RINGS, FIELDS AND CHINESE REMAINDER THEOREM AND AN EXTENSION .2. APPLICATIONS TO DIGITAL SIGNAL-PROCESSING

In Part I of the research work, we introduced an extension to the well known Chinese remainder theorem for processing polynomials with coeff icients defined over a finite integer ring. We term this extension as the American-Indian-Chinese extension of the Chinese remainder theorem . A systematic procedure for factorizing a monic polynomial into pairw ise relatively prime monic factor polynomials over integer rings was p resented. This factorization is based on the corresponding factor poly nomials, monic and relatively prime, over the associated finite field containing prime number of elements. In this paper, we study the appli cation of the theory developed in Part I to deriving computationally e fficient algorithms for performing tasks having multilinear form. Espe cially, we focus on the cyclic and acyclic convolution as they are two of the most frequently occurring computationally intensive tasks in d igital signal processing.