A hearing aid includes: a first microphone system configured for conversion of sound emitted by a sound source into a first audio signal; a first matched filter configured for filtering the first audio signal into a first filtered audio signal, the first matched filter having a first matching transfer function that substantially matches a first transfer function of a first sound propagation path leading from the sound source to the first microphone system, when a user wears the hearing aid; and a hearing loss processor configured to provide a hearing loss compensated output signal that compensates for a hearing loss of the user based at least in part on the first filtered audio signal.