Period Histogram and Product Spectrum: New Methods for Fundamental-Frequency Measurement

TLDR

When the fundamental component of a periodic signal is unavailable, its frequency can be inferred by measuring higher harmonic frequencies and computing their greatest common divisor, and its period by measuring harmonic periods and finding their least common multiple. The paper aims to describe several methods for measuring fundamental frequency and period based on these concepts. These methods involve computing the greatest common divisor of harmonic frequencies or the least common multiple of harmonic periods. Computer simulations and analog instrumentation show that the new methods reduce complexity and, in some cases, outperform cepstrum analysis.

Abstract

The fundamental frequency of a periodic signal whose fundamental component is not available for measurement can be determined by measuring the frequencies of its higher harmonic components and computing the largest common divider of these frequencies. Similarly, the fundamental period can be determined by measuring the periods of individual harmonics and finding their smallest common multiple. Several methods of fundamental frequency and period measurement, based on these concepts, are described in this paper. The results of computer simulations and analog instrumentations indicate that these new methods. at a considerable reduction in complexity, compare favorably with, and in some cases exceed, the capabilities of cepstrum analysis.