Engineering Department, UMass Boston XXXXXXXXXXSpring 2022 ENGIN 322: Probability and Random Processes Project #3: Correlation Functions and Spectral Density Project Description In this project, you...

Note: Your grade is based on the PROJECT REPORT.

  • You should submit your code as well; but grading will be based on code and results described within the report.

  • Include images of figures in the report along with your description of results.

  • Use appendices to include relevant code (appendices do not count towards page limits)




Submission: Two files

  • Single pdf file for the project report

  • Zip file with all relevant code for your project




Engineering Department, UMass Boston Spring 2022 ENGIN 322: Probability and Random Processes Project #3: Correlation Functions and Spectral Density Project Description In this project, you will observe the binary process in more detail. The binary process is a basic method for transmitting data in a digital communication system. Your objectives are to determine/analyze the spectral density of the process (i.e., of a transmitted signal) and use cross-correlation to find a preamble that indicates where your data falls within a received signal. (Hint: Start with Lecture 22/23 Matlab code). Part I Create a Matlab script to generate 50,000 symbols of a random binary process with symbol rate of 1kHz (i.e., ???? = 0.001) and sample rate of 100kHz (i.e., 100 samples or repetitions for every symbol). Using this signal, generate the autocorrelation function and power spectral density of the process using Matlab’s xcorr() and periodogram() functions. Be sure to label plots and set axis values appropriately. Question 1: Relate your observations of the simulated signal to the theoretical autocorrelation function and spectral density function for this process. Use the ACF determined in class (and in section 6-2 of the textbook) in order to evaluate the spectral density for this function: ????(??) = ℱ{????(??)} HINT: Use the Fourier Transform pairs and operations described in Appendix A (Tables A-4 and A-5) Question 2: Use the equation for ????(??) determined in question 1 to determine the approximate frequency where 90% of the average power is below. Rather than integrating, you can approximate this by summing the values from the equation using a resolution of 1Hz. Compare your result to the simulated spectral density in Matlab. Part II The file ‘part2_2022.mat’ has a saved array that contains a simulated received signal. The transmitted data signal has been delayed and noise has been added. Luckily, the transmitted data contains a known preamble at the start of the transmission. The preamble was transmitted 4 times in a row directly prior to starting the data transmission. PREAMBLE: [-1 1 1 1 -1 -1 -1 -1 -1 1 1 -1 -1 -1 1 1 1 1 -1 -1] • Use the cross-correlation function to determine the start of the first preamble AND the start of the data transmission. You can determine the start of the preamble by observing a plot of the cross- correlation function. • Create a Matlab function that takes an array of values as an input, determines the likely location of the preamble, and returns this value. For example, if you input the array from ‘part2.mat’, the function should return the value for the start of the first preamble as determined above. Question 3: When looking for the preamble, is it preferable to compare the observed signal with the preamble or with the preamble repeated multiple times? Why? Question 4: How does your output change when changing the order of the processes? In other words, if the observed signal is defined as X and the preamble is defined as Y, how does ??????(??) compare to ??????(??)? Part III Question 5: Include a section (approximately 1 paragraph) in your report that discusses the relationship between this project and other real-world issues. Clearly label the section. Grading Metrics • Coding and Results: 30% • Theoretical Analysis: 40% • Written Report: 30% Coding and Results: This portion of the project will be graded based on the implementation of code as described for Part I and II above. Results should include a description of the observed outcomes and some depiction of the results from your code. Theoretical Analysis: This portion of the project will be graded based on your answers to the questions above. Be sure to clearly indicate the answers AND REASONING for each of the questions within your written report. Written Report: The written report should be submitted on blackboard by midnight on May 11. The report should be 3-5 pages including an overview of the project, expected outcomes, your analysis method, results, and observations. You may include any code as an appendix. Project Description Part I Part II Part III Grading Metrics
Apr 30, 2022
SOLUTION.PDF

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here