Variable kernel functions for efficient event detection and classification

The author introduces Gaussian-like symmetric kernel functions that can be realized efficiently. The kernels are based on recursive substructures that reduce the amount of computation in convolving the signals with the kernels, specifically, FIR (finite impulse response) filters whose tap coefficients are related to each other recursively. Since the number of coefficients does not depend on the standard deviation of the prototype Gaussian kernels or on the number of samples used in approximating the noncausal Gaussian kernels, the proposed causal kernels are especially suitable for large standard deviations. Several examples illustrate their performance and computational efficiency.