What Is a Phase Space?

In mathematics and physics, phase space is a space used to represent all possible states of a system; each possible state of the system has a corresponding phase space point.

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So why so far

The phase space dispersion effect also has an astonishing implication. It tells us that classical mechanics cannot really describe our world! I said a little bit too much, but not too much. Classical mechanics works well for fluids--especially the behavior of gases, and to a large extent for liquids--where people only care about the "average" nature of particle systems, but when it comes to calculating solids, For problems, here requires more detailed organizational structure. A solid is made up of hundreds of millions of point-like particles. Because the order of the arrangement in the phase space is constantly decreasing, how can it keep its shape substantially unchanged? As we already know, quantum mechanics is indispensable in understanding the actual structure of solids. Quantum effects can more or less prevent the dispersion of phase space.

This is also related to the problem of making "computers". Phase space dispersion is something that must be controlled. Areas in the phase space that correspond to a "discrete" state of a computer (such as the aforementioned R0) should not be allowed to disperse excessively. We remember that even the Fletcher-Toffry "pool computer" needed some kind of solid wall on the outside to work. The "rigidity" of an object consisting of many particles is exactly something that requires quantum mechanics to work.

Based on the phase space reconstruction theory, Takens theorem is used to reconstruct the phase space of speech signals and extract similar sequence repeat (RPT) feature parameters. Using the differences in unvoiced and voiced RPT parameters, a new method using BP neural network The method of linear unvoiced voiced speech judgment has obtained significantly better results than traditional algorithms. The method in this paper provides a new approach for speech feature extraction and recognition research.