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Fourier Series - QUIZ

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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 ?

8. Team B: What is ?

9. Team A: What is ?

10. Team B: Describe the following step function in terms of f(x) and x ?

11. Team A: What is ?

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

13. Team A: What is the integral of f(x) over one period ?

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

15. Team A: What is the integral of f(x) over one period ?

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

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

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 ?

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

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?

Team A find coefficients an?

3.

4.

Team B find coefficients bn?

Find Fourier series to represent this repeat pattern.

Period is 2p

Team A find coefficients an?

3.

Integrate by parts

so set u = x and cos (nx) dx = dv

and du = dx

Find Fourier series to represent this repeat pattern.

Period is 2p

Team B find coefficients bn?

4.

Integrate by parts

so set u = x and sin (nx) dx = dv

du = dx