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On Orthogonal Modes of Continuous and Discrete Frequency Modulation


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/12924

On Orthogonal Modes of Continuous and Discrete Frequency Modulation

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Title: On Orthogonal Modes of Continuous and Discrete Frequency Modulation
Author: Santhanam, Balu
Subject(s): Frequency modulation, Sturm-Liouville differential and difference equation, orthogonal FM modes, Sturm-Liouville FM spectrum, instantaneous frequency response.
Abstract: Fourier analysis techniques remain the staple tools for the processing of sinusoidal signals with stationary frequency content. These techniques however, are unsuitable for the analysis of signals with time-varying frequency content such as those with frequency and amplitude modulation unless approximations regarding stationarity are made over smaller signal time windows. In this paper, we study and extend a recently introduced Sturm-Liouville model for both continuous and discrete FM modulation for the purpose of studying orthogonal modes of continuous and discrete FM modulation. These FM modes are first shown to form an orthogonal system and further shown to have the same connection with respect to the FM Sturm-Liouville system operator, that complex exponentials or sinusoids have with LTI systems and the convolution operator. The notion of a finite Sturm-Liouville FM spectrum that measures the strength of the orthogonal FM modes present in a FM signal analogous to the Finite Fourier Transform, is formally introduced.
Date: 2011-08-01
URI: http://hdl.handle.net/1928/12924

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