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Estimating and Interpreting the Instantaneous Frequency of a Signal – Part 2 Algorithms an.pdf

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Estimating and Interpreting the Instantaneous Frequency of a Signal – Part 2 Algorithms an

Estimating and Interpreting The Instantaneous Frequency of a Signal-Part 1: Fundamentals BOUALEM BOASHASH, SENIOR MEMBER, IEEE The frequency of a sinusoidal signal is a well defined quantity. However, often in practice, signals are not truly sinusoidal, or even aggregates of sinusoidal components. Nonstationary signals in particular do not lend themselves well to decomposition into sinusoidal components. For such signals, the notion of frequency loses its effectiveness, and one needs to use a parameter which accounts for the time-varying nature of the process. This need has given rise to the idea of instantaneous frequency. The instantaneous frequency (IF) of a signal is a parame- ter which is often of significant practical importance. In many situations such as seismic, radar, sonar, communications, and biomedical applications, the IF is a good descriptor of some physical phenomenon. This paper discusses the concept of instantaneous frequency, its definitions, and the correspondence between the various mathe- matical models formulated for representation of IF. The paper also considers the extent to which the IF corresponds to our intuitive expectation of reality. A historical review of the successive attempts to define the IF is presented. Then the relationships between the IF and the group-delay, analytic signal, and bandwidth-time (BT) product are explored, as well as the relationship with time-frequency distribu- tions. Finally, the notions of monocomponent and multicomponent signals, and instantaneous bandwidth are discussed. It is shown that all these notions are well described in the context of the theory presented. I . INTRODUCTION This paper presents a tutorial review of the theory nec- essary to understand and utilize the notion of the instanta- neous frequency (IF) of a signal. Like many other signal processing concepts, the IF was originally defined in the context of FM modulation theory in communications. The importan