A time‐frequency approximation with applications in target recognition

Abstract

In active sonar, the received signal can often be modeled as a convolution of the transmitted signal with the channel impulse response and the target impulse response. Because the received signal may have a time‐varying spectrum, due, for example, to target motion or to changes in the channel impulse response, time‐frequency methods have been used to characterize propagation effects and target effects, and to extract features for classification. In this presentation, we consider the Wigner time‐frequency representation of a received signal modeled as the convolution of the transmitted signal with the channel and target responses. We derive a simple but very insightful approximation that shows the effects of the magnitude and phase of the frequency response of the target and of the channel on the Wigner representation of the transmitted signal. The results suggest possible features for classification, which we discuss. We also consider time‐varying effects on the Wigner representation, such as changes in reflected energy due to changes in aspect angle, which we model by amplitude modulation. [Research supported by ONR Grant No. N000140610009.]