# Fourier Series - QUIZ - PowerPoint PPT Presentation

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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 ?.

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Fourier Series - QUIZ

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### 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 ?

### Fourier Series - QUIZ

8. Team B: What is ?

### Fourier Series - QUIZ

9. Team A: What is ?

### Fourier Series - QUIZ

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

### Fourier Series - QUIZ

11. Team A: What is ?

### Fourier Series - QUIZ

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

### Fourier Series - QUIZ

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

### Fourier Series - QUIZ

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

### Fourier Series - QUIZ

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

### 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

### 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

### 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 ?

### 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

### 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?

Team A find coefficients an?

3.

4.

Team B find coefficients bn?

### Finding coefficients of the Fourier Series - QUIZ

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

### Finding coefficients of the Fourier Series - QUIZ

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