BLIND QUADRATIC AND TIME-FREQUENCY BASED DETECTORS FROM 
TRAINING DATA

Douglas L. Jones and Akbar M. Sayeed

Coordinated Science Laboratory  
University of Illinois 
Urbana, IL 61801  

Proceedings of  ICASSP'95 ,  pp. 1033-1036 


ABSTRACT:

Time-frequency based methods, particularly quadratic (Cohen's-class) 
representations, are often considered for detection in applications 
ranging from sonar to machine monitoring.  We propose a method of 
obtaining near-optimal quadratic detectors directly from training 
data using Fisher's optimal linear discriminant to design a quadratic 
detector.  This detector is optimal in terms of Fisher's scatter 
criterion as applied to the quadratic outer product of the data 
vector, and in early simulations appears to closely approximate the 
true optimal quadratic detector.  By relating this quadratic detector 
to an equivalent operation on the Wigner distribution of a signal, we 
derive near-optimal time-frequency detectors.  A simple example 
demonstrates the excellent performance of the method.