Lossless transform coding system for digital signals

Abstract

The invention provides a reversible eight-element discrete cosine transform system which can be realized with a practical circuit and provide transform values proximate to those obtained by actual eight-element discrete cosine transform. In 4.times.4 matrix transform which appears when eight-element discrete cosine transform is decomposed in accordance with a high speed calculation method, transform values (X.sub.1, X.sub.7, X.sub.3, X.sub.5) are divided into (X.sub.1, X.sub.7) and (X.sub.3, X.sub.5), and if (X.sub.1, X.sub.7) are determined, then possible values as (X.sub.3, X.sub.5), are limited. This is utilized for quantization of the elements. (X.sub.1, X.sub.7) are quantized with step sizes of k.sub.1 and k.sub.2 by operators to obtain quantization values (Q.sub.1,) Q.sub.7). Meanwhile, from (X.sub.3, X.sub.5), global quantization values are obtained by a quantizer using a conventional reversible quantization technique while local quantization values are obtained using a second numerical value table, and quantization values (Q.sub.3, Q.sub.5) are obtained from the values of the gloval quantization values and the local quantization values. Then, an eight-element discrete cosine transform system is constructed by a combination of reversible transform quantization of a 4.times.4 matrix and conventional reversible transform quantization of a 2.times.2 matrix.