A Computational Primitive for Convolution based on Coupled Oscillator Arrays

In this paper we present a new computational primitive for convolution using coupled oscillator arrays. It is based on a Degree of Match (DOM) operation for pairs of vectors of analog voltage encoded data. The convolution operation is synthesized from these DOM circuits and computes the precise mathematical convolution of the two vectors. We present an example circuit design for the DOM operator and SPICE simulations of the circuit behavior. A MATLAB model is curve fit to an inverted copy of this output and shown to be roughly equivalent to the square of the Euclidian distance between the vectors. Using a parameterized version of this model we conducted a MATLAB study to analyze the accuracy of the DOM and convolution operations under variations in oscillator array symmetry, locking range, and additive noise. We also show a small example of convolution with an edge enhancement filter.