Searching for authors named "Andreas Klappenecker" – sorted by Relevance.
26 documents found, showing 1 through 10.
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On Some Limits of Lattice and Lifting Structures
- …We discuss the relation between lattice and ladder structures for two-channel filter banks. It is wellknown that both lattice and ladder steps are powerful enough to generate all perfect reconstructing filter banks provided that the filter coefficients may take arbitrary values in a field. However, …
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Computing with a Quantum Flavor
- …This paper gave a short introduction to the main principles of quantum computing. The quantum mechanical principles allow rapid computation of certain problems. The famous integer factoring algorithm by Shor indicates that some problems can be rapidly solved on a quantum computer which do not seem t…
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On Multirate Filter Bank Structures
- …We introduce a framework for treating multirate filter banks for signal and image processing applications, as well as communication applications, in a unified way. We show how methods from group and ring theory can be applied to derive structural properties of filter banks. 1 Introduction Multirat…
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Twisted Filter Banks For Communication Applications
- …We present a novel class of multirate filter banks that are based on a special class of time-varying filters. The filter operations are done by modifying the usual convolution operations with a twist. We will show that the filter banks allow perfect reconstruction, in spite of the fact that the filt…
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Twisted Filter Banks
- …The main idea of a lter bank is to transform an input signal by subjecting it to some convolution operations, possibly followed by sampling rate reductions. We extend this idea to lter banks that are based on more general twisted convolution operations, which are not necessarily time invariant. Roug…
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Unitary Error Bases: Constructions, Equivalence, and Applications
- …Unitary error bases are fundamental primitives in quantum computing, which are instrumental in the design of quantum error-correcting codes, teleportation and superdense coding schemes. There are two prominent constructions of such bases: an algebraic construction using projective representations of…
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Basefield Transforms Derived From Character Tables
- …We show that it is possible to define Hartley-like transforms for (generalized) character tables of finite groups. This large class of transforms include Hartley transforms for discrete Fourier transforms over abelian groups and Hartley-like transforms for the discrete cosine transform of type I. IN…
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On Algebraic Properties of Selfreciprocal Polynomials and of Daubechies Filters of Low Order
- …We show that the generic selfreciprocal polynomial of degree 2n has the Galois group S2 o Sn : Consequently, "most" selfreciprocal polynomials of degree 2n with coefficients in an algebraic number field have the same Galois group. We use these results to determine algebraic properties of the Daubech…
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Algebraic Wavelet Filters
- …| A method to compute the Discrete Wavelet Transform for certain wavelet lters is proposed that takes advantage of conjugacy properties in number elds. It is shown that wavelet lters derived from compactly supported orthonormal wavelets can be approximated with arbitrary precision by the proposed wa…
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Wavelets and Wavelet Packets on Quantum Computers
- …We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer. 1. INTRODUCTION …
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