A spatial-audio recording system includes a processor, and instructions stored in a computer-readable medium that, when read by the processor, cause the processor to perform operations. The operations include retrieving audio data recorded at a number of microphones, determining a recorded signal vector based on the audio data, and initializing values for an operator. The operations further include determining a plurality of waves from directions by performing operations comprising iteratively, until an exit condition is satisfied - initializing or incrementing an index “i”; determining an ith direction using the operator; and updating the operator to correspond to the ith iteration.