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Create a time vector that contains values from 0 to 5 in steps of .01. Create a sine wave [sin(2πft)] such that there are exactly 25 cycles in 5 seconds. Using the 5-cycle of this sine wave, you will be adding noise from either uniform or Gaussian distributions and analyzing the differences between the distributions using covariance and correlation. A. Generate two noise vectors to add to your signal that span from -1 to 1 using the following distributions. Choose a standard deviation such that 99.7% of the Gaussian noise falls within -1 to 1. Uniform Noise: a + (b-a)*rand(R, C) Gaussian Noise: normrnd(u, o, R, C) where a = Lower Limit, b = Upper Limit, R = rows, C = columns, and μ = mean of distribution, o = standard deviation of the distribution. Create a figure using subplots to show: the original signal, both noise vectors, and each noise vector added to the original signal versus time. B. Calculate the SNR in dB for the original signal with each added noise vector. For which combination is there a greater signal to noise ratio? C. Calculate the covariance matrix for the original signal and each signal + noise. Use the covariance matrix to convert to the correlation matrix. What is the correlation between the original signal and each signal + noise? Which signal + noise shows better correlation to the original signal? What conclusions can you draw about the differences between uniform and Gaussian distributions?

Create a time vector that contains values from 0 to 5 in steps of .01. Create a sine wave [sin(2πft)] such that there are exactly 25 cycles in 5 seconds. Using the 5-cycle of this sine wave, you will be adding noise from either uniform or Gaussian distributions and analyzing the differences between the distributions using covariance and correlation. A. Generate two noise vectors to add to your signal that span from -1 to 1 using the following distributions. Choose a standard deviation such that 99.7% of the Gaussian noise falls within -1 to 1. Uniform Noise: a + (b-a)*rand(R, C) Gaussian Noise: normrnd(u, o, R, C) where a = Lower Limit, b = Upper Limit, R = rows, C = columns, and μ = mean of distribution, o = standard deviation of the distribution. Create a figure using subplots to show: the original signal, both noise vectors, and each noise vector added to the original signal versus time. B. Calculate the SNR in dB for the original signal with each added noise vector. For which combination is there a greater signal to noise ratio? C. Calculate the covariance matrix for the original signal and each signal + noise. Use the covariance matrix to convert to the correlation matrix. What is the correlation between the original signal and each signal + noise? Which signal + noise shows better correlation to the original signal? What conclusions can you draw about the differences between uniform and Gaussian distributions?

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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This is only one question! I'm having trouble figuring out this code in Matlab; I'd appreciate the help. Thank you!

Create a time vector that contains values from 0 to 5 in steps of .01. Create a sine wave [sin(2πft)] such that there are exactly 25 cycles in 5 seconds. Using the 5-cycle of this sine wave, you will be adding noise from either uniform or Gaussian distributions and analyzing the differences between the distributions using covariance and correlation. A. Generate two noise vectors to add to your signal that span from -1 to 1 using the following distributions. Choose a standard deviation such that 99.7% of the Gaussian noise falls within -1 to 1. Uniform Noise: a + (b-a)*rand(R, C) Gaussian Noise: normrnd(u, o, R, C) where a = Lower Limit, b = Upper Limit, R = rows, C = columns, and μ = mean of distribution, o = standard deviation of the distribution. Create a figure using subplots to show: the original signal, both noise vectors, and each noise vector added to the original signal versus time. B. Calculate the SNR in dB for the original signal with each added noise vector. For which combination is there a greater signal to noise ratio? C. Calculate the covariance matrix for the original signal and each signal + noise. Use the covariance matrix to convert to the correlation matrix. What is the correlation between the original signal and each signal + noise? Which signal + noise shows better correlation to the original signal? What conclusions can you draw about the differences between uniform and Gaussian distributions?
Transcribed Image Text:Create a time vector that contains values from 0 to 5 in steps of .01. Create a sine wave [sin(2πft)] such that there are exactly 25 cycles in 5 seconds. Using the 5-cycle of this sine wave, you will be adding noise from either uniform or Gaussian distributions and analyzing the differences between the distributions using covariance and correlation. A. Generate two noise vectors to add to your signal that span from -1 to 1 using the following distributions. Choose a standard deviation such that 99.7% of the Gaussian noise falls within -1 to 1. Uniform Noise: a + (b-a)*rand(R, C) Gaussian Noise: normrnd(u, o, R, C) where a = Lower Limit, b = Upper Limit, R = rows, C = columns, and μ = mean of distribution, o = standard deviation of the distribution. Create a figure using subplots to show: the original signal, both noise vectors, and each noise vector added to the original signal versus time. B. Calculate the SNR in dB for the original signal with each added noise vector. For which combination is there a greater signal to noise ratio? C. Calculate the covariance matrix for the original signal and each signal + noise. Use the covariance matrix to convert to the correlation matrix. What is the correlation between the original signal and each signal + noise? Which signal + noise shows better correlation to the original signal? What conclusions can you draw about the differences between uniform and Gaussian distributions?
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