Random-noise filter based on circular correlation

In this work we consider various Fourier series representations of an additive noise-contaminated signal f(t). Fourier estimates of the signal are obtained by first establishing a fundamental frequency estimate and a residual error signal. Repeated additions of higher harmonics yield smaller root-mean-square error signals. However, a minimal square error is not used to terminate the iterations. The minimum circular correlation coefficient [1] is used to terminate the iteration at a five percent level of confidence. The resulting Fourier series g(t) is used as the analytic estimate of the original signal. The resulting filter, known as an SFilter, have been applied in the electromagnetic pulse processing area [2,3]. The filter follows from classical works in digital signal processing [4,5].