2. Consider the following signal x given at time t. t1 2 3 4 5 6...

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2. Consider the following signal x given at time t. t1 2 3 4 5 6 7 8 x 2.4 3.1 4.2 3.1 2.3 4.1 7.2 8.4 a) Use cftool to approximate the signal by Fourier series with one term. Show the graph, the answer for the coefficients of this approximation and the R-square. b) Use this answer to predict the signal at time t=15. Show your MATLAB code and the final answer. c) Find the second derivative of x with respect to variable t for all pints t=2,3,4,5,6, by writing a for-loop, and using the three-point forward difference formula f" (xi) = f(xi) 2f(xi+1) + (xi+2) h2 Show your MATLAB code and the answers for derivatives. d) Use a for-loop to write a MATLAB pseudo code which computes S xdt using trapezoidal method. Show your MATLAB code and the final answer. (You can NOT use trapz built function) 2. Consider the following signal x given at time t. t1 2 3 4 5 6 7 8 x 2.4 3.1 4.2 3.1 2.3 4.1 7.2 8.4 a) Use cftool to approximate the signal by Fourier series with one term. Show the graph, the answer for the coefficients of this approximation and the R-square. b) Use this answer to predict the signal at time t=15. Show your MATLAB code and the final answer. c) Find the second derivative of x with respect to variable t for all pints t=2,3,4,5,6, by writing a for-loop, and using the three-point forward difference formula f" (xi) = f(xi) 2f(xi+1) + (xi+2) h2 Show your MATLAB code and the answers for derivatives. d) Use a for-loop to write a MATLAB pseudo code which computes S xdt using trapezoidal method. Show your MATLAB code and the final answer. (You can NOT use trapz built function)