22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples...
Transcript of 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples...
![Page 1: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/1.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
00.20.40.60.81
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 2: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/2.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
![Page 3: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/3.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
00.20.40.60.81
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
![Page 4: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/4.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
00.20.40.60.81
20
40
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
![Page 5: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/5.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
10
20
30
10
20
30
0
2
4
6
10
20
30
10
20
30
0 5 10 15 20 25 30
0
5
10
15
20
25
30
![Page 6: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/6.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
10
20
30
10
20
30
0
2
4
6
10
20
30
10
20
30
20
40
60
20
40
60
00.20.40.60.81
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
![Page 7: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/7.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 5 10 15 20 25 30
0
5
10
15
20
25
30
0 5 10 15 20 25 30
0
5
10
15
20
25
30
0 5 10 15 20 25 30
0
5
10
15
20
25
30
![Page 8: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/8.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
10
20
30
10
20
30
0
2
4
6
10
20
30
10
20
30
10
20
30
10
20
30
0
2
4
6
10
20
30
10
20
30
10
20
30
10
20
30
0
2
4
6
10
20
30
10
20
30
![Page 9: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/9.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
0
10
20
20
40
60
20
40
60
20
40
60
20
40
60
0
5
10
15
20
20
40
60
20
40
60
![Page 10: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/10.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
0
10
20
20
40
60
20
40
600 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
0
10
20
30
40
20
40
60
20
40
60
![Page 11: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/11.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
0
10
20
20
40
60
20
40
600 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
0
20
40
20
40
60
20
40
60
![Page 12: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/12.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
0 10 20 30 40 50 60
0
10
20
30
40
50
60
0 10 20 30 40 50 60
0
10
20
30
40
50
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
![Page 13: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/13.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
0
20
40
20
40
60
20
40
60
20
40
60
20
40
60
0
10
20
30
40
20
40
60
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
![Page 14: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/14.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
-0.1
0
0.1
20
40
60
20
40
60
20
40
60
0
1
2
3
4
20
40
60
20
40
60
20
40
60
20
40
60
0
20
40
20
40
60
20
40
60
20
40
60
20
40
60
00.20.40.60.81
20
40
60
![Page 15: 22.058 - lecture 3a. Examples of Fourier Transforms · 2020-07-10 · 22.058 - lecture 3a. Examples of Fourier Transforms 20 40 60 20 40 60 0 0.25 0.5 0.75 1 20 40 60 20 40 60 0 5](https://reader033.fdocuments.in/reader033/viewer/2022050611/5fb2c117bc35c74b4125b269/html5/thumbnails/15.jpg)
22.058 - lecture 3a. Examples of Fourier Transforms
20
40
60
20
40
60
0
0.25
0.5
0.75
1
20
40
60
20
40
60
20
40
60
0
5
10
15
20
40
60
20
40
60
20
40
60
20
40
60
0
10
20
20
40
60
20
40
60
20
40
60
20
40
60
-0.25
0
0.25
0.5
20
40
60