Spring 2020 Assignment 10

1. Start by loading the data structure called fall2019_StudentData_Responses.mat into matlab. This file contains two variables:
   • allClassResponseData is a cell array containing the analyzed response data from each group. Each element of the cell array is a 3-column matrix containing the response data. The columns represent (in order): the time (in seconds), the mean response (the average correlation between GFP and RFP in each cell), and the standard error of the response. To access the matrix of the iith group, you can use curly braces: allClassResponseData{ii}.
   • allClassOscillationPeriods is a vector containing the oscillation period (in seconds) for each of the elements in allClassResponseData.
2. For each set of data, fit a sine function to extract the amplitude and phase of the response at that input frequency.
   • There are a few important, but subtle points here.
     • Since the response data is not centered around zero, you must include a constant offset in your model function.
     • The frequency of oscillations that we are interested in is determined by our experiment, and should not be left as a fit parameter.

For each set of response data: Plot the response vs time in one subplot, and the pinch valve state (1 for high salt, 0 for low salt) in a second subplot. Write a function to fit the response to a sinusoid and extract the predicted amplitude and phase shift of the response signal. Plot the best fit function on the same plot as your data. On one set of axes, plot the Hog1-response vs. time and the best fit sinusoid. Make a Bode Plot (amplitude and phase) of the Hog1-response as a function of frequency. How does your data compare to the amplitude and phase found in the paper? If your measurements do not agree, describe two or three reasons why they might differ.

Turn in all your MATLAB code in pdf format. No need to include functions that you used but did not modify.