Calculate the fourier series for that function

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Reference no: EM131239467

Question 1: The following function/equation is given:

            1: for 2 < x ≤ 5

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

            1: for - 5 < x ≤ -2 

with f(x + 10) = f(x)

a) Sketch the function!

b) Calculate the Fourier series for that function!

c) Write down the fifth partial sum!

Question 2: The following function/equation is given where f(x) is from question 1:

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 3: The following integral is given:

-2Π∫2Π(∑n=1 n=10m=1 m=10 [sin(ω0mt)])dt with ω0 = 5

TIP: A trigonometric system such as sin(at)cos(bt) has one important characteristic that will help you simplifying the given integral. What is that characteristic and how does it simplify the integral?

Calculate the integral.

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.

Reference no: EM131239467

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Reviews

inf1239467

11/2/2016 5:40:50 AM

i still lots of assignments im going to be submitting in the near future. i'll pay part payment now i'll pay the rest later. i thought i had the money. sorry for the inconvenience.tell him to start i will 110% pay . ive been here for awhile now . you can trust me. is it ready ? if i pay now can you give it to me . my dead line is tomorrow 1 pm!! thats this Monday 1pm Auckland new Zealand time. if i do not receive it before 12pm ( i need time to get to uni. if you want i can send the q2 answers for part a and b you have to finsih the rest with matlab and q4. 18259085_1IMG-20161015-WA0002.jpg

len1239467

10/12/2016 3:29:57 AM

hi, i ONLY WANT QUESTION (4) AND QUESTION (2) ONLY !!! PLEASE MAKE SURE ITS THE BEST SOLUTION I CAN GET • Please hand this assignment in to the box at reception level 3 of WS building before 1300 (1pm) • Remember to include your name, student ID, date, course code, and assignment # on your assignment solutions, and if you use more than one sheet, please staple them together. • Your solutions must include all workings to show how you derived the answers. Simply giving the numerical solutions (as is given in the textbook in the drill exercises) is not enough. • When including plots and figures, incorporate them in your submission with appropriate axis labels. Always label your plot axes with titles and units. Title your plot.

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