Philipp Walk

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In this note we show that stable recovery of complex-valued signals x ∈ C n up to a global sign can be achieved from the magnitudes of 4n − 1 Fourier measurements when a certain symmetrization and zero-padding is performed before measurement (4n − 3 is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is(More)
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non–adaptive estimation problems. It is therefore an advisable strategy for noncoherent information retrieval in, for example, sporadic blind and semi–blind communication and sampling problems. But,(More)
In this paper we consider the design of spectrally efficient time-limited pulses for ultra-wideband (UWB) systems using an overlapping pulse position modulation scheme. For this we investigate an orthogonalization method, which was developed in 1950 by Löwdin [1, 2]. Our objective is to obtain a set of N orthogonal (Löwdin) pulses, which remain time-limited(More)
In this work we characterize all ambiguities of the linear (aperiodic) one-dimensional convolution on two fixed finite-dimensional complex vector spaces. It will be shown that the convolution ambiguities can be mapped one-to-one to factorization ambiguities in the z−domain, which are generated by swapping the zeros of the input signals. We use this(More)