Fourier Analysis with Spike-Based Signal Representations

The paper discusses signal processing techniques that use signal representations in the form of a sequence of spikes generated at the output of the Integrate-and-Fire (IF) spiking neuron model. The input-output relationship of the spiking neuron model is analyzed and a spike-based input signal model is proposed. The use of this model for Fourier analysis is considered. The focus is on two processing schemes. In the first scheme, an algorithm that computes the Fourier decomposition using a direct spike-based representation of the input signal is proposed. In the second scheme, called inverse spike encoding scheme, a novel algorithm for computing the Fourier series coefficients is derived using a spike-based representation of the basis function. The main advantage of the proposed algorithms is the absence of multiplication operations, which allows them to work on resource-constrained devices. Examples of using the proposed algorithms for spectral analysis of signals are demonstrated.