scispace - formally typeset
Search or ask a question
Journal ArticleDOI

On amplitude and frequency demodulation using energy operators

TL;DR: It is shown that the nonlinear energy-tracking signal operator Psi and its discrete-time counterpart can estimate the amplitude envelope of AM signals and the instantaneous frequency of FM signals.
Abstract: It is shown that the nonlinear energy-tracking signal operator Psi (x)=(dx/dt)/sup 2/-xd/sup 2/x/dt/sup 2/ and its discrete-time counterpart can estimate the AM and FM modulating signals. Specifically, Psi can approximately estimate the amplitude envelope of AM signals and the instantaneous frequency of FM signals. Bounds are derived for the approximation errors, which are negligible under general realistic conditions. These results, coupled with the simplicity of Psi , establish the usefulness of the energy operator for AM and FM signal demodulation. These ideas are then extended to a more general class of signals that are sine waves with a time-varying amplitude and frequency and thus contain both an AM and an FM component; for such signals it is shown that Psi can approximately track the product of their amplitude envelope and their instantaneous frequency. The theoretical analysis is done for both continuous- and discrete-time signals. >
Citations
More filters
Journal ArticleDOI
TL;DR: Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research.
Abstract: [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

1,533 citations


Cites background or methods from "On amplitude and frequency demodula..."

  • ...[36] There are indeed methods other than Hilbert transform that can be used to calculate instantaneous frequency, such as the Wigner-Ville distribution [Cohen, 1995], the Teager energy operator [Kaiser, 1990; Maragos et al., 1993a, 1993b], and wavelet analysis....

    [...]

  • ...More recently, Huang [2005b] has also identified the Teager energy operator [Kaiser, 1990; Maragos et al., 1993a, 1993b] as an extremely local and sharp test for harmonic distortions within any IMF derived from data....

    [...]

Journal ArticleDOI
TL;DR: A physiological signal-based emotion recognition system is reported, developed to operate as a user-independent system, based on physiological signal databases obtained from multiple subjects, and consisted of preprocessing, feature extraction and pattern classification stages.
Abstract: A physiological signal-based emotion recognition system is reported. The system was developed to operate as a user-independent system, based on physiological signal databases obtained from multiple subjects. The input signals were electrocardiogram, skin temperature variation and electrodermal activity, all of which were acquired without much discomfort from the body surface, and can reflect the influence of emotion on the autonomic nervous system. The system consisted of preprocessing, feature extraction and pattern classification stages. Preprocessing and feature extraction methods were devised so that emotion-specific characteristics could be extracted from short-segment signals. Although the features were carefully extracted, their distribution formed a classification problem, with large overlap among clusters and large variance within clusters. A support vector machine was adopted as a pattern classifier to resolve this difficulty. Correct-classification ratios for 50 subjects were 78.4% and 61.8%, for the recognition of three and four categories, respectively.

903 citations

Journal ArticleDOI
TL;DR: The experimental results provide evidence that bandpass-filtered speech signals around speech formants contain amplitude and frequency modulations within a pitch period, and several efficient algorithms are developed and compared for estimating the amplitude envelope and instantaneous frequency of discrete-time AM-FM signals.
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. >

822 citations

Journal ArticleDOI
TL;DR: A systematic review of over 20 major time-frequency analysis methods reported in more than 100 representative articles published since 1990 can be found in this article, where their fundamental principles, advantages and disadvantages, and applications to fault diagnosis of machinery have been examined.

719 citations

Journal ArticleDOI
TL;DR: This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF, and finds that the NHT and direct quadrature gave the best overall performance.
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...

618 citations

References
More filters
Proceedings ArticleDOI
03 Apr 1990
TL;DR: The results of applying this algorithm to a number of well-known signals are shown and some of the invariance and noise properties of the algorithm are derived and verified by simulation.
Abstract: A simple algorithm is derived that permits on-the-fly calculation of the energy required to generate, in a certain sense, a signal. The results of applying this algorithm to a number of well-known signals are shown. Some of the invariance and noise properties of the algorithm are derived and verified by simulation. The implementation of the algorithm and its application to speech processing are briefly discussed. >

1,221 citations


"On amplitude and frequency demodula..." refers background in this paper

  • ...Kaiser [ 2 ] showed that if w(n) is a discrete-time zero-mean white noise sequence, then...

    [...]

  • ...The discrete operator also has similar properties [ 2 ], [3]:...

    [...]

  • ...The reasoning [ 2 ], [3] proceeds as follows: Consider an undriven linear undamped oscillator consisting of a mass m and a spring of constant k. Its displacement x(t) is governed by the motion equation mx + kx = 0, for which the general solution is a cosine x(t) = A cos (wot + e) with wo = m. The instantaneous energy E,, of this undamped oscillator is constant and equal to the sum of its kinetic and potential energy; i.e.,...

    [...]

Journal ArticleDOI
TL;DR: The experimental results provide evidence that bandpass-filtered speech signals around speech formants contain amplitude and frequency modulations within a pitch period, and several efficient algorithms are developed and compared for estimating the amplitude envelope and instantaneous frequency of discrete-time AM-FM signals.
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. >

822 citations

Journal ArticleDOI
H. Teager1
TL;DR: In this paper, a compact array of hot wire anemometers was used to measure intraoral air velocity with a vertical cross section at the rear of the mouth during sustained phonation of the vowel "I".
Abstract: Reproducible intraoral air velocity measurements were made with a compact array of hot wire anemometers moved laterally within a vertical cross section at the rear of the mouth during sustained phonation of the vowel "I". The results indicate "separated" flow patterns at variance with laminar flow of vocal tract vowel models.

353 citations

Proceedings ArticleDOI
14 Apr 1991
TL;DR: An AM-FM model for representing modulations in speech resonances is investigated and it is found that Psi can approximately track the envelope of AM signals, the instantaneous frequency of FM signals, and the product of these two functions in the general case of AM- FM signals.
Abstract: An AM-FM model for representing modulations in speech resonances is investigated. Specifically, an FM model is proposed for the time-varying formants whose amplitude varies as the envelope of an AM signal. To detect the modulations the energy operator Psi ( chi ) and its discrete counterpart are applied. It is found that Psi can approximately track the envelope of AM signals, the instantaneous frequency of FM signals, and the product of these two functions in the general case of AM-FM signals. Several experiments on the application of this AM-FM modeling to speech signals, band pass filtered via Gabor filters are reported. >

137 citations

Proceedings ArticleDOI
23 Mar 1992
TL;DR: The theoretical and experimental results demonstrate that the energy separation algorithm, due to its low computational complexity and instantaneously adapting nature, is very useful in detecting modulation patterns in speech and other time-varying signals.
Abstract: To estimate the amplitude envelope and instantaneous frequency of an AM-FM signal the authors developed a novel approach that uses nonlinear combinations of instantaneous signal outputs from an energy-tracking operator to separate its output energy product into its amplitude modulation and frequency modulation components. This energy separation algorithm is then applied to search for modulations in speech resonances, which the authors model using AM-FM signals. The theoretical and experimental results demonstrate that the energy separation algorithm, due to its low computational complexity and instantaneously adapting nature, is very useful in detecting modulation patterns in speech and other time-varying signals. >

136 citations