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# On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

Venkitaraman, Arun and Seelamantula, Chandra Sekhar (2013) On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal. In: IEEE SIGNAL PROCESSING LETTERS, 20 (12). pp. 1187-1190.

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Official URL: http://dx.doi.org/10.1109/LSP.2013.2284963

## Abstract

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Item Type: Journal Article Publisher Copyright for this article belongs to IEEE Xplore Amplitude modulation; analytic signal; fractional hilbert transform; frequency modulation; phase modulation; squared analytic signal Division of Electrical Sciences > Electrical Engineering 19 Nov 2013 06:36 19 Nov 2013 06:36 http://eprints.iisc.ernet.in/id/eprint/47774

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