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Fourier Series - QUIZ Team A questions in white

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Presentation on theme: "Fourier Series - QUIZ Team A questions in white"— Presentation transcript:

1 Fourier Series - QUIZ Team A questions in white
Team B questions in red 1. What is when n = 3 ? 2. What is when n = 52 ? 3. What is when n = 1 ? 4. What is when n = 17 ? 5. What is when n = 52 ? 6. What is when n = 1 ? 7. What is when n = 4 ?

2 Fourier Series - QUIZ 8. Team B: What is ?

3 Fourier Series - QUIZ 9. Team A: What is ?

4 Fourier Series - QUIZ 10. Team B: Describe the following step function in terms of f(x) and x ?

5 Fourier Series - QUIZ 11. Team A: What is ?

6 Fourier Series - QUIZ 12. Team B: Describe the following step function over one period in terms of f(x) and x ?

7 Fourier Series - QUIZ 13. Team A: What is the integral of f(x) over one period ?

8 Fourier Series - QUIZ 14. Team B: Describe the following step function over one period in terms of f(x) and x ?

9 Fourier Series - QUIZ 15. Team A: What is the integral of f(x) over one period ?

10 Fourier Series - QUIZ Fourier series
16. Team B: If we were to represent the function below as a Fourier series what could you say about the value of a0 ? a0 is baseline shifter. Half way between 20 and 70 is 45. So ao = 90

11 Fourier Series - QUIZ Fourier series
17. Team A: If we were to represent the function below as a Fourier series what could you say about the values of the an terms ? odd function so all an terms are zero

12 Fourier Series - QUIZ Fourier series
18. Team B: If we were to represent the function below as a Fourier series what could you say about the sign of the b1 term ?

13 Fourier Series - QUIZ Fourier series
18. Team B: If we were to represent the function below as a Fourier series what could you say about the value of the b1 term ? It would have a negative amplitude

14 Finding coefficients of the Fourier Series - QUIZ
Find Fourier series to represent this repeat pattern. Steps to calculate coefficients of Fourier series 1. Write down the function f(x) in terms of x. What is period? Period is 2p 2. Use equation to find a0? 3. Team A find coefficients an? 4. Team B find coefficients bn?

15 Finding coefficients of the Fourier Series - QUIZ
Find Fourier series to represent this repeat pattern. Period is 2p 3. Team A find coefficients an? Integrate by parts so set u = x and cos (nx) dx = dv and du = dx n=1 n=2 n=3 n=4 n=5

16 Finding coefficients of the Fourier Series - QUIZ
Find Fourier series to represent this repeat pattern. Period is 2p 4. Team B find coefficients bn? Integrate by parts so set u = x and sin (nx) dx = dv du = dx n=1 n=2 n=3 n=4 n=5

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