2-5.5 A common method for detecting a signal in the presence of noise is to establish a threshold level and compare the value of any observation with this threshold. If the threshold is exceeded, it is decided that 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 should be as close to 1.0 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V2 and we set a threshold level of 5 V. a) Find the probability of false alarm. b) If a signal having a value of 8 V is observed in the presence of this noise, find the probability of detection.
2-5.5 A common method for detecting a signal in the presence of noise is to establish a threshold level and compare the value of any observation with this threshold. If the threshold is exceeded, it is decided that 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 should be as close to 1.0 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V2 and we set a threshold level of 5 V. a) Find the probability of false alarm. b) If a signal having a value of 8 V is observed in the presence of this noise, find the probability of detection.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 2-5.5. But change the problem to say Gaussian noise variance of 2, and threshold of 6V.
Transcribed Image Text:2-5.5 A common method for detecting a signal in the presence of noise is to establish a
threshold level and compare the value of any observation with this threshold. If the
threshold is exceeded, it is decided that 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 should be as close to
1.0 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1
V2 and we set a threshold level of 5 V.
a) Find the probability of false alarm.
b) If a signal having a value of 8 V is observed in the presence of this noise, find the
probability of detection.
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