Digital Signal Processing 20 (2010) 42–62 Contents lists available at ScienceDirect Digital Signal Processing www.elsevier.com/locate/dsp Analysis of multicomponent AM-FM signals using FB-DESA method Ram Bilas Pachori a,∗ , Pradip Sircar b a Communication Research Center, International Institute of Information Technology, Hyderabad, India 500032 b Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, India 208016 article info abstract Article history: Available online 7 May 2009 Keywords: AM-FM signal DESA method Fourier–Bessel expansion Speech analysis The discrete energy separation algorithm (DESA) together with the Gabor’s filtering provides a standard approach to estimate the amplitude envelope (AE) and the instant- aneous frequency (IF) functions of a multicomponent amplitude and frequency modulated (AM-FM) signal. The filtering operation introduces amplitude and phase modulations in the separated monocomponent signals, which may lead to an error in the final estimation of the modulation functions. In this paper, we have proposed a method called the Fourier– Bessel expansion-based discrete energy separation algorithm (FB-DESA) for component separation and estimation of the AE and IF functions of a multicomponent AM-FM signal. The FB-DESA method does not introduce any amplitude or phase modulation in the separated monocomponent signal leading to accurate estimations of the AE and IF functions. Simulation results with synthetic and natural signals are included to illustrate the effectiveness of the proposed method.  2009 Elsevier Inc. All rights reserved. 1. Introduction In the present work, we consider real multicomponent amplitude modulated (AM) and frequency modulated (FM) signals comprising of individual components of the form A(t ) cos(ωt + φ(t )) for analysis and synthesis [1]. The signal model finds application in speech analysis/synthesis where each formant of speech is represented by an individual AM-FM signal [2–6]. In the parametric approach of analysis of an AM-FM signal, the functions A(t ) and φ(t ) are expanded in terms of some basis functions whose coefficients are to be determined [7,8]. In the nonparametric approach, an individual component is separated by band-pass filtering, and the time-varying amplitude and phase functions are estimated conveniently by the energy separation algorithm (ESA) [9]. It should be pointed out that the optimum choice of the center frequency and that of the bandwidth of the filter may be difficult when φ(t ) is arbitrary. Moreover, a band-pass filtering process imposes amplitude and phase distortions in an isolated component leading to inaccurate estimations of the time-varying functions. In this paper, we consider the non-parametric approach of signal analysis, where the amplitude and frequency functions are estimated by the discrete ESA (DESA) [3,9]. The main purpose of this work is to present a technique which will allow us to separate an AM-FM component of a multicomponent signal with out introducing any distortion in the amplitude or the phase of the separated channel. It is intended that the process of separation of all channels of the composite signal should be a one-step process [10], and the technique will need no prior information about the frequency-bands of the individual channels. In the sequel, we present a method based on the Fourier–Bessel (FB) expansion, which can separate the individual channels with all desirable properties. * Corresponding author. E-mail addresses: pachori@iiit.ac.in (R.B. Pachori), sircar@iitk.ac.in (P. Sircar). 1051-2004/$ – see front matter  2009 Elsevier Inc. All rights reserved. doi:10.1016/j.dsp.2009.04.013