Fast algorithm for “error-free” convolution computation using Mersenne–Lucas codes

In this paper a new “error-free” algorithm for discrete circular convolution is proposed. The algorithm is based on new type of discrete orthogonal transforms for which there exist efficient multiplication-free implementations. The structure of these transforms is associated with the representation of data in the redundant number system associated with Lucas numbers. Numerical experiments to investigate the properties of these transform were performed, the obtained results are provided.