MAP detection and ML estimation of signals overlapping in time and frequency for both Gaussian and Laplacian noise

The magnitude error function is the optimal criterion for detection and parameter estimation under Laplacian (double-sided exponential density) noise. Its use is compared to the commonly used squared error function (equivalent to the matched filter), derived under the condition of Gaussian (normal density) noise, and found to possess the following advantages: (1) The performance of the magnitude error detector is better than that of the squared error detector for signals with unknown delays in low-level noise and within overlappings; (2) The algorithms are simpler to implement on a digital processor and they run faster because no multiply operations are needed and because the dynamic range is suitable for a 16-bit arithmetic. The theory is developed for a detection and estimation scheme on nonlinear functions of non-random parameters. It is applied to a problem in electromyography (EMG), namely the problem of separating superpositions of finite-duration signals which overlap both in the time and frequency domains. For the sake of completeness it is shown that the amplitude density of the noise in EMG is Laplace distributed rather than Gaussian.