Acoustic waveVibrate the membrane

Can you tell me my tone of voice?

Low or High?

What do you think about my voice?

Human voice (time signals)

EqualizerFrequency

Fourier transform

PhD student of GeophysicsSeogi Kang

12 Oct. 2012

Objectives

Contents

Fourier transform

Applications

Conclusions

“Qualitatively” identify the meaning of Fourier transform

Explain the application of Fourier transform

Objectives

Self QuizProblem 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”.

( ) sin( ) sin( )f t at bt

2 1sin( ) , .

2

aPeriod of at is frequency

a Period

a=4πfa=2

b=πfb=0.5

Solutionsin(4 )t

sin( )t

sin(4 ) sin( )t t

Frequency = 2 Hz

Frequency = 0.5 Hz

“It is not easy to decompose mixed signals to specific frequency component”

Fourier transform Fourier series

01

( ) cos( ) sin( )n n n nn

f t a a w t b w t

“Any periodic function can be expressed as the sum of sine and cosine functions”

cos sinie i Think Euler’s theorem

Fourier transform

( ) ( ) , 2i tF f t e dt f

“Any time signals can be decomposed in to specific frequency components”

Time signal

Specific frequency component

Applying Fourier transform

Time domain

Frequency domain Fourier transform

“We can get each component frequency component of signal”

Making filter using Fourier transform

Mixed voice

Brett’s Seogi’s

ApplyingFilter

Almost onlyBrett’s Go back to

time domain

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?

Conclusions