In this letter, we define the generalized doubly stochastic processing via Jacket matrices of order-2n and 2n with the integer, n≥2. Different from the Hadamard factorization scheme, we propose a more general case to obtain a set of doubly stochastic matrices according to decomposition of the fundaments of Jacket matrices. From order-2n and order-2n Jacket matrices, we always have the orthostochastoc case, which is the same as that of the Hadamard matrices, if the eigenvalue λ1 = 1, the other ones are zeros. In the case of doubly stochastic, the eigenvalues should lead to nonnegative elements in the probability matrix. The results can be applied to stochastic signal processing, pattern analysis and orthogonal designs.

The paper shows some of benefits of multi-unitary decomposition in signal analysis applications. It is emphasized that decompositions of complex discrete-time signals onto a single basis provide an incomplete and in such way potentially misleading image of the signals in signal analysis applications. It is shown that the multi-unitary decimated filter banks which decompose the analyzed signal onto several bases of the given vector space can serve as a tool which provides a more complete information about the signal and at the same time the filter banks can enjoy efficient polyphase component implementation of maximally decimated, i. e. nonredundant, filter banks. An insight into the multi-unitary signal decomposition is provided. It is shown that the multiple-bases representation leads to an efficient computation of frequency domain representations of signals on a dense not necessarily uniform frequency grid. It is also shown that the multiple-bases representation can be useful in the detection of tones in digital implementations of multifrequency signaling, and in receivers of chirp systems. A proof is provided that there are possible benefits of the multiple-bases representations in de-noising applications.