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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of displacement with respect to time. Like average velocity, the instantaneous velocity is a vector with the dimensions of length per unit time. Instantaneous velocity can have both positive and negative values. The instantaneous velocity can be...
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Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. Although commonly referred to as deceleration, this causes confusion in our analysis as deceleration is not a vector, and does not point to a specific direction with respect to a coordinate system. Therefore, the term deceleration is not used. For example, when a subway train slows down, it...
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Instantaneous Power01:22

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Instantaneous power is important in electrical circuits, mainly when dealing with sinusoidal input. Instantaneous power, denoted as p(t), results from the multiplication of the instantaneous voltage (v(t)) across an element and the instantaneous current (i(t)) flowing through it. This relationship adheres to the passive sign convention and represents a fundamental principle in electrical engineering.
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The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To calculate this, it is important to know the instantaneous velocity, which is the velocity at a specific instant of time or at a specific point along the path. Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity vx of an object is the limit of the average...
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Phase Diagram-Based Sensing with Adaptive Waveform Design and Recurrent States Quantification for the Instantaneous

Angela Digulescu1, Cornel Ioana2, Alexandru Serbanescu3

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Summary

This study introduces a novel phase-space waveform design for high-speed active sensing systems. The method improves time-of-flight estimation accuracy in dynamic acoustic environments by three times compared to traditional techniques.

Keywords:
dynamic phenomenainstantaneous frequency law trackingphase space diagramphase space loberecurrence quantification analysis

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Area of Science:

  • Signal Processing
  • Acoustics
  • Waveform Design

Background:

  • Monitoring dynamic environments requires high-speed sensing systems.
  • Overlapped responses in active sensing necessitate a new representation space for separation.
  • Existing methods struggle with complex dynamic phenomena.

Purpose of the Study:

  • To introduce novel concepts for high-speed active sensing systems.
  • To develop a phase-space-based waveform design for improved signal separation.
  • To enhance the accuracy of time-of-flight estimation in dynamic acoustic environments.

Main Methods:

  • Proposed a phase-space-based waveform design (phase space lobe) on the emitter side.
  • Developed a method to estimate instantaneous frequency (IF) law in the phase diagram representation domain.
  • Utilized quantification of recurrent states in the phase diagram for IF estimation.

Main Results:

  • Generated distinct signals that are non-orthogonal in time/frequency but orthogonal in the phase diagram.
  • Achieved three times more accurate time-of-flight estimation compared to spectrogram-based techniques in experimental trials.
  • Demonstrated the capability to generate separable IF law components for high-speed sensing.

Conclusions:

  • The proposed phase-space waveform design enables high-speed sensing for complex dynamic phenomena.
  • The phase diagram representation and IF law quantification are key elements for accurate sensing.
  • This approach offers a significant improvement for time-of-flight estimation in dynamic acoustic environments.