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15. Coherently integrating N samples of signal-plus-noise produces an integration gain of N on a linear (not dB) scale; that is, if the SNR of a single sample y, is x, the SNR of z=is Nx. It is also often said that noncoherent integration produces an integration gain of about √N. In problems 15 through 18, Albersheim's equation will be used to see if this is accurate for one example case. Throughout these problems, assume Pp = 0.9 and PA 10-6 is required and that a linear (not square law) detector is used. Start by considering detection based on a single sample, N = 1. Use Albersheim's equation to estimate the signal-to-noise ratio, X₁, needed for this single sample to meet the previously given specifications. Give the answer in dB. Be careful about comparing or combining things on the same (linear or dB) scales throughout these four related problems.

15. Coherently integrating N samples of signal-plus-noise produces an integration gain of N on a linear (not dB) scale; that is, if the SNR of a single sample y, is x, the SNR of z=is Nx. It is also often said that noncoherent integration produces an integration gain of about √N. In problems 15 through 18, Albersheim's equation will be used to see if this is accurate for one example case. Throughout these problems, assume Pp = 0.9 and PA 10-6 is required and that a linear (not square law) detector is used. Start by considering detection based on a single sample, N = 1. Use Albersheim's equation to estimate the signal-to-noise ratio, X₁, needed for this single sample to meet the previously given specifications. Give the answer in dB. Be careful about comparing or combining things on the same (linear or dB) scales throughout these four related problems.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Integration of Signal-plus-Noise for Educational Purposes** 15. Coherently integrating \( N \) samples of signal-plus-noise produces an integration gain of \( N \) on a linear (not dB) scale. This means if the Signal-to-Noise Ratio (SNR) of a single sample \( y_i \) is \( \chi \), the SNR of \( z = \sum_{i=1}^{N} y_i \) is \( N \chi \). It is also often stated that noncoherent integration results in an integration gain of about \( \sqrt{N} \). In problems 15 through 18, Albersheim's equation will be used to verify if this is accurate for one example case. Throughout these problems, assume: - Probability of Detection (\( P_D \)): 0.9 - Probability of False Alarm (\( P_{FA} \)): \( 10^{-6} \) A linear (not square law) detector is used. Start by considering detection based on a single sample, \( N = 1 \). Use Albersheim's equation to estimate the signal-to-noise ratio, \( \chi_1 \), needed for this single sample to meet the specified requirements. Provide the answer in dB. Be cautious when comparing or combining metrics on the same (linear or dB) scales throughout these four related problems.
Transcribed Image Text:**Integration of Signal-plus-Noise for Educational Purposes** 15. Coherently integrating \( N \) samples of signal-plus-noise produces an integration gain of \( N \) on a linear (not dB) scale. This means if the Signal-to-Noise Ratio (SNR) of a single sample \( y_i \) is \( \chi \), the SNR of \( z = \sum_{i=1}^{N} y_i \) is \( N \chi \). It is also often stated that noncoherent integration results in an integration gain of about \( \sqrt{N} \). In problems 15 through 18, Albersheim's equation will be used to verify if this is accurate for one example case. Throughout these problems, assume: - Probability of Detection (\( P_D \)): 0.9 - Probability of False Alarm (\( P_{FA} \)): \( 10^{-6} \) A linear (not square law) detector is used. Start by considering detection based on a single sample, \( N = 1 \). Use Albersheim's equation to estimate the signal-to-noise ratio, \( \chi_1 \), needed for this single sample to meet the specified requirements. Provide the answer in dB. Be cautious when comparing or combining metrics on the same (linear or dB) scales throughout these four related problems.
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