Estimating zero-crossings of uniformly sampled data

Abstract

Analysis of the zero-crossing times of angle-modulated signals provides a computationally efficient means of implementing a number of processing functions, including demodulation and spectral estimation. Unfortunately, sampling of a bandlimited signal is typically accomplished using uniformly spaced amplitude samples rather than detecting the zero-crossing times. This paper investigates the use of linear interpolation to estimate zero-crossing times from the uniformly-sampled data. The statistical properties of the error due to interpolation, additive Gaussian noise and'quantization are each considered separately as a function of the sampling interval.

Accuracy assessment of the two-sample zero-crossing detection in a sinusoidal signal

“…For higher frequencies, an empirical expression is adopted (figures 6 and 7). At the Nyquist rate the experimental normalized standard deviation tends to its maximum of 0.14, which agrees with that derived in [14]: 1/(4 √ 3) ≈ 0.144. Finally, combining (6) with the results of figures 6 and 7, the fractional phase standard deviation due to the linear interpolation is approximated as…”

“…Then a standard deviation of that mean is exactly equal to (13). There are two other estimates [14,16] which are close, but not identical to (13). Figure 9 compares experimental and theoretical standard deviations.…”

“…Suppose that a zero-crossing time is computed as the mean of two transitions through two non-zero levels with opposite signs and infinitesimal small separation, such that each transition is detected with the standard deviation (14). Then a standard deviation of that mean is exactly equal to (13).…”

“…In this method, a zero-crossing event in a periodic signal is found by a linear interpolation between two consecutive signal samples with opposite signs. Different studies usually consider individual error sources [13][14][15][16] without an evident dissemination to conditions of other experiments. The same limitation also pertains to the results of the numerical simulations [9,11,21,25].…”

“…It is possible to evaluate the uncertainty of a detected zerocrossing theoretically, as the probability density functions of the input quantities are generally known. However, such closed-form solutions usually become impractical to handle or even intractable [14]. This motivates the development of a simplified analytical tool of uncertainty evaluation in the twosample zero-crossing detection method.…”