The relationship between instantaneous frequency and time-frequency representations

Author

Lovell, Brian C. ; Williamson, Robert C. ; Boashash, Boualem

Author_Institution

Dept. of Electr. Eng., Queensland Univ., Brisbane, Qld., Australia

Volume

41

Issue

3

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

1458

Lastpage

1461

Abstract

The relationship between instantaneous frequency estimation based on the derivative of the phase of the analytic signal and the first moment of the general time-frequency representation from Cohen´s (1989) class is given in the continuous- and discrete-time domains. Application of the standard linear definition of first moment to discrete-time-frequency representations leads to biased instantaneous frequency estimators with high variance. To correct this problem, it is shown that periodic (circular) definitions of moments must be used to account for the periodization of the frequency variable due to sampling

Keywords

estimation theory; frequency-domain analysis; signal processing; time-domain analysis; analytic signal; circular definitions; continuous time domain; discrete-time domains; first moment; frequency variable; instantaneous frequency estimation; periodic definitions; sampling; time-frequency representation; Feedback; Frequency estimation; Least squares methods; Notice of Violation; Phase estimation; Signal analysis; Signal processing; Signal processing algorithms; Speech processing; Time frequency analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.205756

Filename

205756