Systems and methods are provided for source localization and separation by sampling a large scale microphone array asynchronously to simulate a smaller size but moving microphone array. Signals that arrive from different angles at the array are shifted differently in their frequency content. The sources are separated by evaluating correlated and even equal frequency content. Compressive sampling enables the utilization of extremely large scale microphone arrays by reducing the computational effort orders of magnitude in comparison to standard synchronous sampling approaches. Processor based systems to perform the source separation methods are also provided.