Hope this helps

Problems Problem 1. Write a function called FS that returns the Fourier series of a given function to a given degree. You'll have to keep this as a separate function file so you can complete the problems below, but you should also copy the function code to the answer sheet. Problem 2. Using the Matlab function piecewise, create the following function called f1: f1(x) = 2.1 +1 if 10 r if I >0. Observe that this function has a jump discontinuity at x = 0. Problem 3. Using the Matlab function piecewise, create the following function called f2: S cos() if so f2(x) = 1-22 if x >0. Observe that this function is continuous, but not differentiable, at r = 0. Problem 4. Create the following function called f3: f3(2) = log(2 + 2) - I sin(3.7.0). Observe that this function is infinitely differentiable on the interval (-7,7]. Problem 5. Create the following function called f4: f4(x) = 1 11 11 11 11 122|||||- Observe that this function is continuous, but very "spiky". Problem 6. Calculate the 7th degree Fourier series of the four functions above. Call them FSf1, FSf2, FSf3, and FSf4. Problem 7. On the same graph, plot the functions f1 and FSf1. Use the axis command to only display I values in the interval (-7, pi]. Repeat this process for f2 and FSf2, f3 and FSf3, and f4 and FSf4. Be sure to type figure; hold on; each time in order to force Matlab to create a new figure for each pair of functions. Problem 8. Describe how well Fourier series approximate the four functions above. Your answer should discuss the role of continuity, differentiability, "spikiness, and the endpoints - and . Problem 7. On the same graph, plot the functions f1 and FSf1. Use the axis command to only display I values in the interval [-2, pi]. Repeat this process for f2 and FSf2, f3 and FSf3, and f4 and FSf4. Be sure to type figure; hold on; each time in order to force Matlab to create a new figure for each pair of functions. Problems Problem 1. Write a function called FS that returns the Fourier series of a given function to a given degree. You'll have to keep this as a separate function file so you can complete the problems below, but you should also copy the function code to the answer sheet. Problem 2. Using the Matlab function piecewise, create the following function called f1: f1(x) = 2.1 +1 if 10 r if I >0. Observe that this function has a jump discontinuity at x = 0. Problem 3. Using the Matlab function piecewise, create the following function called f2: S cos() if so f2(x) = 1-22 if x >0. Observe that this function is continuous, but not differentiable, at r = 0. Problem 4. Create the following function called f3: f3(2) = log(2 + 2) - I sin(3.7.0). Observe that this function is infinitely differentiable on the interval (-7,7]. Problem 5. Create the following function called f4: f4(x) = 1 11 11 11 11 122|||||- Observe that this function is continuous, but very "spiky". Problem 6. Calculate the 7th degree Fourier series of the four functions above. Call them FSf1, FSf2, FSf3, and FSf4. Problem 7. On the same graph, plot the functions f1 and FSf1. Use the axis command to only display I values in the interval (-7, pi]. Repeat this process for f2 and FSf2, f3 and FSf3, and f4 and FSf4. Be sure to type figure; hold on; each time in order to force Matlab to create a new figure for each pair of functions. Problem 8. Describe how well Fourier series approximate the four functions above. Your answer should discuss the role of continuity, differentiability, "spikiness, and the endpoints - and . Problem 7. On the same graph, plot the functions f1 and FSf1. Use the axis command to only display I values in the interval [-2, pi]. Repeat this process for f2 and FSf2, f3 and FSf3, and f4 and FSf4. Be sure to type figure; hold on; each time in order to force Matlab to create a new figure for each pair of functions