An efficient unified systolic architecture for the computation of discrete trigonometric transforms

In this paper, a novel unified systolic architecture which can efficiently implement various discrete trigonometric transforms (DXT) including the discrete Fourier transform (DFT), the discrete Hartley transform (DHT), the discrete cosine transform (DCT), and the discrete sine transform (DST) is described. Based on Clenshaw's recurrence formula, a set of efficient recurrences for computing the DXT is developed first. Then, the inherent symmetry of the trigonometric functions is further exploited to render a hardware-efficient, systolic structure. For the computation of any N-point DXT of interest, the proposed structure re quires only about N/2 multipliers and N adders,.thus providing substantial hardware savings compared with previous works. Furthermore, the new scheme can be easily adapted to compute any type of DXT with only minor modification. The complete I/O buffers have been addressed as well which allows for a continuous flow of successive blocks of input data and transformed results in natural order.