528 research outputs found

    Time Encoding Sampling of Bandpass Signals

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    This paper investigates the problem of sampling and reconstructing bandpass signals using time encoding machine(TEM). It is shown that the sampling in principle is equivalent to periodic non-uniform sampling (PNS). Then the TEM parameters can be set according to the signal bandwidth and amplitude instead of upper-edge frequency and amplitude as in the case of bandlimited/lowpass signals. For a bandpass signal of a single information band, it can be perfectly reconstructed if the TEM parameters are such that the difference between any consecutive values of the time sequence in each channel is bounded by the inverse of the signal bandwidth. A reconstruction method incorporating the interpolation functions of PNS is proposed. Numerical experiments validate the feasibility and effectiveness of the proposed TEM scheme.Comment: 5 pages, 6 figure

    POCS-based framework of signal reconstruction from generalized non-uniform samples

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    We formalize the use of projections onto convex sets (POCS) for the reconstruction of signals from non-uniform samples in their highest generality. This covers signals in any Hilbert space H\mathscr H, including multi-dimensional and multi-channel signals, and samples that are most generally inner products of the signals with given kernel functions in H\mathscr H. An attractive feature of the POCS method is the unconditional convergence of its iterates to an estimate that is consistent with the samples of the input, even when these samples are of very heterogeneous nature on top of their non-uniformity, and/or under insufficient sampling. Moreover, the error of the iterates is systematically monotonically decreasing, and their limit retrieves the input signal whenever the samples are uniquely characteristic of this signal. In the second part of the paper, we focus on the case where the sampling kernel functions are orthogonal in H\mathscr H, while the input may be confined in a smaller closed space A\mathscr A (of bandlimitation for example). This covers the increasingly popular application of time encoding by integration, including multi-channel encoding. We push the analysis of the POCS method in this case by giving a special parallelized version of it, showing its connection with the pseudo-inversion of the linear operator defined by the samples, and giving a multiplierless discrete-time implementation of it that paradoxically accelerates the convergence of the iteration.Comment: 12 pages, 4 figures, 1 tabl

    Chaotic communications over radio channels

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    Improved detection scheme for chipless RFIDs using prolate spheroidal wave function-based noise filtering

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    A novel, highly sensitive scheme to detect the resonance peaks in the spectrum of chipless RFID signals is presented. The detection is based on finding the zeros in the derivative of the group delay of the received signal. In order to be able to accurately detect these zeros in the presence of noise, the received signal is filtered using a prolate spheroidal wave function-based model. This allows great increases in the distance at which chipless RFIDs can be accurately read. The detection method can be used standalone or in addition to traditional amplitude-based detection schemes

    Sampling and Reconstruction of Bandlimited Signals with Multi-Channel Time Encoding

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    Sampling is classically performed by recording the amplitude of the input at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the devices have an unknown shift in their clocks. Alternatively, one can record the times at which a signal (or its integral) crosses given thresholds. This can model integrate-and-fire neurons, for example, and has been studied by Lazar and Tóth under the name of "Time Encoding Machines". This sampling method is closer to what is found in nature. In this paper, we show that, when using time encoding machines, reconstruction from multiple channels has a more intuitive solution, and does not require the knowledge of the shifts between machines. We show that, if single-channel time encoding can sample and perfectly reconstruct a 2Ω-bandlimited signal, then M-channel time encoding can sample and perfectly reconstruct a signal with M times the bandwidth. Furthermore, we present an algorithm to perform this reconstruction and prove that it converges to the correct unique solution, in the noiseless case, without knowledge of the relative shifts between the machines. This is quite unlike classical multi-channel sampling, where unknown shifts between sampling devices pose a problem for perfect reconstruction
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