Topic

# Instantaneous phase

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

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01 Jan 1995

TL;DR: In this article, the authors present a general approach and the Kernel Method for reduced interference in the representation of signal signals, which is based on the Wigner distribution and the characteristic function operator.

Abstract: 1. The Time and Frequency Description of Signals. 2. Instantaneous Frequency and the Complex Signal. 3. The Uncertainty Principle. 4. Densities and Characteristic Functions. 5. The Need for Time-Frequency Analysis. 6. Time-Frequency Distributions: Fundamental Ideas. 7. The Short-Time Fourier Transform. 8. The Wigner Distribution. 9. General Approach and the Kernel Method. 10. Characteristic Function Operator Method. 11. Kernel Design for Reduced Interference. 12. Some Distributions. 13. Further Developments. 14. Positive Distributions Satisfying the Marginals. 15. The Representation of Signals. 16. Density of a Single Variable. 17. Joint Representations for Arbitrary Variables. 18. Scale. 19. Joint Scale Representations. Bibliography. Index.

2,951 citations

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01 Apr 1992TL;DR: The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed in this paper, and the extent to which the IF corresponds to the intuitive expectation of reality is also considered.

Abstract: The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed. The extent to which the IF corresponds to the intuitive expectation of reality is also considered. A historical review of the successive attempts to define the IF is presented. The relationships between the IF and the group-delay, analytic signal, and bandwidth-time (BT) product are explored, as well as the relationship with time-frequency distributions. The notions of monocomponent and multicomponent signals and instantaneous bandwidth are discussed. It is shown that these notions are well described in the context of the theory presented. >

1,952 citations

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01 Jun 1946

TL;DR: In this paper, a differential equation is derived which gives the oscillator phase as a function of time, and with the aid of this equation, the transient process of "pull-in" as well as the production of distorted beat note are described in detail.

Abstract: Impression of an external signal upon an oscillator of similar fundamental frequency affects both the instantaneous amplitude and instantaneous frequency. Using the assumption that time constants in the oscillator circuit are small compared to the length of one beat cycle, a differential equation is derived which gives the oscillator phase as a function of time. With the aid of this equation, the transient process of "pull-in" as well as the production of a distorted beat note are described in detail. It is shown that the same equation serves to describe the motion of a pendulum suspended in a viscous fluid inside a rotating container. The whole range of locking phenomena is illustrated with the aid of this simple mechanical model.

1,751 citations

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TL;DR: A set of simple new procedures has been developed to enable the real-time manipulation of speech parameters by using pitch-adaptive spectral analysis combined with a surface reconstruction method in the time–frequency region.

1,741 citations

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TL;DR: In this article, the significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas in the US and the UK, showing that color patterns can help an interpreter see their interrelationship and spatial changes.

Abstract: The conventional seismic trace can be viewed as the real component of a complex trace which can be uniquely calculated under usual conditions. The complex trace permits the unique separation of envelope amplitude and phase information and the calculation of instantaneous frequency. These and other quantities can be displayed in a color-encoded manner which helps an interpreter see their interrelationship and spatial changes. The significance of color patterns and their geological interpretation is illustrated by examples of seismic data from three areas.

1,290 citations