DocumentCode :
1407322
Title :
Quickest detection of a tonal burst
Author :
Stahl, Robert J. ; Willett, Peter K.
Author_Institution :
Atlantic Aerosp. Electron. Corp., Waltham, MA, USA
Volume :
45
Issue :
8
fYear :
1997
fDate :
8/1/1997 12:00:00 AM
Firstpage :
2037
Lastpage :
2047
Abstract :
We describe and analyze the performance of a technique for the quickest detection of a sinusoid of unknown frequency, amplitude, and phase in additive white noise. The approach is based on the work of Broder and Schwartz (1989) and relies on asymptotic results, that is, the “signal” to be detected as quickly as possible is assumed to be of vanishingly small amplitude, which is the most difficult (and interesting) situation. In the literature, the relationship between the small-signal Page´s test and locally optimal fixed-length detection theory is explored in detail for the case of a known contaminant. Here, these results are extended to the case of a stochastic contaminant (i.e., the unknown sinusoid). We derive the version of Page´s (1954) test optimized under the assumptions that the amplitude is small, the data arrives in blocks, and the frequency of the sinusoid is uniformly distributed in a given band, and we verify the performance predictions via simulation. To detect a sinusoid of completely unknown frequency, an ensemble of such detectors is required, and this ensemble is very close to an FFT-based scheme. If FFTs are to be used, however, the best performance is obtained when each is augmented by a half-band-shifted version of itself
Keywords :
fast Fourier transforms; signal detection; stochastic processes; white noise; FFT based scheme; additive white noise; asymptotic results; data blocks; locally optimal fixed length detection theory; performance; phase; quickest detection; signal detection; simulation; sinusoid; small-signal Page´s test; stochastic contaminant; tonal burst; uniformly distributed frequency; vanishingly small amplitude signal; Additive white noise; Performance analysis; Performance evaluation; Phase detection; Phase frequency detector; Predictive models; Signal detection; Statistical analysis; Stochastic processes; Testing;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.611202
Filename :
611202
Link To Document :
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