Techniques for the identification of a spike-processing circuit are provided. An exemplary method includes receiving spike trains corresponding to a circuit input over a time period, and selecting a number of spikes for each of input spike trains over a predetermined time window. Each of the selected spikes can be replaced with a sampled reproducing kernel to obtain a plurality of signals, and each obtained signal can correspond to one of the input spike trains. Each of the obtained signals can be passed through a plurality of receptive fields or filters to obtain an aggregate filter output signal. The filter output signal can be encoded into an output spike train, and the output spike train can correspond to a response of the circuit to the plurality of input spike trains.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for identification of a spike-processing circuit, comprising: receiving a plurality of spike trains corresponding to a circuit input over a time period; selecting a number of spikes for each of the plurality of input spike trains over a predetermined time window; replacing each of the selected spikes with a sampled reproducing kernel to obtain a plurality of signals, each obtained signal corresponding to one of the plurality of input spike trains; passing each of the obtained signals through a plurality of receptive fields or filters to obtain an aggregate filter output signal; and encoding the filter output signal into an output spike train, the output spike train corresponding to a response of the circuit to the plurality of input spike trains. 2. The method of claim 1, wherein the circuit input corresponds to an input to a neuron, an asynchronous sampling circuits, or an oscillator circuit. 3. The method of claim 1, wherein the circuit input comprises a lateral input and a feedback input. 4. The method of claim 1, wherein one or more of the obtained signals comprises a periodic signal. 5. The method of claim 1, wherein the filter output signal comprises a dendritic current. 6. The method of claim 1, wherein the encoding the filter output signal comprises encoding using an integrate-and-fire neuron. 7. The method of claim 1, wherein the encoding the filter output signal comprises encoding using a Hodgkin-Huxley neuron. 8. The method of claim 1, wherein the encoding the filter output signal comprises encoding using an Asynchronous Sigma Delta Modulator (ASDM). 9. The method of claim 1, wherein the encoding the filter output signal comprises encoding using an oscillator. 10. The method of claim 9, wherein the oscillator comprises additive or multiplicative coupling. 11. The method of claim 9, wherein the oscillator comprises a van der Pol oscillator. 12. The method of claim 1, wherein the predetermined time window corresponds to 2πL/Ω, where L corresponds to an order of a signal space of the plurality of input spike trains and Ω corresponds to a bandwidth of the plurality of input spike trains. 13. The method of claim 1, wherein the number of windows is N, the number of receptive fields is M, and the number of selected spikes is greater than or equal to M(2L+1)+N. 14. The method of claim 1, wherein each of the plurality of receptive fields consists of a single dimension over time. 15. The method of claim 1, further comprising receiving a plurality of continuous, one-dimensional signals corresponding to the circuit input, wherein each of the plurality of receptive fields consists of a single dimension over time. 16. The method of claim 1, further comprising receiving a plurality of continuous signals having a dimension greater than one, and one or more of the plurality of receptive fields comprises a one-dimensional filter and one or more of the plurality of receptive fields comprises a multi-dimensional filter. 17. The method of claim 16, wherein the plurality of continuous signals comprises one or more audio-visual signals. 18. A system for identification of a spike-processing circuit, comprising: one or more inputs configured to receive a plurality of spike trains corresponding to a circuit input over a time period; a windowing circuit operatively coupled to the one or more inputs and configured to select a number of spikes for each of the plurality of spike trains over a predetermined time window; a kernel processor configured to receive the selected spikes and replace each of the selected spikes with a sampled reproducing kernel to obtain a plurality of signals, each obtained signal corresponding to one of the plurality of input spike trains; a plurality of receptive fields or filters configured to obtain an aggregate filter output signal from the obtained signals; and a neuronal encoder configured to receive the aggregate dendritic current and encode an output spike train, the output spike train corresponding to a response of the circuit to the plurality of input spike trains. 19. The system of claim 18, wherein the circuit input corresponds to an input to a neuron, an asynchronous sampling circuits, or an oscillator circuit. 20. The system of claim 18, wherein the circuit input comprises a lateral input and a feedback input. 21. The system of claim 18, wherein one or more of the obtained signals comprises a periodic signal. 22. The system of claim 18, wherein the filter output signal comprises a dendritic current. 23. The system of claim 18, wherein the neuronal encoder comprises an integrate-and-fire neuron. 24. The system of claim 18, wherein the neuronal encoder comprises a Hodgkin-Huxley neuron. 25. The system of claim 18, wherein the neuronal encoder comprises an Asynchronous Sigma Delta Modulator (ASDM). 26. The system of claim 18, wherein the neuronal encoder comprises an oscillator. 27. The system of claim 26, wherein the oscillator comprises additive or multiplicative coupling. 28. The system of claim 26, wherein the oscillator comprises a van der Pol oscillator. 29. The system of claim 18, wherein the predetermined time window corresponds to 2πL/Ω, where L corresponds to an order of a signal space of the plurality of input spike trains and Ω corresponds to a bandwidth of the plurality of input spike trains. 30. The system of claim 18, wherein the number of windows is N, the number of receptive fields is M, and the number of selected spikes is greater than or equal to M(2L+1)+N. 31. The system of claim 18, wherein each of the plurality of receptive fields consists of a single dimension over time. 32. The system of claim 18, wherein the one or more inputs is further configured to receive a plurality of continuous, one-dimensional signals corresponding to the circuit input, wherein each of the plurality of receptive fields consists of a single dimension over time. 33. The system of claim 18, wherein the one or more inputs is further configured to receive a plurality of continuous signals having a dimension greater than one, one or more of the plurality of receptive fields comprises a one-dimensional filter, and one or more of the plurality of receptive fields comprises a multi-dimensional filter. 34. The system of claim 33, wherein the plurality of continuous signals comprises one or more audio-visual signals.