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Normal_pdf_detection

# Normal_pdf_detection - The Use of the Gaussian Distribution...

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The Use of the Gaussian Distribution in a Detection Problem EEE 554 Fall 2010 Consider the problem of detecting the presence of a crack on the winglet of an airplane wing. A piezoelectric (PZT) actuator and a PZT receiver sensor are placed on the winglet. A known signal is transmitted and the returned signal is measured at the receiver. For this simple test, it is assumed that the presence of a crack is detected if there is a signal amplitude loss by 6 dB. At the receiver, we measure a single sample (or random variable) R . We consider a two hy- pothesis problem: under hypothesis H 0 , the received signal sample contains the transmitted signal sample s > 0 (known and deterministic) and a Gaussian noise sample W ; under hypothesis H 1 , the received signal sample contains the faded signal sample and the Gaussian noise sample. In particular, the detection problem can be stated as: H 0 : R = s + W H 1 : R = a s + W = 0 . 5 s + W where a = 0 . 5 is obtained from - 6 = (20 log 10 a ) dB. We assume that W is an additive Gaussian

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