Question

2-5.5 - A common method for detecting a signal in a presence of noise is to establish a threshold value and compare the value of any observation with this threshold. If the threshold is exceeded, it is decided that a signal is present. Sometimes, of course, noise alone will exceed the threshold and this is known as a “false alarm”. Usually, it is desired to make the probability of a false alarm very small. At the same time, we would like any observation that does contain a signal plus the noise to exceed the threshold with a large probability. This is the probability of detection and it should be as close to 1 as possible. Suppose we have Gaussian noise with zero mean and variance of 2 V² and we set a threshold level of 6 V.

2-8.4 - Consider again the threshold detection system described in Problem 2-5.5.

A) When noise only is present, find the conditional mean value of the noise that exceeds the threshold.

B) Repeat part (A) when both the specified signal and noise are present.

Answer 1