Representation and Analysis of Signals. Part 16. Representation and Detection of Multiple-Epoch Signals
JOHNS HOPKINS UNIV BALTIMORE MD CARLYLE BARTON LAB
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A multiple-epoch signal consists of several signals which for one reason or another, ovrlap one another. The purpose of this report is to design a procedure for the detection of the individual epochs of the overlapping signals and to represent them properly. The multiple-epoch signal may be corrupted with random Gaussian noise of zero mean. The individual signals are assumed to be representable by a set of exponential functions with acceptable error, and the ex ponents of this set of exponentials are assumed known. Any two adjacent epochs are assumed to be separated at least To seconds apart. For the signal uncorrupted with noise a criterion based on the error energy is described which is of theoretical interest. This criterion is useful for the detection of first epoch only. To detect the second epoch, the first signal is subtracted from the original signal by means of the complementary operator concept. For a noisy signal, a likelihood ratio criterion is proposed. The preliminary experimental results carried out on a digit al computer justify the theoretical study.