1. Vibrate the membrane
Acoustic wave

2. What do you think about my voice?
Can you tell me my tone of voice?
Low or High?

3. Human voice (time signals)
Equalizer
Frequency

4. Fourier transform
12 Oct. 2012
PhD student of Geophysics
Seogi Kang

5. Contents
Objectives
Fourier transform
Applications
Conclusions

6. Objectives “Qualitatively” identify the meaning of Fourier transform
Explain the application of Fourier transform

7. Self Quiz
Problem 1. This time signal composed of two sine functions, can you find the period and frequency of each sine functions? So Find “a” and “b”.
a=4π
fa=2
b=π
fb=0.5

8. Solution
Frequency = 2 Hz
Frequency = 0.5 Hz
“It is not easy to decompose mixed signals to specific frequency component”

9. Specific frequency component
Fourier transform
Fourier series
“Any periodic function can be expressed as the sum of sine and cosine functions”
Think Euler’s theorem
Fourier transform
“Any time signals can be decomposed in to specific frequency components”
Time signal
Specific frequency component

10. Applying Fourier transform
Time domain
Fourier transform
Frequency domain
“We can get each component frequency component of signal”

11. Making filter using Fourier transform
Mixed voice
Brett’s
Seogi’s
Applying
Filter
Almost only
Brett’s
Go back to time domain

12. Conclusions
By using Fourier transform, you can decompose your time signals into specific frequency components
Not only time signals but any signals such as ocean wave
Transform is a different lens to see the world differently
What else we can?