that in the absence of salient frequency modulations, the decomposition of speech signals into local cosine packets allows for a sparse, noise-robust speaker separation. As the main result, we present analytical limitations inherent in the approach, where we propose strategies of how to deal with this situation. Our results offer new perspectives toward efficient noise cleaning and auditory signal separation and provide a new perspective of how the brain might achieve these tasks.