Time-Interleaved Analog-to-Digital Converter (TIADC) Compensation Using Multichannel Filters

Published methods that employ a filter bank for compensating the timing and bandwidth mismatches of an M-channel time-interleaved analog-to-digital converter (TIADC) were developed based on the fact that each sub-ADC channel is a downsampled version of the analog input. The output of each sub-ADC is filtered in such a way that, when all the filter outputs are summed, the aliasing components are minimized. If each channel of the filter bank has N coefficients, the optimization of the coefficients requires computing the inverse of an MN times MN matrix if the weighted least squares (WLS) technique is used as the optimization tool. In this paper, we present a multichannel filtering approach for TIADC mismatch compensation. We apply the generalized sampling theorem to directly estimate the ideal output of each sub-ADC using the outputs of all the sub-ADCs. If the WLS technique is used as the optimization tool, the dimension of the matrix to be inversed is N times N. For the same number of coefficients (and also the same spurious component performance given sufficient arithmetic precision), our technique is computationally less complex and more robust than the filter-bank approach. If mixed integer linear programming is used as the optimization tool to produce filters with coefficient values that are integer powers of two, our technique produces a saving in computing resources by a factor of approximately (100.2N(M- 1)/(M-1) in the TIADC filter design.published_or_final_versio

Quantifying interspecific variation in dispersal ability of noctuid moths using an advanced tethered flight technique

This is the final version. Available on open access from Wiley via the DOI in this recordDispersal plays a crucial role in many aspects of species' life histories, yet is often difficult to measure directly. This is particularly true for many insects, especially nocturnal species (e.g. moths) that cannot be easily observed under natural field conditions. Consequently, over the past five decades, laboratory tethered flight techniques have been developed as a means of measuring insect flight duration and speed. However, these previous designs have tended to focus on single species (typically migrant pests), and here we describe an improved apparatus that allows the study of flight ability in a wide range of insect body sizes and types. Obtaining dispersal information from a range of species is crucial for understanding insect population dynamics and range shifts. Our new laboratory tethered flight apparatus automatically records flight duration, speed, and distance of individual insects. The rotational tethered flight mill has very low friction and the arm to which flying insects are attached is extremely lightweight while remaining rigid and strong, permitting both small and large insects to be studied. The apparatus is compact and thus allows many individuals to be studied simultaneously under controlled laboratory conditions. We demonstrate the performance of the apparatus by using the mills to assess the flight capability of 24 species of British noctuid moths, ranging in size from 12-27 mm forewing length (~40-660 mg body mass). We validate the new technique by comparing our tethered flight data with existing information on dispersal ability of noctuids from the published literature and expert opinion. Values for tethered flight variables were in agreement with existing knowledge of dispersal ability in these species, supporting the use of this method to quantify dispersal in insects. Importantly, this new technology opens up the potential to investigate genetic and environmental factors affecting insect dispersal among a wide range of species.Rothamsted Research receives grant aided support from the Biotechnology and Biological Sciences Research Council. H.B.C.J. was funded by a BBSRC Quota studentship awarded to J.W.C. and J.K.H

Recursive formula for the double-barrier Parisian stopping time

In this paper, we obtain a recursive formula for the density of the double barrier Parisian stopping time. We present a probabilistic proof of the formula for the first few steps of the recursion, and then a formal proof using explicit Laplace inversions. These results provide an efficient computational method for pricing double barrier Parisian options

A variation of the Azéma martingale and drawdown options

In this paper, we derive a variation of the Azéma martingale using two approaches—a direct probabilistic method and another by projecting the Kennedy martingale onto the filtration generated by the drawdown duration. This martingale links the time elapsed since the last maximum of the Brownian motion with the maximum process itself. We derive explicit formulas for the joint densities of (τ,W τ , M τ ), which are the first time the drawdown period hits a prespecified duration, the value of the Brownian motion, and the maximum up to this time. We use the results to price a new type of drawdown option, which takes into account both dimensions of drawdown risk—the magnitude and the duration

Parisian Option Pricing: A Recursive Solution for the Density of the Parisian Stopping Time

In this paper, we obtain the density function of the single barrier one-sided Parisian stopping time. The problem reduces to that of solving a Volterra integral equation of the first kind, where a recursive solution is consequently obtained. The advantage of this new method as compared to that in previous literature is that the recursions are easy to program as the resulting formula involves only a finite sum and does not require a numerical inversion of the Laplace transform. For long window periods, an explicit formula for the density of the stopping time can be obtained. For shorter window lengths, we derive a recursive equation from which numerical results are computed. From these results, we compute the prices of one-sided Parisian options

Evidence for a pervasive 'idling-mode' activity template in flying and pedestrian insects

This is the final version. Available on open access from the Royal Society via the DOI in this recordUnderstanding the complex movement patterns of animals in natural environments is a key objective of 'movement ecology'. Complexity results from behavioural responses to external stimuli but can also arise spontaneously in their absence. Drawing on theoretical arguments about decision-making circuitry, we predict that the spontaneous patterns will be scale-free and universal, being independent of taxon and mode of locomotion. To test this hypothesis, we examined the activity patterns of the European honeybee, and multiple species of noctuid moth, tethered to flight mills and exposed to minimal external cues. We also reanalysed pre-existing data for Drosophila flies walking in featureless environments. Across these species, we found evidence of common scale-invariant properties in their movement patterns; pause and movement durations were typically power law distributed over a range of scales and characterized by exponents close to 3/2. Our analyses are suggestive of the presence of a pervasive scale-invariant template for locomotion which, when acted on by environmental cues, produces the movements with characteristic scales observed in nature. Our results indicate that scale-finite complexity as embodied, for instance, in correlated random walk models, may be the result of environmental cues overriding innate behaviour, and that scale-free movements may be intrinsic and not limited to 'blind' foragers as previously thought.Rothamsted research receives grant aided support from the Biotechnology and Biological Sciences Research Council. S.W. was funded jointly by a grant from BBSRC, Defra, NERC, the Scottish Government and the Wellcome Trust, under the Insect Pollinators Initiative (grant nos. BB/I00097/1). A.J.P. was funded by a BBSRC Doctoral Training Partnership in Food Security awarded to K.W. and J.W.C. H.B.C.J. was funded by a BBSRC Quota studentship awarded to J.W.C. and J.K.