Weak Signal Detection Method Based on Adaptive Fractional Stochastic Resonance System
A weak signal detection and stochastic resonance technology, which is applied in complex mathematical operations, electrical digital data processing, special data processing applications, etc., can solve problems such as application limitations, and achieve a wide range of applications and good application prospects.
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[0016] The traditional integer-order stochastic resonance model is bistable stochastic resonance, and its potential function is
[0017]
[0018] In the traditional bistable system, there are only two parameters a and b, and its structure is relatively simple, so it cannot be effectively applied to the detection of various weak signals. It has limitations, that is, for objective conditions such as weak signals and noise signals have greater limitations. What the present invention uses is the fractional-order bistable system with more complicated structure, and its potential function is
[0019]
[0020] According to the Caputo definition in fractional order theory, the Langevin equation of this system can be expressed as follows:
[0021]
[0022] in, is the β-order fractional derivative of x(t), and 0<β<1. a, b, c, k, q are system structure parameters. ξ(t) is the noise signal, s(t) is the target weak signal.
[0023] Because the system structure has good varia...
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