OPTIMAL REDUCED-RANK TIME-FREQUENCY/TIME-SCALE 
QUADRATIC DETECTORS

Akbar M. Sayeed and Douglas L. Jones
Coordinated Science Laboratory
University of Illinois
Urbana, IL 61801

1996 IEEE International Symposium on Time-Frequency and 
Time-Scale Analysis, Paris, France   

Optimal detectors based on time-frequency/time-scale representations 
(TFRs/TSRs) admit a representation in terms of a bank of 
spectrograms/scalograms that yields a large class of detectors. These 
range from the conventional matched filter to the more complex 
higher-rank detectors offering a superior performance in a wider 
variety of detection situations. In this paper, we optimize this 
complexity versus performance tradeoff by characterizing TFR/TSR 
detectors that optimize performance (based on the deflection criterion) 
for any given fixed rank. We also characterize the gain in performance 
as a function of increasing complexity thereby facilitating a judicious 
tradeoff.  Our experience with real data shows that, in many cases, 
relatively low-rank optimal detectors can provide most of the gain in 
performance relative to matched-filter processors.