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 accu- rate 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.