Error analysis on distribution-based frequency estimator

Frequency estimation is a useful technology for analyzing oscillatory phenomena. In these days, there is a demand for rapid and highly accurate frequency estimator. Though various frequency estimation methods have been proposed, most of them can not respond to the demand. An algebraic approach is succeeded in achieving the demand but it requires a lot of multiple integrations due to eliminating differential operations. The present paper proposes a frequency estimator of a sinusoidal signal based on the notion of distribution theory. Then the estimator is realized by single integrations. The proposed method relaxes the complexity of multiple integrations into single integrations but the integration is theoretically evaluated over the infinite interval (-∞, ∞). The paper firstly reduces the infinite interval to a finite observation interval [0, T] and secondly approximates the integration by a numerical integration. The authors introduce Gaussian function as a test function and perform an error analysis to ensure the accuracy of the frequency estimator. As a result of the error analysis, the suitable conditions of the Gaussian function are clarified. Under the derived conditions, the authors confirmed that the proposed frequency estimator brings out enough the estimation performance.