Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We present the necessary properties of the quaternion Fourier transform, particularly its symmetries in the frequency domain and formulae for convolution and the quaternion Fourier transform of the Hilbert transform. The hypercomplex representation may be interpreted as an ordered pair of complex signals or as a quaternion signal. We discuss its derivation and properties and show that its quaternion Fourier transform is one-sided. It is shown how to derive from the hypercomplex representation a complex envelope and a phase. A classical result in the case of real signals is that an amplitude modulated signal may be analysed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Orthonormal complex modulation can be represented mathematically by a polar representation of quaternions previously derived by the authors. As in the classical case, there is a restriction of non-overlapping frequency content between the modulating complex signal and the orthonormal complex exponential. We show that, under these conditions, modulation in the time domain is equivalent to a frequency shift in the quaternion Fourier domain. Examples are presented to demonstrate these concepts

H-band observations of the Chandra Deep Field South

We report preliminary results of our H-band survey of the Chandra Deep Field South (CDFS). The observations were made using SofI on the NTT, and cover 0.027 square degrees with a 50% completeness limit of H = 20.5, and 0.17 square degrees with a 50% completeness limit of H =19.8. We used SExtractor to extract sources from our fields. In total we have detected 4819 objects. Star-galaxy separation was performed using the SExtractor parameter ``stellarity index''. All objects with an index of 0.5 or lower were classified as galaxies. According to this criterion, 80 % of our detections are galaxies. We then compare our results with previous observations of the CDFS. Our astrometric solutions are in good agreement with the Las Campanas Infrared Survey (LCIRS), the COMBO-17 and the ESO-EIS surveys. The photometry of our catalog compares satisfactorily with the results of the LCIRS, as well as with the GOODS data. Galaxy number counts are presented and compared with the LCIRS results. The present data are intended to complement the recent and future multi-wavelenghth observations of the CDFS and will be used, in conjuction with additional multiband photometry, to find counterparts of the upcoming mid-infrared surveys with SIRTF.Comment: 7 figures, submitted to Astronomy and Astrophysics, catalogue available at http://www.mpe.mpg.de/~dmr/table1.da

Povodom puštanja u pogon nove Gradske mljekare u Zagrebu

Dne 2. kolovoza 1952. godine u 8 sati svečano je puštena u pogon nova Centralna Gradska Mljekara u Zagrebu na Žitnjaku. Svečanom činu otvorenja mljekare prisustvovali su u ime Međunarodne organizacije za pomoć djeci Unicef-a gg. Julius Perstein, šef glavnog centra Unicef-a u Parizu, G. I. R. Cooper, šef odjela za izgradnju mljekara u Evropi i na Bliskom Istoku, gdja Helen Glassey, šef misije za Jugoslaviju i g. J. L. Vinck, član Unicefa u Parizu

Emergence of New Norovirus Variants on Spring Cruise Ships and Prediction of Winter Epidemics

A reporting system could provide early warning

Monitoring one-electron photo-oxidation of guanine in DNA crystals using ultrafast infrared spectroscopy

To understand the molecular origins of diseases caused by ultraviolet and visible light, and also to develop photodynamic therapy, it is important to resolve the mechanism of photoinduced DNA damage. Damage to DNA bound to a photosensitizer molecule frequently proceeds by one-electron photo-oxidation of guanine, but the precise dynamics of this process are sensitive to the location and the orientation of the photosensitizer, which are very difficult to define in solution. To overcome this, ultrafast time-resolved infrared (TRIR) spectroscopy was performed on photoexcited ruthenium polypyridyl–DNA crystals, the atomic structure of which was determined by X-ray crystallography. By combining the X-ray and TRIR data we are able to define both the geometry of the reaction site and the rates of individual steps in a reversible photoinduced electron-transfer process. This allows us to propose an individual guanine as the reaction site and, intriguingly, reveals that the dynamics in the crystal state are quite similar to those observed in the solvent medium