Synthesis of new composite orthonormal kernels

A number of products of arrays can be defined by using various functional relations to define the indexes of the resulting array in terms of the corresponding indexes of the component arrays. Some examples of such products are proposed in this paper which give an orthonornal matrix of higher order in terms of component orthonormal matrices of lower order. The technique developed in this paper can be used in the annlysis and design of linear systems with longer inputs in terms of component systems with smaller inputs.