The bearing data that were previously posted on cuLearn course website are the acceleration signals collected from a bearing testing system with a sampling frequency fs = 20480 Hz. Program Matlab codes that can implement the following analysis on these bearing data. All the codes should be coded in a way that can be conveniently verified by the instructor with a simple "click and run". Provide a brief "readme" file when necessary. All the codes should be submitted to the instructor through his email (given in the course outline) by the due time. (a) [6 points] Implement FFT and Hanning window function on the bearing data and plot both the magnitude and phase of the spectra. The number of the data for each window is 65536. (b) [6 points] Implement the first-level Exponential Moving Average (EMA) (as discussed in the lecture notes) on the bearing data and plot the level-1 EMA series for the first 200000 data. T=2048. (c) [6 points] Implement the Detrended Fluctuation Analysis technique on the bearing data and plot the curve of logF(n) versus log". Use the following Matlab code to generate the box sizes for your analysis, n=floor(exp([3:0.2:8])). Estimate the scaling exponent a. (d) [10 points bonus] Implement the wavelet analysis on the bearing data. Use Morlet mother wavelet. Wavelet transform should be applied to the frequency band [1000 8000] Hz. Calculate the center frequencies for the dilated wavelets. Plot the frequency spectra for the dilated wavelets. Plot the wavelet coefficients you obtained.