Systems and methods for interference suppression with directional sensing patterns

System (10) is disclosed including an acoustic sensor array (20) coupled to processor (42). System (10) processes inputs from array (20) to extract a desired acoustic signal through the suppression of interfering signals. The extraction/suppression is performed by modifying the array (20) inputs in the frequency domain with weights selected to minimize variance of the resulting output signal while maintaining unity gain of signals received in the direction of the desired acoustic signal. System (10) may be utilized in hearing, cochlear implants, speech recognition, voice input devices, surveillance devices, hands-free telephony devices, remote telepresence or teleconferencing, wireless acoustic sensor arrays, and other applications.