ABSTRACT
It is generally believed that the algorithms for one- and higher-dimensional digital signal processing of sequences defined in finite integer rings Z(M) and CZ(M) are more complex computationally than their counterparts in the infinite fields. This belief manifests itself in what is termed as the word sequence length constraint (WSLC). There has been some progress on tackling WSLC but, by and large, it has remained a bottleneck in the finite integer ring based algorithms. In this part, we present four research papers that the author has recently submitted for publication. The first two papers are on two- and one-dimensional cyclic convolution in Z(M) and CZ(M), where it is shown that under the non-restrictive conditions (N 1, M) = (N 2, M) = 1 and (N, M) = 1, the two- and one-dimensional cyclic convolution are as computationally complex as their counterparts in infinite fields https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/z.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/cz.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> only in the worst case.
