Some statistical aspects of digital Wiener filtering and detection of prescribed frequency components in time averaging of biological signals

A statistical analysis of digital a posteriori Wiener filtering as applied to time averaging techniques for biological signals is presented. The authors show that when ap.w.f. is applied to the average signal hardly any effect can be expected, where as when applied to the individual responses, ap.w.f. improves the signal to noise ratio. The applied analysis leads to a simple test to check whether a prescribed frequency component is present.     

Some notes on the combinatorial properties of haplotype tagging

Tagging haplotypes with a small number of genetic markers is becoming an increasingly interesting and important problem. Surprisingly little work has been done to characterize the mathematical framework of this problem. In this paper we present a mathematical frame, based on Boolean algebras, that adequately describe the structure of a set of genetic bi-allelic markers and the corresponding set of haplotypes. We derive a number of results that relate the number of markers required to tag a set of haplotypes to the set of markers themselves.     

A posteriori time-varying filtering of averaged evoked potentials

The problem of estimating an unknown transient signal, given an ensemble of waveforms, in which this signal appears as a nonrandom component in the presence of additive noise is considered. This problem is solved by generalizing the method of a posteriori Wiener filtering. In the new method, the ensemble average is filtered by a time-varying system which is based on estimated time-varying power spectra of signal and noise. The nature of this system, and the computational procedures involved, are discussed in detail. A software package for time-varying filtering is briefly described. Application of the method is illustrated by a simulation example, which also provides a comparison to time-invariant a posteriori Wiener filtering.     

Some statistical properties of the miniature endplate potentials

I will demonstrate that series of miniature endplate potentials (m.e.p.ps) showing a high proportion of so-called giant m.e.p.ps (g.m.e.p.ps) have different statistical structures from series where the proportion of g.m.e.p.ps is low. The nature of the different structures will be discussed on the basis of two statistical models, one for the distribution of the m.e.p.p. amplitudes and one for the series of point events occurring in time.     

Denoising of surface EMG with a modified Wiener filtering approach

The correlation dimension D₂ yields good results in several biomedical fields. Nonetheless, no clinical application to electromyography has been developed yet. One reason is the high electromagnetic noise typical of clinical environments. This noise is characterized by sharp spectral lines of variable intensity and frequency. The filtering techniques commonly implemented in electromyographs can efficiently deal with this kind of noise. They allow a safe estimate of linear quantities like the root mean square (r.m.s.) or the median frequency (MF). Their performance is not as good for nonlinear purposes. The filters may modify the nonlinear properties of the signal, leading to unacceptable estimates of D₂. We consider a simple procedure based on a modified Wiener filter. Its performance is compared with that from a bandpass followed by multiple notch filters. Our procedure leads to a gain in precision and accuracy when estimating D₂. The two filtering approaches are also compared with respect to a biomedical application proposed by others. Using data from 12 healthy subjects, the modified Wiener procedure raises the percentage of successes in that application from 17% to 83%. New experimental data suggest D₂ carries information not carried by r.m.s. or MF.     

Additional comments on the use of Wiener filtering for the estimation of evoked potentials

The problem of average potentials filtration in the case of periodic stimulation is discussed in the paper. Some considerations proving the correctness of Wiener filtering processes suggested by Doyle are presented here. The basic assumtion of the proof is an approximation of the noise power density by means of a step function.     

Some notes on the terminology of brassinosteroids

In this paper the definitions of brassinolide, brassinolide activity andbrassins are reviewed, and definitions for the terms brassin, naturalbrassinosteroids and brassinosteroid analogues, based on biosynthetic reasoningand structure similarity are proposed.