For the problem below, the expectation is that you submit a standalone HTML file (any images should be embedded) back to GitHub. The problem has data provided in the starting repository. Because this is the first assignment of a new unit, you’ll need to create new groups in GitHub Classroom. The first person to accept the assignment should form an easily identifiable group name (likely using the names of your group members). Others in the group should also accept the assignment, and then they can just join the existing group.
Accept AssignmentProblem: Finding Fourier Fragments
For this problem you are starting with a mixed signal of cosine waves that have had some noise added. The file signal.csv in the starting repository has your initial data, which includes a time column (in seconds) and a signal column (in arbitrary units. Take them to be meters if you want). As can be seen by the values in the time column, all time increments are consistent, and thus Fourier analysis can be used to extract the components of the mixed signal. Your task here is to:
- Determine the dominant components of the signal. How many are there?
- Extract the period, amplitude, and phase of each of these components.
- Plot each of these components individually over the first 10 seconds on the same graph. Remember that the base form of each component of the signal was: y(t) = A \cos\left(\frac{2\pi t}{T} + \phi\right)
- Compute the residual (difference) between the original data and the total summed signal (all the components added together). These residuals should represent the noise that was added to the signal. If you make a histogram of these residuals, it should appear Gaussian if the added noise was also Gaussian. Does it? This is one way you can tease out information about what processes might be contributing to noise in a signal.