An algebraic derivative-based approach for the zero-crossings estimation

A new approach to the design of a zero-crossings estimation algorithm is proposed. The approach uses elementary differential algebraic operations in the frequency domain for accurate derivative estimation. Such estimates are composed of iterated integrals of noisy observed signal. A detector-signal, which is exactly equal to zero when there is no intersection between the observed signal and the real axis and is greater than zero when a zero-crossing occurs, is obtained. To justify the theoretical analysis and to investigate the performances of the developed method, simulated experiments are performed.