Instantaneous phase

About: Instantaneous phase is a research topic. Over the lifetime, 5013 publications have been published within this topic receiving 86477 citations.

Energy separation in signal modulations with application to speech analysis

Abstract: An efficient solution to the fundamental problem of estimating the time-varying amplitude envelope and instantaneous frequency of a real-valued signal that has both an AM and FM structure is provided. Nonlinear combinations of instantaneous signal outputs from the energy operator are used to separate its output energy product into its AM and FM components. The theoretical analysis is done first for continuous-time signals. Then several efficient algorithms are developed and compared for estimating the amplitude envelope and instantaneous frequency of discrete-time AM-FM signals. These energy separation algorithms are used to search for modulations in speech resonances, which are modeled using AM-FM signals to account for time-varying amplitude envelopes and instantaneous frequencies. The experimental results provide evidence that bandpass-filtered speech signals around speech formants contain amplitude and frequency modulations within a pitch period. >

Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications

Abstract: For pt.I see ibid., vol.80, no.4, p.520-38 (1992). The concept of instantaneous frequency (IF) is extended to discrete-time signals. The specific problem explored is that of estimating the IF of frequency-modulated (FM) discrete-time signals embedded in Gaussian noise. Well-established methods for estimating the IF include differentiation of the phase and smoothing thereof, adaptive frequency estimation techniques such as the phase locked loop (PLL), and extraction of the peak from time-varying spectral representations. More recently, methods based on a modeling of the signal phase as a polynomial have been introduced. These methods are reviewed, and their performance compared on both simulated and real data. Guidelines are given as to which estimation method should be used for a given signal class and signal-to-noise ratio (SNR). >

The local mean decomposition and its application to EEG perception data.

Abstract: This paper describes the local mean decomposition (LMD), a new iterative approach to demodulating amplitude and frequency modulated signals. The new method decomposes such signals into a set of functions, each of which is the product of an envelope signal and a frequency modulated signal from which a time-varying instantaneous frequency can be derived. The LMD method can be used to analyse a wide variety of natural signals such as electrocardiograms, functional magnetic resonance imaging data, and earthquake data. The paper presents the results of applying LMD to a set of scalp electroencephalogram (EEG) visual perception data. The LMD instantaneous frequency and energy structure of the EEG is examined, and compared with results obtained using the spectrogram. The nature of visual perception is investigated by measuring the degree of EEG instantaneous phase concentration that occurs following stimulus onset over multiple trials. The analysis suggests that there is a statistically significant difference between the theta phase concentrations of the perception and no perception EEG data.

On instantaneous frequency

Abstract: Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the m...

Wave propagation and sampling theory—Part II: Sampling theory and complex waves

Abstract: Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using the Goupillaud-Kunetz algorithm. Now we present sampling methods for complex signals or traces corresponding to received waves, and sampling methods for complex characterization of multilayered or heterogeneous media. Regarding the complex signals, we present a twodimecsional(2-D) method of sampling in the time-frequency domain using a special or “extended” Gabor expansion on a set of basic wavelets adapted to phase preservation. Such a 2-D expansion permits us to handle in a proper manner instantaneous frequency spectra. We show the differences between “wavelet resolution” and “sampling grid resolution.” We also show the importance of phase preservation in high-resolution seismic. Regarding the media, we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution. Analytical studies of wave propagation in periodic structures are well known in solid state physics, and lead to the so-called “Bloch waves.” The introduction of complex waves leads to replacing the classical wave equation by a Schriidinger equation. Finally, we show that complex wave equations, Gabor expansion, and Bloch waves are three different ways of ‘introducing the tools of quantum mechanics in highresolution seismic (Gabor, 1946; Kittel, 1976, Morlet, 1975). And conversely, the Goupillaud-Kunetz algorithm and an extended Gabor expansion may be of some use in solid state physics.