Fig. 1: Principle of non-reciprocal acoustic harmonic conversion.
From: Observation of non-reciprocal harmonic conversion in real sounds

a Forward configuration, b Backward configuration. Active controls are defined by using the pressures (PNL, PL1, and PL2) sensed in front of each cell (cell NL, L1, and L2) as the respective control inputs. Non-linear control is applied to the cell NL for higher harmonic generations, with GNL the constant gain to tune the level of non-linearity. Linear control is applied to the cells L1 and L2 for fundamental wave elimination, with Φ1 and Φ2 the transfer functions for the impedance adjustments (See the Method section and Supplementary Note 2 for details).