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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 for 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 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V² and we set the threshold level of 5 volts. a) Find the probability of false alarm. b) If a signal having a value of 8 volts is observed in the presence of the noise, find the probability of detection.

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 for 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 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V² and we set the threshold level of 5 volts. a) Find the probability of false alarm. b) If a signal having a value of 8 volts is observed in the presence of the noise, find the probability of detection.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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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 for 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 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V² and we set the threshold level of 5 volts. a) Find the probability of false alarm. b) If a signal having a value of 8 volts is observed in the presence of the noise, find the probability of detection.
Transcribed Image Text: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 for 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 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V² and we set the threshold level of 5 volts. a) Find the probability of false alarm. b) If a signal having a value of 8 volts is observed in the presence of the noise, find the probability of detection.
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