
- Read more about TIME-DOMAIN CONCENTRATION AND APPROXIMATION OF COMPUTABLE BANDLIMITED SIGNALS
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Turing computability deals with the question of what is theoretically computable on a digital computer, and hence is relevant whenever digital hardware is used. In this paper we study different possibilities to define computable bandlimited signals and systems. We consider a definition that uses finite Shannon sampling series as approximating functions and another that employs computable continuous functions together with an effectively computable time concentration. We discuss the advantages and drawbacks of both definitions and analyze the connections and differences.
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- Read more about Error estimate in second-order continuous-time sigma-delta modulators
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Continuous-time Sigma-Delta modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are established for high-order discrete time Sigma-Delta modulators, theoretical analysis of the error between the filtered output and the input remain scarce.
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- Read more about Grid Optimization for Matrix-based Source Localization under Inhomogeneous Sensor Topology
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- Read more about A Time-Based Sampling Framework for Finite-Rate-of-Innovation Signals
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Time-based sampling of continuous-time signals is an alternate sampling paradigm in which the signal is encoded using a sequence of non-uniform instants time. The standard methods for reconstructing bandlimited and shift-invariant signals from their time-encoded measurements employ alternating projections type methods. In this paper, we consider the problem of sampling and perfect reconstruction of periodic finite-rate-of-innovation (FRI) signals using crossing time-encoding machine (C-TEM) and integrate-and-fire TEM (IF-TEM).
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- Read more about Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions
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Although the Hilbert transform and the spectral factorization are of central importance in signal processing,
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A Turing machine is a model describing the fundamental limits of any realizable computer, digital signal processor (DSP), or field programmable gate array (FPGA). This paper shows that there exist very simple linear time-invariant (LTI) systems which can not be simulated on a Turing machine. In particular, this paper considers the linear system described by the voltage-current relation of an ideal capacitor. For this system, it is shown that there exist continuously differentiable and computable input signals such that the output signal is a continuous function which is not computable.
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- Read more about Effective Approximation of Bandlimited Signals and Their Samples
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- Read more about Track-before-detect for sub-Nyquist radar
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Sub-Nyquist radars require fewer measurements, facilitating low-cost design, flexible resource allocation, etc. By applying compressed sensing (CS) method, such radars achieve close performance to traditional Nyquist radars. However in low signal-to-noise ratio (SNR) scenarios, detecting weak targets is challenging: low probability of detection and many spurious targets could occur in the recovery results of traditional CS method.
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- Read more about MANIFOLD GRADIENT DESCENT SOLVES MULTI-CHANNEL SPARSE BLIND DECONVOLUTION PROVABLY AND EFFICIENTLY
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Multi-channel sparse blind deconvolution refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. It is challenging to learn the filter efficiently due to the bilinear structure of the observations with respect to the unknown filter and inputs, leading to global ambiguities of identification. We propose a novel approach based on nonconvex optimization over the sphere manifold by minimizing a smooth surrogate of the sparsity-promoting loss function.
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