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Since 1974 considerable interest has been shown in the literature in the topic of number theoretic transforms. These transforms provide an efficient integer processing technique for convolution. Microprocessors are suited to integer processing particularly for applications where the required processing load is small. It was therefore a natural step to investigate and tailor the properties of number theoretic transforms to the capabilities of microprocessors to provide cheap and compact processors using efficient signal processing algorithms. It was found that efficient number theoretic transforms could be defined using the Modulus M = 65521 and this is especially convenient for a microprocessor implementation. Relevant aspects of modular arithmetic are investigated. The techniques developed are extended to allow for complex signal processing. In conclusion it is shown that number theoretic transforms can be used to encode and decode Reed-Soloman error correcting codes.

The initial phase of the research programme involves the design, development and construction of a reliable and versatile Video Acquisition and Display System (VADS) to provide a means of subjective evaluation of the results of computer simulations. An orthogonal transformation generates a set of uncorrelated coefficients and has, in addition, an energy compaction property which leads to more efficient coding of the source data. As an introduction to its application, its use in the detection and correction of transmission errors is considered. Simulations are performed on two-dimensional Gauss-Markov sequences. One-dimensional Hadamard transformation is performed in the horizontal direction and the vertical correlation of the simulated data is exploited to achieve partial error detection and correction. Viewphone signals, particularly those derived from head and shoulder scenes, possess much spatial and temporal redundancy which may be significantly reduced at the expense of a slight, but subjectively tolerable, degree of degregation in picture quality. The discrete Cosine transform offers a corriparatively fast and efficient transformation for achieving this objective, and is used extensively here, in conjunction with various adaptive algorithms which select and code the transform coefficients for transmission on the basis of the statistical and local content of the data. Initially, twodimensional adaptive techniques are employed followed by an extension of the ideas developed to the time domain. It is demonstrated that a marked reduction in the signal transmission rate can be achieved by this method.

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