This paper proposes systolic array architectures for compuataion of the 1-D and 2-D discrete wavelet transform (DWT). The proposed systolic array for compuataion of the 1-D DWT consists of L processing element (PE) arrays, where the PE array denotes the systolic array for computation of the one level DWT. The proposed PE array computes only the product terms that are required for further computation and the outputs of low and high frequency filters are computed in alternate clock cycles. Therefore, the proposed architecuter can compute the low and high frequency outputs using a single architecture. The proposed systolic array for computation of the 2-D DWT consists of two systolic array architectures for comutation of the 1-D DWT and memory unit. The required time and hardware cost of the proposed systolic arrays are comparable to those of the conventional architectures. However, the conventional architectures need extra processing units whereas the proposed architectures fo not. The proposed architectures can be applied to subband decomposition by simply changing the filter coefficients.