Consider the following signal x given at time

t=1,2,3,4,5,6,7,8

x= 2.4, 3.1, 4.2, 3.1, 2.3, 4.1, 7.2, 8.4

USE MATLAB to answer the following questions

a) Use cftool app to interpolate the data by a Fourier series. How many terms you need to have the R-square=1?

b) Use this answer to predict the signal at time t=15.

c) Find the first derivative of x with respect to variable t at all points, with second order accuracy.

d) Plot both x and the derivative of x with respect to t.