In this paper, we propose a unified systolic array for the computation of the 2D discrete cosine transform/discrete sine transform/discrete hartley transform (DCT/DST/DHT). The unified systeolic array for the 2D DCT/DST/DHT is a generalization of the unified systolic array for the 1D DCT/DST/DHT. In order to calculate the 2D transform, we compute 1D transforms along the row, transpose them, and obtain 1D transforms along the column. When we compare the proposed systolic array with the conventional method, our architecture exhibits a lot of advantages in terms of latency, throughput, and the number of PE's. The simulation results using very high speed integrated circuit hardware description language (VHDL), international standard language for hardware description, show the functional validity of the proposed architecture.