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In this paper we show that convolutions of sufficiently sparse signals always admit a non–zero lower bound in energy if oversampling of its Fourier transform is employed. This bound is independent of the signals and the ambient dimension and is determined only be the sparsity of both input signals. This result has several implications for blind system and… (More)

We will establish in this note a stability result for sparse convolutions on torsion-free additive (discrete) abelian groups. Sparse convolutions on torsion-free groups are free of cancellations and hence admit stability, i.e. injectivity with a universal lower bound α = α(s, f), only depending on the cardinality s and f of the supports of both input… (More)

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)

—For several communication models, the dispersive part of a communication channel is described by a bilinear operation T between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image T (X, Y) of the input signal difference sets X and the channel state sets Y. The main goal in this… (More)

We give a stability result for sparse convolutions on 2 (G) × 1 (G) for torsion-free discrete Abelian groups G such as Z. It turns out, that the torsion-free property prevents full cancellation in the convolution of sparse sequences and hence allows to establish stability in each entry, that is, for any fixed entry of the convolution the resulting linear… (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)