Acoustic wave Vibrate the membrane. Can you tell me my tone of voice? Low or High? What do you think...
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Transcript of Acoustic wave Vibrate the membrane. Can you tell me my tone of voice? Low or High? What do you think...
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