This paper presents unified VLSI architectures which can efficiently realize some widespread one-dimensional (1-D) and two-dimensional (2-D) real discrete trigonometric transforms, including the discrete Hartley transform (DHT), discrete sine transform (DST), and discrete cosine transform (DCT). First, succinct and unrestrictive Clenshaw's recurrence formula along with the inherent symmetry of the trigonometric functions are adequately employed to render efficient recurrences for computing these 1-D RDTT. By utilizing an appropriate row-column decomposition approach, the same set of recurrences can also be used to compute both of the row transform and column transform of the 2-D RDTT. Array architectures, basing on the developed recurrences, are then introduced to implement these 1-D and 2-D RDTT. Both architectures provide substantial hardware savings as compared with previous works. In addition, they are not only applicable to the 1-D and 2-D RDTT of arbitrary size, but they can also be easily adapted to compute all aforementioned RDTT with only minor modifications. A complete set of input/output (I/O) buffers along with a bidirectional circular shift matrix are addressed as well to enable the architectures to operate in a fully-pipelined manner and to rectify the transformed results in a natural order. Moreover, the resulting architectures are both highly regular, modular, and locally-connected, thus being amenable to VLSI implementations.
