A closed frequencies estimation by using the phase property of an all-pass filter.

Abstract

The purpose of this paper is to shorten the analytical duration with keeping high resolution in frequency for the closed frequencies estimation. Existence of the closed frequencies in an input signal makes difficult the estimation with high resolution, because of a spectral leakage. It is difficult to eliminate the leakage. We utilize the leakage to estimate the closed frequencies without attempt to eliminate it. In general, the magnitude of leakage changes with the phase of an input signal. For changing the phase, an all-pass filter (APF) is used. This paper makes clear the relationships among three factors: the leakage, the phase, and the input frequencies (i.e., periodic components forming an input signal). The experimental results for estimating closed frequencies clearly show that the use of APF results in the duration shorter than 60% of the conventional methods with high resolution in frequency.