2011
DOI: 10.1007/s10444-011-9180-9
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Approximate reconstruction of bandlimited functions for the integrate and fire sampler

Abstract: Abstract. In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and is specially convenient in situations where the sampling device is limited in terms of power, area and bandwidth.Although perfect reconstruction for this sampler is impossible, we give a general approximate reconstruction procedure and bound the corresponding error.… Show more

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Cited by 50 publications
(22 citation statements)
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“…The deterministic spike model consists of a continuous RBF model in the form (20) combined with an LIF sampler that converts the RBF into a square wave function. The LIF sampler developed in [28] for the approximate reconstruction of bandlimited functions is adopted, which converts any continuous signal f (t) into a square wave function by integrating it against an averaging function u k,z (t). The integrated result is compared to a positive threshold and a negative threshold, such that when either one of the two thresholds is reached, a pulse is generated at time t k = z.…”
Section: Deterministic Spike Modelmentioning
confidence: 99%
See 1 more Smart Citation
“…The deterministic spike model consists of a continuous RBF model in the form (20) combined with an LIF sampler that converts the RBF into a square wave function. The LIF sampler developed in [28] for the approximate reconstruction of bandlimited functions is adopted, which converts any continuous signal f (t) into a square wave function by integrating it against an averaging function u k,z (t). The integrated result is compared to a positive threshold and a negative threshold, such that when either one of the two thresholds is reached, a pulse is generated at time t k = z.…”
Section: Deterministic Spike Modelmentioning
confidence: 99%
“…The value of the integrator is then reset and the process repeats. In this paper, the averaging function u k,z (t) is chosen to be the exponential e α(t−z) X [tk,z] , where X I is the characteristic function of I and α > 0 is a constant that models the leakage of the integrator, as due to practical implementations [28]. Then, the LIF sampler firing condition that generates the square wave (or sequence of pulses) is…”
Section: Deterministic Spike Modelmentioning
confidence: 99%
“…State-of-the-art signal reconstruction methods rely on assumptions or estimations of characteristics like spectral moments or signal bandwidth [9,[11][12][13][14]. Deviations or inaccurate estimates can impair the quality of the signal reconstruction.…”
Section: Motivationmentioning
confidence: 99%
“…For applications as sampler in electronic systems see, e.g., [6,7]. For a survey regarding the recovery problem see, e.g., [8,9].…”
Section: Introductionmentioning
confidence: 99%
“…Time encoding and decoding has been studied for different signal classes, from bandlimited signals [3,4] to the more general shift-invariant subspaces [5] and even to some classes of finite rate of innovation signals [6], mostly by relating the recorded times to irregular samples and performing reconstruction from irregular samples [7,8].…”
Section: Introductionmentioning
confidence: 99%