Sketch the function - without calculation explain how does

Question

Question 2: The following function/equation is given where f(x) is:

            1: for 2 < x ≤ 5

f(x) =  -1: for - 2 < x < 2  for - 5 < x ≤ 5

            1: for - 5 < x ≤ -2

g(x) = f(x) - 1 for - 5 ≤ x ≤ 5

with g(x + 10) = g(x)

a) Sketch the function

b) Without calculation explain how does the Fourier series of f(x)(as derived in Question 1) differ from the Fourier series of g(x)? Explain why?

c) Calculate the minimal N (number of components of the Fourier series), so that the Square Error of.the Fourier series of g(x)is E* < 10^-2 (Hint: Use Excel, Matlab or any other tool to calculate N.)

d) Sketch the development of E*(n)! (Hint: Use Excel, Matlab or any other tool to calculate N.)

Question 4: Draw the following function in frequency domain (amplitude spectrum) and time domain (for t=0 until 4Π):

y = 4/Π² + 1/Π²sin(0.5t) - 3/Π²sin(t) + 2/Π²sin(1.5t) - 1/Π²sin(2t)

Hint: Use Matlab, or Excel to draw the function in time domain.