A COMPLEX MAPPING NETWORK FOR PHASE SENSITIVE CLASSIFICATION

There are many signal processing applications involving complex-valued data in which phase information is an essential discriminant and for which nonlinear, nonparametric classification would be valuable. This is evident when utilizing the output from a Fourier transform, interpreting chaotic oscillator phase plane data, or analyzing time-sensitive impedance plane information generated from the phase quadrature detection of a modulated time domain signal. Artificial neural networks have the potential for being useful in such cases, but must rely on training alone to capture the complex relationships present in the data in order to perform a complex mapping. This paper details the design of a network which incorporates the complex relation in the structure and learning algorithm, thereby enforcing the formation of a complex mapping of the problem space. The network is applied to two phase-sensitive problems: 1) interpretation of chaotic oscillator phase plane plots, and 2) eddy current defect detection and characterization. In chaotic oscillator analysis, the network, in conjunction with the oscillator, demonstrates the ability to interpret small signal behavior. In eddy current impedance plane analysis, the network demonstrates a clear performance advantage over both real-valued multilayer feed-forward networks (MFFN's) and human subjects, with overall classification accuracy improvements of 45% (to a 99% level) and 48%, respectively. This network structure and learning algorithm should provide similar results in other signal processing applications where time or phase considerations are critical for class discrimination.