12  Signal Detection Techniques

The probability of detection (Pd) and the probability of a false alarm (Pfa or false detection) define the essential receiver operating characteristic (ROC) for any wavenumber or other signal detection system. The ROC for a particular detection system is based on practical models for signals and noise using assumptions of underlying Gaussian probability density functions (PDFs). When many random variables are included in a model, the central limit theorem leads us to assume an underlying Gaussian model because a large number of separate random events with arbitrary density functions will tend to be Gaussian when taken together (see Section 7.1). Therefore, it is reasonable to assume that the background noise ...

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