Vector space framework for unification of one- and multidimensional filter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem

Understanding macroscale functionality of metal halide perovskites in terms of nanoscale heterogeneities

Hybrid metal halide perovskites have shown an unprecedented rise as semiconductor building blocks for solar energy conversion and light-emitting applications. Currently, the field moves empirically towards more and more complex chemical compositions, including mixed halide quadruple cation compounds that allow optical properties to be tuned and show promise for better stability. Despite tremendous progress in the field, there is a need for better understanding of mechanisms of efficiency loss and instabilities to facilitate rational optimization of composition. Starting from the device level and then diving into nanoscale properties, we highlight how structural and compositional heterogeneities affect macroscopic optoelectronic characteristics. Furthermore, we provide an overview of some of the advanced spectroscopy and imaging methods that are used to probe disorder and non-uniformities. A unique feature of hybrid halide perovskite compounds is the propensity for these heterogeneities to evolve in space and time under relatively mild illumination and applied electric fields, such as those found within active devices. This introduces an additional challenge for characterization and calls for application of complimentary probes that can aid in correlating the properties of local disorder with macroscopic function, with the ultimate goal of rationally tailoring synthesis towards optimal structures and compositions

A Mathematical model to guide Genetic Engineering of Photosynthetic Metabolism

open5noThe optimization of algae biomass productivity in industrial cultivation systems requires genetic improvement of wild type strains isolated from nature. One of the main factors affecting algae productivity is their efficiency in converting light into chemical energy and this has been a major target of recent genetic efforts. However, photosynthetic productivity in algae cultures depends on many environmental parameters, making the identification of advantageous genotypes complex and the achievement of concrete improvements slow. In this work, we developed a mathematical model to describe the key factors influencing algae photosynthetic productivity in a photobioreactor, using experimental measurements for the WT strain of Nannochloropsis gaditana. The model was then exploited to predict the effect of potential genetic modifications on algae performances in an industrial context, showing the ability to predict the productivity of mutants with specific photosynthetic phenotypes. These results show that a quantitative model can be exploited to identify the genetic modifications with the highest impact on productivity taking into full account the complex influence of environmental conditions, efficiently guiding engineering efforts.embargoed_20181201Perin, Giorgio; Bernardi, Andrea; Bellan, Alessandra; Bezzo, Fabrizio; Morosinotto, TomasPerin, Giorgio; Bernardi, Andrea; Bellan, Alessandra; Bezzo, Fabrizio; Morosinotto, Toma

Terrestrial applications: An intelligent Earth-sensing information system

For Abstract see A82-2214

Design Of Polynomial-based Filters For Continuously Variable Sample Rate Conversion With Applications In Synthetic Instrumentati

In this work, the design and application of Polynomial-Based Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis function coefficients. The frequency domain optimization of PBFs via linear programming has been proposed in the literature, however, the algorithm was not detailed nor were explicit formulas derived. In this contribution, a minimax optimization procedure is derived for the frequency domain optimization of a PBF with time-domain constraints. Explicit formulas are given for direct input to a linear programming routine. Additionally, accompanying Matlab code implementing this optimization in terms of the derived formulas is given in the appendix. In the literature, it has been pointed out that the frequency response of the Continuous-Time (CT) filter decays as frequency goes to infinity. It has also been observed that when implemented in SRC, the CT filter is sampled resulting in CT frequency response aliasing. Thus, for example, the stopband sidelobes of the Discrete-Time (DT) implementation rise above the CT designed level. Building on these observations, it is shown how the rolloff rate of the frequency response of a PBF can be adjusted by adding continuous derivatives to the impulse response. This is of great advantage, especially when the PBF is used for decimation as the aliasing band attenuation can be made to increase with frequency. It is shown how this technique can be used to dramatically reduce the effect of alias build up in the passband. In addition, it is shown that as the number of continuous derivatives of the PBF increases the resulting DT implementation more closely matches the Continuous-Time (CT) design. When implemented for SRC, samples from a PBF impulse response are computed by evaluating the polynomials using a so-called fractional interval, µ. In the literature, the effect of quantizing µ on the frequency response of the PBF has been studied. Formulas have been derived to determine the number of bits required to keep frequency response distortion below prescribed bounds. Elsewhere, a formula has been given to compute the number of bits required to represent µ to obtain a given SRC accuracy for rational factor SRC. In this contribution, it is shown how these two apparently competing requirements are quite independent. In fact, it is shown that the wordlength required for SRC accuracy need only be kept in the µ generator which is a single accumulator. The output of the µ generator may then be truncated prior to polynomial evaluation. This results in significant computational savings, as polynomial evaluation can require several multiplications and additions. Under the heading of applications, a new Wideband Digital Downconverter (WDDC) for Synthetic Instruments (SI) is introduced. DDCs first tune to a signal\u27s center frequency using a numerically controlled oscillator and mixer, and then zoom-in to the bandwidth of interest using SRC. The SRC is required to produce continuously variable output sample rates from a fixed input sample rate over a large range. Current implementations accomplish this using a pre-filter, an arbitrary factor resampler, and integer decimation filters. In this contribution, the SRC of the WDDC is simplified reducing the computational requirements to a factor of three or more. In addition to this, it is shown how this system can be used to develop a novel computationally efficient FFT-based spectrum analyzer with continuously variable frequency spans. Finally, after giving the theoretical foundation, a real Field Programmable Gate Array (FPGA) implementation of a novel Arbitrary Waveform Generator (AWG) is presented. The new approach uses a fixed Digital-to-Analog Converter (DAC) sample clock in combination with an arbitrary factor interpolator. Waveforms created at any sample rate are interpolated to the fixed DAC sample rate in real-time. As a result, the additional lower performance analog hardware required in current approaches, namely, multiple reconstruction filters and/or additional sample clocks, is avoided. Measured results are given confirming the performance of the system predicted by the theoretical design and simulation

Basics of RF electronics

RF electronics deals with the generation, acquisition and manipulation of high-frequency signals. In particle accelerators signals of this kind are abundant, especially in the RF and beam diagnostics systems. In modern machines the complexity of the electronics assemblies dedicated to RF manipulation, beam diagnostics, and feedbacks is continuously increasing, following the demands for improvement of accelerator performance. However, these systems, and in particular their front-ends and back-ends, still rely on well-established basic hardware components and techniques, while down-converted and acquired signals are digitally processed exploiting the rapidly growing computational capability offered by the available technology. This lecture reviews the operational principles of the basic building blocks used for the treatment of high-frequency signals. Devices such as mixers, phase and amplitude detectors, modulators, filters, switches, directional couplers, oscillators, amplifiers, attenuators, and others are described in terms of equivalent circuits, scattering matrices, transfer functions; typical performance of commercially available models is presented. Owing to the breadth of the subject, this review is necessarily synthetic and non-exhaustive. Readers interested in the architecture of complete systems making use of the described components and devoted to generation and manipulation of the signals driving RF power plants and cavities may refer to the CAS lectures on Low-Level RF.Comment: 36 pages, contribution to the CAS - CERN Accelerator School: Specialised Course on RF for Accelerators; 8 - 17 Jun 2010, Ebeltoft, Denmar

Synthesis and photochromic properties of a bis(diarylethene)-naphthopyran hybrid

The synthesis and photochromic properties of a triphotochromic molecule consisting of one naphthopyran flanked by two diarylethene units investigated by UV-Visible and NMR spectroscopies are reported. Six different states resulting from the open/closed naphthopyran associated with one or two open/cyclized diarylethenes have been characterized. Switching of the naphthopyran group is possible, independently of the state of the diarylethene groups, permitting the controlled generation of electronically connected diarylethene groups. However, the diarylethene groups cannot be closed if the naphthopyran group is open

Synthetic Aperture Radar (SAR) data processing

The available and optimal methods for generating SAR imagery for NASA applications were identified. The SAR image quality and data processing requirements associated with these applications were studied. Mathematical operations and algorithms required to process sensor data into SAR imagery were defined. The architecture of SAR image formation processors was discussed, and technology necessary to implement the SAR data processors used in both general purpose and dedicated imaging systems was addressed