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Algorithms for designing a mother wavelet () such that it matches a signal of interest and such that the family of wavelets 2 (2) (2) forms an orthonormal Riesz basis of 2 () are developed. The algorithms are based on a closed form solution for finding the scaling function spectrum from the wavelet spectrum. Many applications of signal representation, adaptive coding and pattern recognition require wavelets that are matched to a signal of interest. Most current design techniques, however, do not design the wavelet directly. They either build a composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution analysis or design a scaling function that generates a multiresolution analysis with some desired properties. In this paper, two sets of equations are developed that allow us to design the wavelet directly from the signal of interest. Both sets impose bandlimitedness, resulting in closed form solutions. The first set derives expressions for continuous matched wavelet spectrum amplitudes. The second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum. The discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies. An interesting byproduct of this work is the result that Meyer's spectrum amplitude construction for an orthonormal bandlimited wavelet is not only sufficient but necessary. Specific examples are given which demonstrate the performance of the wavelet matching algorithms for both known orthonormal wavelets and arbitrary signals.

IntroductionInformation technology has become a decisive element in modern warfare, in particular when armed forces of developed countries are involved. Modern weapon systems would not function without sophisticated computing power, but also the planning and executing of military operations in general heavily rely on information technology. In addition, armed forces, but also police, border control and civil protection organizations increasingly rely on robotic systems with growing autonomous capacities. This poses tactical and strategic, but also ethical and legal issues that are of particular relevance when procurement organizations are evaluating such systems for security applications.In order to support the evaluation of such systems from an ethical perspective, this report presents an evaluation schema for the ethical use of autonomous robotic systems in security applications, which also considers legal aspects to some degree. The focus is on two types of applications: First, systems whose purpose is not to destroy objects or to harm people (e.g. rescue robots, surveillance systems); although weaponization cannot be excluded. Second, systems that deliberately possess the capacity to harm people or destroy objects -both defensive and offensive, lethal and non-lethal systems. The cyber-domain where autonomous systems also are increasingly used (software agents, specific types of cyber weapons etc.) has been excluded from this analysis.The research that has resulted in this report outlines the most important evaluations and scientific publications that are contributing to the international debate on the regulation of autonomous systems in the security context, in particular in the case of so-called lethal autonomous weapons systems (LAWS). The goal of the research is twofold: First, it should support the procurement of security/defense systems, e.g. to avoid reputation risks or costly assessments for systems that are ethically problematic and entail political risks. Second, the research should contribute to the international discussion on the use of autonomous systems in the security context (e.g

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