Orthogonal Approximation of the Discrete Cosine Transform

The eecient implementation of the discrete cosine tansform is discussed in this paper. The architecture, that is used, is a systolic processor array consisting of orthonormal rotations. The angles of these rotations are denoted by ij. With respect to a simple VLSI implementation an approximation of the DCT is realized. The approximation is obtained by using approximate (orthogonal) rotations. I.e. the exact rotations (ij) are replaced by approximate rotations (~ ij), whereby a rotation over ~ ij can easily be implemented using simple shift and add operations. The use of approximate rotations guarantees an eecient implementation of each rotation and, therefore, for the whole transform. The orthogonality of the transform is preserved, and therefore, also the possibility of perfect reconstruction. The coeecients of the transform matrix are approximated to a high accuracy, such that the diierence to the exact DCT can be neglected with respect to practical applications. The Discrete Cosine Transform (DCT) 5, 8] is the core of many signal processing algorithms. This is due to the fact, that this transform seems to be nearly optimal to decorrelate certain signals. Therefore, the DCT has its rm place in image processing 6]. An image is usually divided in subblocks of size 8x8 or 16x16, which are then transformed by the DCT. The transformed subblocks are quantized and coded, before being sent to the receiver, where the image is restored by using the inverse Discrete Cosine Transform (IDCT). With the advent of High Deenition TV (HDTV) and its large amount of image data, it is more important than ever to compress the data without loosing too much information. In addition HDTV demands processing of the image data in real time necessitating an eecient implementation of the used algorithm. In this paper an architecture for the DCT using a sy-stolic processor array is introduced 1]. This array can also be used for any other orthogonal signal transform. The systolic array performs the transform by n(n?1)=2 orthogonal rotations. Each processor must execute an orthogonal rotation. Implementing a fast DCT would be an alternative, but less exible. For the presented approach not the overall implementation of the transform is of primary interest, but the realization of the orthonormal rotation in each processor. In order to obtain a simple implementation of these rotations, the exact rotations are approximated by a sequence of {rotations 7]. Thereby, the exact angle can be approximated to an arbitrary high …