A digital signal generation assumes that a base frequency (the frequency with which the primitive phase angles are specified relative to) is equal to the carrier frequency for all relevant times. But this causes errors in the digital signals output to each array element transducer. Thus, it is necessary for the development of a signal generation system that is capable of producing a digital signal using the free selection of amplitude and phase. This is used to produce a substantially error-free signal that preserves the amplitude and phase relative to a constant base frequency while allowing the carrier frequency to vary.