Task 2
A periodic function f (x) is defined by
a) Sketch the graph of f (x) through 3 periods and calculate the Fourier array of f (x). Write the
array on the form without expression like .
b) b) What converge the Fourier row against when X = 3? Use x = 3 in the Fourier array of f (x)
to find an exact value for the sum of the row
Task 3
Given the function by
Let H (x) be the even half–periodic expansion of G (X).
a) Write down the formula for H (x) and sketch the graph of h (x) at the interval . Show
that the Fourier row of this becomes
c) Use the Fourier series to H (x) in x = 0 and x = 2 to find an exact value for the sum of the rows
Hint: By evaluating FH (x) I x = 0 and x = 2, you get 2 equations with 2 unknown: and
As you can solve as a regular linear system.
Problem 4
Given the function by
La k (x) be the odd half–periodic expansion of J (x). Write down the formula for k (x) and
sketch the graph of k (x) through 3 periods. How many paragraphs do we have to take from
the Fourier series to K (X) to get an average square deviation less than
