Loudspeaker array beamforming technology has been widely used; however, current frequency-domain; time-domain design methods for calculating FIR filters face challenges, including the need for modeling delay; high computational complexity. To address these issues, this paper proposes a time–frequency integrated framework. This framework supports both pressure matching; amplitude matching methods, enabling not only the realization of traditional superdirective beams but also the design of frequency-invariant beams. For the nonlinear optimization problem in amplitude matching, an efficient solving algorithm based on the Alternating Direction Method of Multipliers (ADMM) is introduced. Experimental results demonstrate that the proposed method combines the advantages of existing frequency-domain; time-domain approaches, directly computing FIR filter coefficients without delay modeling while maintaining high computational efficiency. This provides an effective solution for beam control in loudspeaker arrays.
