Does anyone knows about leaky integrate and fire sampler?

I was doing the sampling problem that samples continuous signal f(t) to a square pulse function, and I am studying the thesis:

H. G. Feichtinger, “Approximate reconstruction of bandlimited functions for the integrate and fire sampler,” Advanced Computational Mathematics, p. 12, 2010

The LIF sampler does the task that similar to ADC, by integrate the input against an average function Uk, and it says that the equation comes by the image.

<f,Uk> integrate work was implemented by the result, which shows that the result value = threshold.

However, I can’t understand what is going through the sampling. Does the sampling result shows that the square function has magnitude = threshold? That seems strange, because as I see in the thesis, it should result in the output to the neuron fires not long before the square function ends. If the magnitude of the square function equals to the threshold, won’t the membrane potential may reach potential and fires right away?

submitted by /u/Laurence-Lin
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from Artificial Intelligence


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