Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Submillimeter wave frequency selective surface with polarisation independent spectral responses

This paper reports the design, construction and electromagnetic performance of a new freestanding frequency selective surface (FSS) structure which generates coincident spectral responses for dual polarisation excitation at oblique angles of incidence. The FSS is required to allow transmission of 316.5 - 325.5 GHz radiation with a loss = 0.6 dB and to achieve = 30 dB rejection from 349.5 - 358.5 GHz. It should also exhibit crosspolarisation levels below -25 dB, all criteria being satisfied simultaneously for TE and TM polarisations at 45° incidence. The filter consists of two identical, 30 mm diameter, 12.5 ?m thick, optically flat, perforated metal screens separated by 450 ?m. Each of the ˜5000 unit cells contains two nested, short circuited, rectangular loop slots and a rectangular dipole slot. The nested elements provide a passband spectral response centred at 320 GHz in the TE and TM planes; the dipole slot increases the filter roll-off above resonance. The FSS was fabricated from silicon-on-insulator wafers using precision micromachining and plating processes including the use of Deep Reactive Ion Etching (DRIE) to pattern the individual slots and remove the substrate under the periodic arrays. Quasi–optical transmission measurements in the 250 – 360 GHz range yielded virtually identical copolarised spectral responses, with the performance meeting or exceeding the above specifications. Experimental results are in excellent agreement with numerical predictions.

A three-position spectral line survey of sagittarius B2 between 218 and 263 GHz. II. Data analysis

We present an analysis of the data from our Swedish-ESO Submillimetre Telescope molecular line survey in the 1.3 mm band of the N, M, and NW positions in the Sgr B2 molecular cloud. The line emissions from 42 molecular species, and some of their isotopomers, were analyzed assuming a single temperature and a homogeneous source. In cases where a source size much smaller than the antenna beam (23

Joined Spectral Trees for Scalable SPIHT-Based Multispectral Image Compression

In this paper, the compression of multispectral images is addressed. Such 3-D data are characterized by a high correlation across the spectral components. The efficiency of the state-of-the-art wavelet-based coder 3-D SPIHT is considered. Although the 3-D SPIHT algorithm provides the obvious way to process a multispectral image as a volumetric block and, consequently, maintain the attractive properties exhibited in 2-D (excellent performance, low complexity, and embeddedness of the bit-stream), its 3-D trees structure is shown to be not adequately suited for 3-D wavelet transformed (DWT) multispectral images. The fact that each parent has eight children in the 3-D structure considerably increases the list of insignificant sets (LIS) and the list of insignificant pixels (LIP) since the partitioning of any set produces eight subsets which will be processed similarly during the sorting pass. Thus, a significant portion from the overall bit-budget is wastedly spent to sort insignificant information. Through an investigation based on results analysis, we demonstrate that a straightforward 2-D SPIHT technique, when suitably adjusted to maintain the rate scalability and carried out in the 3-D DWT domain, overcomes this weakness. In addition, a new SPIHT-based scalable multispectral image compression algorithm is used in the initial iterations to exploit the redundancies within each group of two consecutive spectral bands. Numerical experiments on a number of multispectral images have shown that the proposed scheme provides significant improvements over related works.

Spectral induced polarization signatures of abiotic FeS precipitation

In recent years, geophysical methods have been shown to be sensitive to microbial-induced mineralization processes. The spectral induced-polarization (SIP) method appears to be very promising for monitoring mineralization and microbial processes. With this work, we study the links of mineralization and SIP signals, in the absence of microbial activity. We recorded the SIP response during abiotic FeS precipitation. We show that the SIP signals are diagnostic of FeS mineralization and can be differentiated from SIP signals from biomineralization processes. More specifically, the imaginary conductivity shows almost linear dependence on the amount of FeS precipitating out of solution, above the threshold value 0.006 gr under our experimental conditions. This research has direct implications for the use of the SIP method as a monitoring and decision-making tool for sustainable remediation of metals in contaminated soils and groundwater.

Palaeoclimate change recorded in Upper Cretaceous (Albian-Cenomanian) Kazhdumi Formation Borehole spectral Gamma-Ray Logs, South Pars Gas field, Persian Gulf

Th/U and Th/K data from spectral gamma-ray logs obtained from outcrop successions have been used as a rapid and inexpensive proxy for determining possible episodes of humid-arid palaeoclimate change. Such outcrop-based measurements have never been tested using spectral gamma-ray data obtained from wireline logs in subsurface boreholes. Th/K and Th/U ratios have traditionally been used to decipher sequence stratigraphic patterns, at outcrop and in borehole. The possible influence of palaeoclimate on such ratio changes has yet to be proven, especially from borehole data. In this work, we compare borehole-derived Th/K (and to a lesser extent Th/U) to palaeoenvironmental changes inferred from palynology and deduce that both sea level and changing hinterland weathering regimes caused discrete fluctuations observed in the spectral gamma-ray logs. This is the first time such subsurface information has been used in this way. Interpretation of wireline logs in terms of palaeoclimate as well as sea level may now be considered, and the use of such logs in palaeoclimate reconstruction is strengthened.

Effect of signal intensity normalization on the multivariate analysis of spectral data in complex 'real-world' datasets

Spectral signal intensities, especially in 'real-world' applications with nonstandardized sample presentation due to uncontrolled variables/factors, commonly require additional spectral processing to normalize signal intensity in an effective way. In this study, we have demonstrated the complexity of choosing a normalization routine in the presence of multiple spectrally distinct constituents by probing a dataset of Raman spectra. Variation in absolute signal intensity (90.1% of total variance) of the Raman spectra of these complex biological samples swamps the variation in useful signals (9.4% of total variance), degrading its diagnostic and evaluative potential.

On the limits of spectral methods for frequency estimation

An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicates the intrinsic limitations of spectral methods when it comes to the task of measuring frequencies. Other examples, one from medicine and one from bifurcation theory, are given, which also exhibit these limitations of spectral methods. For two methods of spectral estimation it is verified that the particular way end points are treated, which is specific to each method, is, for long enough time series, not relevant for the main result.