A novel analytical approach to orthogonal bases extraction from AM-FM signals

This paper presents a new method for extracting orthogonal bases from AM-FM signals. Since AM-FM signals are non-stationary, appropriate basis functions are sought provided that instantaneous frequency can be defined meaningfully. With respect to the intrinsic structure of AM-FM signals, these bases should be in generalized exponential format. Expansion by such bases is known as generalized Fourier expansion. So the oscillating modes embedded in signal would be extracted efficiently. In contrast to exiting methods, the proposed technique provides these functions analytically, by utilizing orthogonal rational functions. This method is founded on two main steps. First, the corresponding generating system of AM-FM signal should be determined. A model is developed in this paper based on the concept of linear time-varying systems. Second, this system is expanded by appropriate orthogonal rational functions in complex domain. These functions are tantamount to orthogonal generalized exponential functions in time domain which yield the desired properties.