Do Bounded Signals Have Bounded Amplitudes?
Multidimensional Systems and Signal Processing - Special issue on recent developments in time-frequency analysis
On nontrivial analytic signals with positive instantaneous frequency
Signal Processing
Signal-to-noise ratio estimation using higher-order moments
Signal Processing
A sampling theorem for non-bandlimited signals using generalized Sinc functions
Computers & Mathematics with Applications
Higher-order properties of analytic wavelets
IEEE Transactions on Signal Processing
Characterization of analytic phase signals
Computers & Mathematics with Applications
Bivariate instantaneous frequency and bandwidth
IEEE Transactions on Signal Processing
Discrete-time analytic signals and Bedrosian product theorems
Digital Signal Processing
Wavelet ridge estimation of jointly modulated multivariate oscillations
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Rational orthogonal bases satisfying the Bedrosian identity
Advances in Computational Mathematics
On the analytic wavelet transform
IEEE Transactions on Information Theory
B-splines of Blaschke product type
Computers & Mathematics with Applications
Characterization of the peak value behavior of the Hilbert transform of bounded bandlimited signals
Problems of Information Transmission
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In many questions of signal processing, it is important to use the concepts of instantaneous amplitude or phase of signals. This is especially the case in communication systems with amplitude or frequency modulation. These concepts are often introduced empirically. However, it is well known that the correct approach for this purpose is to use the concept of analytic signal. Starting from this point, we show some examples of contradictions appearing when using other definitions of instantaneous amplitude or frequency that are commonly admitted. This introduces the problem of characterizing pure amplitude-modulated or pure phase-modulated signals. It is especially shown that whereas amplitude modulated signals can be characterized by spectral considerations, this is no longer the case for phase-modulated signals. Furthermore, signals with constant amplitude have very specific properties, which are analyzed in detail. Some consequences and extensions to random signals are finally discussed