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# Ex.) Fourier Transform of square wave function

문서에서 Engineering Mathematics 2 (페이지 37-58)

### 1

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T

1/ 2 1/ 4

1/ 2 1/ 4

1 T 1

T

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Series

### 1

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T

1/ 2 1/ 4

1/ 2 1/ 4

1 T 1

T

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Series

### 1

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T

1/ 2 1/ 4

1/ 2 1/ 4

1 T 1

T

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Series

### ˆ( ) f 

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

### )

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

0

### )

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

0

### 1 ( ) s t 

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

1/ 2 1/ 2

f0

f0

0

### 1 ( ) s t 

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

### 1 ( ) s t 

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

0

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

### 1 ( ) s t 

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

0

0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

1/10 1/10

0

0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

### 

1/10 1/10 1/10 1/10

0

0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

1/10 1/10

0 0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

1/10 1/10

0 0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

1/10 1/10

0 0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

1/10 1/10

1/14

1/14

0 0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

0

1/10 1/10

1/14

1/14

1/14

1/14

0 0 0

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

1/10 1/10

1/14

1/14 1/18 1/18

### 2008_Fourier Transform(2)

2

T

2 T t Waveform defined From -∞ to+ ∞

Fourier Transform Synthesize a summation of sinusoids

which add to give the waveform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

+ 6

T 6

T t

1 2

2

T

2 T t

1

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T Fourier Transform

Construct a diagram which displays amplitudeand frequencyof each sinusoid

Fourier Transform

frequency 3

T 3

T 2 T 2

T 1/ 2

1/ 4

1/ 2

1/ 4

1 T 1

T

1/ 2 1/ 2

1/ 6

1/ 6

f0

f0

1/10 1/10

1/14

1/14 1/18 1/18

###   

문서에서 Engineering Mathematics 2 (페이지 37-58)

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