This paper presents descriptions of and results from two quadratic processing workstation accelerators. One of these workstations is used for radar processing apd the other two for signal detection and characterization. These workstations exhibit high dynamic range and real4ime performance in compact packages. The functions generated by these systems are the ambiguity function, WignerVi11e function, and cyclic spectrum. Two ofthese systems are complete and the other is under development.
INTRODUCTION TO GENERALIZED QUADRATIC PROCESSINGGeneralized quadratic processing addresses the interaction of two signals in the product plane. The product plane unifies these signal processing concepts: 1. Correlation 2. Convolution 3. Cross Ambiguity Functions 4. Cross Wigner Functions 5. Cyclostationary Spectrum
Mellin CorrelationThe product plane approach gives insights into the structure ofthe cross products in the cross ambiguity surface, and into the dependent nature of the noise in the CAF and related surfaces. The effect of time compression of one signal with respect to the other in the CAP also becomes apparent in the product plane.The understanding of generalized quadratic processing and its product plane representation began with a study of cyclostationaiy processes. Eliminating second order periodicities (periodicities in lag products) allows application of the mathematics developed for the processing and analysis of stationary signals to nonstationaiy signals. A signal f(t) is cyclostationary if the lag product f(t)f(t-t) contains periodic components. Almost all signals used for communications fall into this class. Often the lag product contains periodic components even when the signal itself does not.
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