A matched filter for chaos
A matched filter for chaos
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DOI：
10.1063/1.3432557
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发表时间：
2010-06-01
期刊：
影响因子：
2.9
通讯作者：
Stahl, Mark T.
中科院分区：
文献类型：
--
作者：
Corron, Ned J.;Blakely, Jonathan N.;Stahl, Mark T.
提出了一种新的混沌振子，它具有精确的解析解和简单的匹配滤波器。振荡器是一个混合动力系统，包括一个微分方程和离散的开关条件。解析解被写为符号序列和固定基函数的线性卷积，类似于常规通信波形的线性卷积。在开关时间的波形返回被证明是共轭的混沌移位映射，有效地证明了系统中的混沌的存在。一个匹配滤波器的延迟微分方程的形式推导出的基函数。应用匹配滤波器的接收波形，检测符号的误码率推导，并提出了显式的封闭形式的表达式的特殊情况。振荡器和匹配滤波器在低频电子电路中实现。观察到显着的协议之间的解析解和测量的混沌波形。[doi：10.1063/1.3432557]
A novel chaotic oscillator is shown to admit an exact analytic solution and a simple matched filter. The oscillator is a hybrid dynamical system including both a differential equation and a discrete switching condition. The analytic solution is written as a linear convolution of a symbol sequence and a fixed basis function, similar to that of conventional communication waveforms. Waveform returns at switching times are shown to be conjugate to a chaotic shift map, effectively proving the existence of chaos in the system. A matched filter in the form of a delay differential equation is derived for the basis function. Applying the matched filter to a received waveform, the bit error rate for detecting symbols is derived, and explicit closed-form expressions are presented for special cases. The oscillator and matched filter are realized in a low-frequency electronic circuit. Remarkable agreement between the analytic solution and the measured chaotic waveform is observed. [doi :10.1063/1.3432557]