Minimum-phase calibration of sampling oscilloscopes

We describe an algorithm for determining the minimum phase of a linear time-invariant response function from its magnitude. The procedure is based on Kramers-Kronig relations in combination with auxiliary direct measurements of the desired phase response. We demonstrate that truncation of the Hilbert transform gives rise to large errors in estimated phase, but that these errors may be approximated using a small number of basis functions. As an example, we obtain a minimum-phase calibration of a sampling oscilloscope in the frequency domain. This result rests on data obtained by an electrooptic sampling (EOS) technique in combination with a swept-sine calibration procedure. The EOS technique yields magnitude and phase information over a broad bandwidth, yet has degraded uncertainty estimates from dc to approximately 1 GHz. The swept-sine procedure returns only the magnitude of the oscilloscope response function, yet may be performed on a fine frequency grid from about 1 MHz to several gigahertz. The resulting minimum-phase calibration spans frequencies from dc to 110 GHz, and is traceable to fundamental units. The validity of the minimum-phase character of the oscilloscope response function at frequencies common to both measurements is determined as part of our analysis. A full uncertainty analysis is provided.     

Genetic studies of the leptin receptor gene in morbidly obese French Caucasian families

Family studies have shown that in some populations up to 75% of the variation of body mass index can be explained by genetic factors. However, in humans, no major obesity gene has been identified to date. In contrast, there are a number of genetically well defined animal models for obesity. In two of those models (ob/ob and db/db), defects in the same pathway are responsible for obesity. Recently, some evidence has been found for the OB gene also being involved in human obesity. In this study we investigated the potential role of the OB receptor (OBR) in the etiology of massive obesity in humans using familial linkage analyses and case-control association studies. The typing of two microsatellite markers (D1S198 and D1S209), flanking the OBR gene, in 256 sib pairs showed no evidence for linkage with obesity. In order to be able to detect small gene effects, association studies with a 3'-UTR insertion/deletion polymorphism were carried out. The results of these analyses remained non-significant (chi 2 = 3.442, P = 0.18). However, subjects heterozygous for the insertion/deletion polymorphism showed a slight trend towards lower insulin values 30 min after an oral glucose load compared to homozygous individuals (P = 0.02). In summary, our results do not support a major role of the human OBR gene in the development of morbid obesity in our population.