Efficiency of real-time Gaussian transient detectors: comparing the Karhunen-Loeve and the wavelet decompositions

In general, finite-dimensional discrete-time representations of continuous-time Gaussian transients is not complete. Such representations typically lead to suboptimal detectors, where the compromise between computational complexity and processor performance requires optimization, specially when real-time processing is mandatory. This paper proposes a procedure for the optimization of the processor parameters, using the Bhattacharyya distance to evaluate the resemblance between the original continuous-time signal and its finite dimensional discrete representation. Two different decompositions are analyzed and compared, namely the Karhunen-Loeve decomposition (KLD) and the discrete wavelet transform (DWT). It is shown that the DWT presents serious advantages when the signals to detect have a large number of important eigenvalues, which is often the case in some applications such as passive sonar.