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12
The Hilbert spectrum via wavelet projections
 Proc. Roy. Soc. London A
, 2004
"... Nonstationary signals are increasingly analysed in the timefrequency domain to determine the variation of frequency components with time. It was recently proposed in this journal that such signals could be analysed by projections onto the timefrequency plane giving a set of monocomponent signals ..."
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Cited by 19 (2 self)
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Nonstationary signals are increasingly analysed in the timefrequency domain to determine the variation of frequency components with time. It was recently proposed in this journal that such signals could be analysed by projections onto the timefrequency plane giving a set of monocomponent signals. These could then be converted to ‘analytic ’ signals using the Hilbert transform and their instantaneous frequency calculated, which when weighted by the energy yields the ‘Hilbert energy spectrum ’ for that projection. Agglomeration over projections yields the complete Hilbert spectrum. We show that superior results can be obtained using waveletbased projections. The maximaloverlap (undecimated/stationary/translation invariant) discrete wavelet transform and wavelet packet transforms are used, with the FejérKorovkin class of wavelet filters. These transforms produce decompositions which are conducive to statistical analysis, in particular enabling noise reduction methodology to be developed and easily and successfully applied.
Bivariate Instantaneous Frequency and Bandwidth
, 902
"... 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 realvalued signals, or as one analytic and one antianalytic signal. A nonstationary but oscillatory bivariate sign ..."
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Cited by 11 (3 self)
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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 realvalued signals, or as one analytic and one antianalytic 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 timevarying ellipse: amplitude modulation with fixed eccentricity, eccentricity modulation, and orientation modulation or precession. A application to the analysis of data from a freedrifting oceanographic float is presented and discussed.
On the Instantaneous Frequencies of Multicomponent AMFM Signals
 IEEE Signal Processing Lett
, 1998
"... We study the instantaneous frequencies (IF's) of multicomponent AMFM signals by extending the recent work on the twocomponent case by Loughlin and Tacer to the more general Mcomponent case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegativel ..."
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We study the instantaneous frequencies (IF's) of multicomponent AMFM signals by extending the recent work on the twocomponent case by Loughlin and Tacer to the more general Mcomponent 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 IFbased monocomponent AMFM decomposition is not appropriate for the modeling and analysis of multicomponent AMFM signals unless all the components are well separated in the time domain. Index TermsAmplitude modulation, frequency domain analysis, frequency modulation, modulation/demodulation.
A New Approach for Estimation of Instantaneous Mean Frequency of a TimeVarying Signal
 EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2005:17, 2848–2855
, 2005
"... Analysis of nonstationary signals is a challenging task. True nonstationary signal analysis involves monitoring the frequency changes of the signal over time (i.e., monitoring the instantaneous frequency (IF) changes). The IF of a signal is traditionally obtained by taking the first derivative of th ..."
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Cited by 1 (0 self)
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Analysis of nonstationary signals is a challenging task. True nonstationary signal analysis involves monitoring the frequency changes of the signal over time (i.e., monitoring the instantaneous frequency (IF) changes). The IF of a signal is traditionally obtained by taking the first derivative of the phase of the signal with respect to time. This poses some difficulties because the derivative of the phase of the signal may take negative values thus misleading the interpretation of instantaneous frequency. In this paper, a novel approach to extract the IF from its adaptive timefrequency distribution is proposed. The adaptive timefrequency distribution of a signal is obtained by decomposing the signal into components with good timefrequency localization and by combining the Wigner distribution of the components. The adaptive timefrequency distribution thus obtained is free of crossterms and is a positive timefrequency distribution but it does not satisfy the marginal properties. The marginal properties are achieved by applying the minimum crossentropy optimization to the timefrequency distribution. Then, IF may be obtained as the first central moment of this adaptive timefrequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. A set of realworld and synthetic signals of known IF dynamics is tested with the proposed method as well as with other common timefrequency distributions. The simulation shows that the method successfully extracted the IF of the signals.
Instantaneous Frequency Estimation Using Discrete Evolutionary
, 2001
"... 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 noiselike signals. The DET provides a representation for nonstationary signals and a timefrequency kernel that permit us to obtain th ..."
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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 noiselike signals. The DET provides a representation for nonstationary signals and a timefrequency kernel that permit us to obtain the timedependent 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 timefrequency 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 nonlinear 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.
AN AMPLITUDE AND FREQUENCYMODULATION VOCODER FOR AUDIO SIGNAL PROCESSING
"... 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 distinc ..."
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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.
– Music transposition – Key mode conversion • Summary
"... From a perceptual view, audio signals are composed of low bandwidth and low frequency subprocesses, which modulate much higher carrier frequencies. • Modulation decomposition? ..."
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From a perceptual view, audio signals are composed of low bandwidth and low frequency subprocesses, which modulate much higher carrier frequencies. • Modulation decomposition?
WEIGHTED AVERAGE INSTANTANEOUS FREQUENCY BASED ON ADAPTIVE SIGNAL DECOMPOSITION
"... It is often claimed that instantaneous frequency, taken as the derivative of the phase of the signal, is appropriate or meaningful only for monocomponent signals, and that for multicomponent signals a weighted average of individual instantaneous frequencies should be used. In this paper, we show i ..."
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It is often claimed that instantaneous frequency, taken as the derivative of the phase of the signal, is appropriate or meaningful only for monocomponent signals, and that for multicomponent signals a weighted average of individual instantaneous frequencies should be used. In this paper, we show if a signal is decomposed adaptively and we compute the matching pursuit distribution, then the first conditional spectral moment is exactly the weighted average instantaneous frequency. Two different signals will be analyzed and the above result will be illustrated in practice. 1.