In this contribution, a new simultaneous amplitude and phase approximation for wave digital lattice structures is introduced. It is relying on the orientation of one of the two branch polynomials to adjust the amplitude, while the other is oriented to adjust the phase. The approximation process starts with proper initial settings for the two branch polynomials according to the given amplitude and phase specifications. Then, the two branch polynomials are generated alternatively. This means that during one polynomial is generated to approximate the amplitude or the phase, the other polynomial is fixed. By iterating this alternative procedure, the two polynomials and consequently the amplitude and phase converge to their optimal response. Interpolation method combined with the Remez-exchange algorithm is employed for this purpose. Finally, the filter structure is synthesized and the wave digital realization is reached.