We study the instantaneous frequencies (IF's) of multicomponent AM--FM signals by extending the recent work on the two-component case by Loughlin and Tacer to the more general M-component case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively weighted average of the IF's of the components is proposed, which we apply as a method of interpreting the IF's of signals having no more than three dominant components at each time. Our quantitative study shows that in general, the IF-based monocomponent AM--FM decomposition is not appropriate for the modeling and analysis of multicomponent AM--FM signals unless all the components are well separated in the time domain. Index Terms---Amplitude modulation, frequency domain analysis, frequency modulation, modulation/demodulation.

In this paper, we propose a method --based on the discrete evolutionary transform (DET)-- to estimate the instantaneous frequency of a signal embedded in noise or noise-like signals. The DET provides a representation for non-stationary signals and a time-frequency kernel that permit us to obtain the time-dependent spectrum of the signal. We will show the instantaneous phase and the corresponding instantaneous frequency (IF) can also be computed from the evolutionary kernel. Estimation of instantaneous frequency is of general interest in time-frequency analysis, and of special interest in the excision of jammers in direct sequence spread spectrum. Implementation of the IF estimation is done by masking and a recursive non-linear correction procedure. The proposed estimation is valid for monocomponent as well as multicomponent signals in the noiseless and noisy situations. Its application to jammer excision in direct sequence spread spectrum communication is considered as an important application. The estimation procedure is illustrated with several examples.

From a perceptual view, audio signals are composed of low bandwidth and low frequency sub-processes, which modulate much higher carrier frequencies. • Modulation decomposition?

The decomposition of audio signals into perceptually meaningful modulation components is highly desirable for the development of new audio effects on the one hand and as a building block for future efficient audio compression algorithms on the other hand. In the past, there has always been a distinction between parametric coding methods and waveform coding: While waveform coding methods scale easily up to transparency (provided the necessary bit rate is available), parametric coding schemes are subjected to the limitations of the underlying source models. Otherwise, parametric methods usually offer a wealth of manipulation possibilities which can be exploited for application of audio effects, while waveform coding is strictly limited to the best as possible reproduction of the original signal. The analysis/synthesis approach presented in this paper is an attempt to show a way to bridge this gap by enabling a seamless transition between both approaches. 1.

The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals, or as one analytic and one anti-analytic signal. A nonstationary but oscillatory bivariate signal has a natural representation as an ellipse whose properties evolve in time, and this representation provides a simple geometric interpretation for the bivariate instantaneous moments. The bivariate bandwidth is shown to consists of three terms measuring the degree of instability of the time-varying ellipse: amplitude modulation with fixed eccentricity, eccentricity modulation, and orientation modulation or precession. A application to the analysis of data from a free-drifting oceanographic float is presented and discussed.