Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

The relationship between kurtosis- and envelope-based indexes for the diagnostic of rolling element bearings

The coupling of kurtosis based-indexes and envelope analysis represents one of the most successful and widespread procedures for the diagnostics of incipient faults on rolling element bearings. Kurtosis-based indexes are often used to select the proper demodulation band for the application of envelope-based techniques. Kurtosis itself, in slightly different formulations, is applied for the prognostic and condition monitoring of rolling element bearings, as a standalone tool for a fast indication of the development of faults. This paper shows for the first time the strong analytical connection which holds for these two families of indexes. In particular, analytical identities are shown for the squared envelope spectrum (SES) and the kurtosis of the corresponding band-pass filtered analytic signal. In particular, it is demonstrated how the sum of the peaks in the SES corresponds to the raw 4th order moment. The analytical results show as well a link with an another signal processing technique: the cepstrum pre-whitening, recently used in bearing diagnostics. The analytical results are the basis for the discussion on an optimal indicator for the choice of the demodulation band, the ratio of cyclic content (RCC), which endows the kurtosis with selectivity in the cyclic frequency domain and whose performance is compared with more traditional kurtosis-based indicators such as the protrugram. A benchmark, performed on numerical simulations and experimental data coming from two different test-rigs, proves the superior effectiveness of such an indicator. Finally a short introduction to the potential offered by the newly proposed index in the field of prognostics is given in an additional experimental example. In particular the RCC is tested on experimental data collected on an endurance bearing test-rig, showing its ability to follow the development of the damage with a single numerical index.

Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.

Combining meta- and mega-analytic approaches for multi-site diffusion imaging based genetic studies: From the enigma-DTI working group

Meta-analyses estimate a statistical effect size for a test or an analysis by combining results from multiple studies without necessarily having access to each individual study's raw data. Multi-site meta-analysis is crucial for imaging genetics, as single sites rarely have a sample size large enough to pick up effects of single genetic variants associated with brain measures. However, if raw data can be shared, combining data in a "mega-analysis" is thought to improve power and precision in estimating global effects. As part of an ENIGMA-DTI investigation, we use fractional anisotropy (FA) maps from 5 studies (total N=2, 203 subjects, aged 9-85) to estimate heritability. We combine the studies through meta-and mega-analyses as well as a mixture of the two - combining some cohorts with mega-analysis and meta-analyzing the results with those of the remaining sites. A combination of mega-and meta-approaches may boost power compared to meta-analysis alone.