A new convolutional formulation of discrete cosine transform for systolic implementation

A simple convolutional formulation of discrete cosine transform (DCT) is proposed to compute an N-point transform through two pairs of [(M-1)/2]-point cyclic convolutions, where M is any odd number and M = N/2. Besides, a regular and locally connected linear array architecture is presented for concurrent pipelined systolization of all the four cyclic convolutions. It is shown that not only the proposed structure is simpler but also it involves significantly less area-time complexity compared with that of the existing structures. Moreover, it does not need control tag-bits that are otherwise involved in most of the existing convolution-based DCT structures. For low-speed applications, the hardware-complexity of the proposed structure can be reduced to half by using a clock period of twice the duration, and folding the multiplications and additions in the processing elements (PEs). Similarly, when higher speed- performance is required, the throughput can be doubled and latency can be reduced to half by doubling the number of multipliers and adders in the PEs.