Abstract
A statistical study is implemented on the short-time spectrum of one main category of random signals. For the signals with massive and random micro-sources, a new statistic feature of the short-time amplitude spectrum is discovered, which reveals the relationship between the amplitude’s average and its standard for each frequency component. Moreover, the association between the amplitude distributions for different frequency components is also studied. A model representing such association is presented, which accords well with the statistic feature discovered. The analysis result has potential application in signal classification, and also in the study of system characteristics underlying the observed signal.
Highlights
From the viewpoint of computing, a signal processing method is a computing process taking the signal as input
The observed signal is the accumulation effect of all the micro-sources. The relationship between these microsources determines the basic characteristic of the signal, which can act as the basis for signal classification
Consider the unavoidable error caused by the instability of the signals, and the noise introduced in the signal capture process, the results indicate that ( k) and ( k) are strongly related by a linear proportional relationship, which is a new statistic feature discovered for this category of signals
Summary
From the viewpoint of computing, a signal processing method is a computing process taking the signal as input. Each element contributes to the generation of the signal. The observed signal is the accumulation effect of all the micro-sources. The relationship between these microsources determines the basic characteristic of the signal, which can act as the basis for signal classification. The statistic characteristic of the spectrum is studied for the later category of signals. For this type of signals, the signal source can be decomposed to massive and random micro-sources. A novel statistical feature for short-time amplitude spectrum is discovered for this category of signals. The validity of the new model is verified by analysis, with the discovered statistic feature as direct evidence
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