A common method for detecting a signal in the presence of noise is to establish a thresholdlevel and compare the value of any observation with this threshold. If the threshold is exceeded, itis decided that signal is present. Sometimes, of course, noise alone will exceed the threshold and thisis 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 toexceed the threshold with a large probability. This is the probability of detection and should be asclose to 1 as possible. Suppose we have Gaussian noise with zero mean and a variance of 1 V² andwe 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 theprobability of detection.

The distribution of noise is Gaussian distribution such that The threshold level is 5V. If the…

Answered: A common method for detecting a signal…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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