A general linear theory is presented which describes the extension of the convolutional method to nonstationary processes. Two alternate extensions are explored. The first, called nonstationary convolution, corresponds to the linear superposition of scaled impulse responses of a nonstationary filter. The second, called nonstationary combination, does not correspond to such a superposition but i...

In this correspondence we investigate the performance of the Lempel–Ziv incremental parsing scheme on nonstationary sources. We show that it achieves the best rate achievable by a finite-state block coder for the nonstationary source. We also show a similar result for a lossy coding scheme given by Yang and Kieffer which uses a Lempel–Ziv scheme to perform lossy coding.

The Baum-Welch algorithm is a technique for the maximum likelihood parameter estimation of probabilistic functions of Markov processes. We apply this technique to nonstationary Markov processes and explore a relationship between the Baum-Welch algorithm and the BCJR algorithm. Furthermore, we apply the Baum-Welch algorithm to two nonstationary Markov processes and obtain the turbo decoding algo...

Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite. Keywords—Linear systems, Hermitian matrices, Positive definite matrices, Iterative methods, Nonstationary methods, Two-stage methods.

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra the solutions of nonstationary Pauli equation are generated. PACS number(s): 03.65.-w; 11.30.Pb

In this paper we consider the problem of source separation for the case that sources are (second-order) nonstationary, especially their variances are slowly time varying. The differential correlation is exploited in order to capture the time-varying statistics of signals. We show that nonstationary source separation can be achieved by differential decorrelation. Algebraic methods are presented ...

A partition of unity (POU) is a discrete set of usually overlapping windows that sum exactly to one for a finite interval on the real line. Multiplying a signal by the POU decomposes it into a set of temporally localized signals or Gabor slices. Applying any stationary operator to these slices and allowing the operator to depend upon the slice defines a nonstationary operator. We apply a statio...

Nonstationary metabolic flux analysis (NMFA) is at present a very computationally intensive exercise, especially for large reaction networks. We applied elementary metabolite unit (EMU) theory to NMFA, dramatically reducing computational difficulty. We also introduced block decoupling, a new method that systematically and comprehensively divides EMU systems of equations into smaller subproblems...

We use the nonstationary equivalent of the Fourier shift theorem to derive a general one-dimensional integral transform for the application and removal of certain seismic data processing steps. This transform comes from the observation that many seismic data processing steps can be viewed as nonstationary shifts. The continuous form of the transform is exactly reversible, and the discrete form ...