Abstract
The instantaneous frequency (IF) and envelope (IE) analysis of signals is very useful in various fields. In this paper, three examples of applications are presented. (1) Representing signals by IF and/or IE. Since signals before and after allpass filtering have the same frequency spectra, there is no way to distinguish them by the spectrum analysis. However, IF and/or IE may show clear differences between them. It is interesting that IF at the onset of a sinusoidal burst signal is twice the frequency of the sinusoid (JAES, September 1980). (2) Analyzing vibratos of violin sounds recorded in CDs in order to find out differences of playing styles of virtuosi such as Grumiaux, Oistrakh, Perlman, and Stern. Some results show clear differences in the speeds and depths of the frequency modulation (vibrato) (ISMA 2004). (3) Analyzing rotation fluctuations of automobile rotating shafts. An electromagnetic or electrostatic sensor located close to a rotating gear measures a quasi-sinusoidal signal. The IF analysis of this signal gives the rotation frequency and details of its fluctuation structure. Not only the steady state rotation, but transient rotation change analysis of a reciprocating engine at the sequence of idling stop and start (ISS) are also possible (https://www.aandd.co.jp/adhome/pdf/catalog/nvhanalysis/casra.pdf).
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