In this paper, we present new techniques for designing systolic arrya and asynchronous arrays for digital-signal processings. More specifically, we propose a systolic array with simple local interconnections which achieves optimal performance without having undesirable features such as preloading input data or global broadcasting. As asynchronous array for digital-signal processings, which can speed up the total computation time significantly is also which can speed up the total computation time significantly is also presented. The key component of the asynchronous array is a presented. The key component of the asynchronous array is a comunicaiton protocol which controls input data flow properly and efficiently. Finally, performance of the arrays is analyzed and a simulation using Occam programmed in a Transputer network is reported.