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Breaking the Limits: Redefining the Instantaneous Frequency

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Abstract

The Carson and Fry introduced the concept of variable frequency as a generalization of the constant frequency. The instantaneous frequency (IF) is the time derivative of the instantaneous phase, and it is well defined only when this derivative is positive. If this derivative is negative, the IF creates problem because it does not provide any physical significance. This study proposes a mathematical solution and eliminates this problem by redefining the IF such that it is valid for all monocomponent, multicomponent signals of nonlinear and nonstationary nature. This is achieved by using the property of the multivalued inverse tangent function that provides base to ensure that the instantaneous phase is an increasing function. The efforts and understanding of all the methods based on the IF would improve significantly by using this proposed definition of the IF. We also demonstrate that the decomposition of a signal, using zero-phase filtering based on the well-established Fourier and filter theory, into a set of desired frequency bands with proposed IF produces accurate time–frequency–energy (TFE) distribution that reveals true nature of signal. Simulation results demonstrate the efficacy of the proposed IF that makes zero-phase filter-based decomposition most powerful for the TFE analysis of a signal.

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Acknowledgements

Author would like to show his gratitude to the Prof. S. D. Joshi (IITD), Prof. R. K. Pateny (IITD), and Dr. Kaushik Saha (CTO, Samsung R&D Institute India—Delhi) for sharing their wisdom and expertise during this research.

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  1. School of Engineering and Applied Sciences (SEAS), Bennett University, Greater Noida, India

    Pushpendra Singh

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  1. Pushpendra Singh
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Correspondence to Pushpendra Singh.

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Singh, P. Breaking the Limits: Redefining the Instantaneous Frequency. Circuits Syst Signal Process 37, 3515–3536 (2018). https://doi.org/10.1007/s00034-017-0719-y

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