Removing noise in biomedical signal recordings by singular value decomposition

Noise reduction or denoising is the process of removing noise from a signal. If some signal properties are known linear filtering is often useful. Fourier, wavelet and similar transform approaches remove unwanted signal components in the codomain. For this, predefined eigen-functions, e.g. wavelets, are used. Here we use singular value decomposition in order to compute a signal driven re-presentation (eigendecompositon). By removing unwanted components of the representation the signal can be denoised. We introduce the new method, apply it to signals and discuss its properties.

Analysis of Markov renewal shock models

A trivariate stochastic process is considered, describing a sequence of random shocks {Xn } at random intervals {Y n} with random system state {Jn }. The triviariate stochastic process satisfies a Markov renewal property in that the magnitude of shocks and the shock intervals are correlated pairwise and the corresponding joint distributions are affected by transitions of the system state which occur after each shock according to a Markov chain. Of interest is a system lifetime terminated whenever a shock magnitude exceeds a prespecified level z. The distribution of system lifetime, its moments and a related exponential limit theorem are derived explicitly. A similar transform analysis is conducted for a second type of system lifetime with system failures caused by the cumulative magnitude of shocks exceeding a fixed level z.

Analysis of Markov renewal shock models

A trivariate stochastic process is considered, describing a sequence of random shocks {Xn} at random intervals {Yn} with random system state {Jn}. The triviariate stochastic process satisfies a Markov renewal property in that the magnitude of shocks and the shock intervals are correlated pairwise and the corresponding joint distributions are affected by transitions of the system state which occur after each shock according to a Markov chain. Of interest is a system lifetime terminated whenever a shock magnitude exceeds a prespecified level z. The distribution of system lifetime, its moments and a related exponential limit theorem are derived explicitly. A similar transform analysis is conducted for a second type of system lifetime with system failures caused by the cumulative magnitude of shocks exceeding a fixed level z.

Two singular integral equations involving confluent hypergeometric functions

Widder(1) obtained an inversion of the convolution transformby the method of the Laplace transform, Ln(x) being the Laguerre polynomial. Buschman (2) inverted a similar transform with a generalized Laguerre polynomial as kernel and also solved (3) the singular integral equationusing Mikusinski operators. Srivastava(4, 4a) solved singular integral equations with kernels involving and Whittaker functions Mk,μ(x).