An Analysis of Error Behavior in the Implementation of 2-D Orthogonal Transformations

The paper analyzes the effect of finite-length arithmetic in the calculation of 2-D linear transformations employed in some picture coding algorithms. Since the condition of zero-error in general direct and reverse transformations leads to results of little practical importance, an analysis is carried out on the statistical properties of error in 2-D linear transformation with given length of arithmetics. Then the important case of discrete cosine transform (DCT) applied to real images is considered in detail. The results of the paper allow a circuit designer to determine the representation accuracy of the one- and two-dimensional coefficients required to satisfy a preassigned reconstruction error on the image.