[Solved] CS 6810/7810: Wavelets and Wavelet Algorithms Assignment 8 Harmonic Recovery and Audio Analysis

Learning Objectives1. Harmonic Recovery2. Discrete Fourier Transform3. Audio File AnalysisIntroductionIn this assignment, you will recover harmonics from data and apply DFT to audio les. This is the last assignment forthis semester. I initially thought of splitting it into two weekly assignments but then decided against it and combinedthem into one assignment due in two weeks. I hope this works out better for all of us.Figure 1: Sample coecient vs. frequency plots; sine coecients vs. frequecy (left); cosine coecients vs. frequency(right)Problem 1The zip archive for this assignment contains data.txt with 6,284 real numbers generate by some function unknown toyou. Apply the harmonic recovery analysis to it to recover the harmonics in the frequency range from 0 to 150 and plot1their coecients. The plots in Figure 1 show two sample plots. Note that the plots are not the plots for this problem.They are just examples. Your plots will have a similar appearance but dierent values. For example, suppose that youhave recovered the values of a0, a10, b10, a40, and b40, i.e., the 0-th, 10-th, and 40-th harmonics are present. Here is asample output that your code may produce.a0 = 1.784a10 = 0.56996b10 = 1.898a40 = 29.18b40 = 7.9209To do harmonic recovery, you will need a threshold to determine if the sine or cosine coecient of a harmonic ispresent. I implemented my solution in Octave and used a threshold of 0.03.Problem 2In this problem, you will perform the DFT analysis of musical audio les. The zip archive contains three audio les:ODE_TO_JOY_RIGHT_HAND.wav, ODE_TO_JOY_BOTH_HANDS.wav, and ODE_TO_JOY_ORCHESTRA.wav. All three les recordthe famous segment from Beethovens Ode to Joy. The le ODE_TO_JOY_RIGHT_HAND.wav records me playing the noteson my piano with my right hand. The le ODE_TO_JOY_BOTH_HANDS.wav records me playing the same segment with bothhands. Finally, the le ODE_TO_JOY_ORCHESTRA.wav is a recording of the segment by an Austrian choir and orchestra. Irecorded these wav les with a ve-dollar microphone so there is some background noise in all three recordings. But itis manageable. So, do the DFT analysis of the three les the way we did in Lecture 12. Speci cally,1. Plot the spectrum analysis of each audio le;2. Identify the top ve frequencies in each audio le;3. Use https://en.wikipedia.org/wiki/Piano_key_frequencies to identify the corresponding musical notes.What To SubmitYou can do this assignment in Octave, Python, or Java. If you do it in Octave, save your solution in HW08.m. If you doit in Python, save it in HW08.py. If you do it in Java, save it in HW08.java. If you do it in Java and use third-party jars,please submit them along with your HW08.java. In your source le, de ne the function/method problem_01() with yoursource code for Problem 1 and the function/method problem_02() with your source code for Problem 2.Enjoy!2