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Nonlinear processing of outputs from a filter bank to reduce ultrasonic clutter is often referred to as split spectrum processing (SSP). In this work, the optimal detector (OD) for a known transient in additive Gaussian noise is formulated as a filter bank followed by a nonlinear operation (decision). Then, the new formulation is used for several purposes. The first purpose is to present a simple framework for comparison of SSP based on the polarity thresholding (PT) method with SSP based on the OD. The second purpose is to point out that although the OD relies on a test statistic which is a linear function of the observed samples, it can be used for nonlinear clutter suppression. This is because the OD output is used to gate (mask) the original ultrasonic signal and the OD output is a nonlinear function of the filter bank outputs. The third purpose is to identify practical advantages of OD-based SSP, including fewer demands on the experimental data used for parameter tuning, a better understanding of the processing performed, improved resolution, and fewer parameters to tune. The fourth purpose is to discuss the difference between contrast enhancement in clutter suppression and receiver operating characteristics in detection theory. Statistical and geometrical interpretations of both PT and OD are also presented, as well as experimental results from simulated and real ultrasonic data.