Sesión_06_SDCD

3. •
•

4. •
•
• ´
´

9. •
•

10. 𝑻 𝑻 = 𝒏𝑻
𝑻: 𝒏 = 𝟎, 𝟏, 𝟐, 𝟑, …
𝒏𝑻′𝒔
: 𝒏𝑻 + 𝒓 − 𝒏𝑻 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕𝒆 𝒏𝑻
𝒏𝑻

12. 𝑇 =
1
𝑓𝑠
𝑇 =
1
8000
𝑇 = 0.000125 s.
• µ

13. 𝑓S
𝑓𝑚á𝑥
𝑓s > 2𝑓𝑚á𝑥

14. •
•
•

15. •
•
•

21. • 𝒙 𝒏 𝒙𝒏 𝒏
𝑛
• 𝟎
𝑛
𝑥𝑛 = 𝑥−2, 𝑥−1, 𝑥0,𝑥1,𝑥2,𝑥3
𝑥[𝑛] = 𝑥[𝑛 − 2], 𝑥[𝑛 − 1], 𝑥[𝑛], 𝑥[𝑛 + 1], 𝑥[𝑛 + 2]

22. 𝑥𝑛 = 3,8,9,10,6
𝑥𝑛 = 3−2, 8−1, 90, 101, 62
3
6
8
9
10
3
6
8
9
1 0
3
− 2
−
3
6
8
9
1 0
3
6
8
9
1 0
3
− 2
− 𝑛
𝑥𝑛

23. 1
𝛿[𝑛] =
1 → 𝑛 = 0
0 → 𝑛 ≠ 0
𝑢[𝑛] = ቊ
1 → 𝑛 ≥ 0
0 → 𝑛 < 0
𝑢[𝑛]
1 2 3
0
1
0
𝛿[𝑛]

24. 1
0 
 a
0
1 

− a
𝑥[𝑛]
2
− 1
−
1
𝑛
1
− 2
−
𝑥 𝑛 = 𝑎𝑛 → −∞ ≤ 𝑛 ≤ ∞
𝑛
2
− 1
−
0
𝑥[𝑛]
1
− 2
−

25. 𝑥[𝑛] = cos[𝑛] + sin[𝑛]
𝑥[𝑛]
𝑛

26. •
𝑻
•
•
𝒕 = 𝟎, 𝑻, 𝟐𝑻, … 𝑻

27. •
𝒚(𝒕) 𝒙[𝒏𝑻]
•
𝒚(𝒕) 𝒏𝑻 ≤ 𝒕 ≤
𝒏 + 𝟏 𝑻 𝝉
𝒚 𝒏𝑻 + 𝝉 = 𝒂𝒏𝝉𝒏 + 𝒂𝒏−𝟏𝝉𝒏−𝟏 + ⋯ + 𝒂𝟏𝝉 + 𝒂𝟎

28. 𝟎 ≤ 𝝉 ≤ 𝑻 𝒚[𝒏𝑻] 𝒙[𝒏𝑻]
𝒚 𝑛𝑻 + 𝝉 = 𝒂𝒏𝝉𝒏 + 𝒂𝒏−𝟏𝝉𝒏−𝟏 + ⋯ + 𝒂𝟏𝝉 + 𝒙[𝒏𝑻]

29. •
•

30. 𝒏 = 𝟎
𝒚 𝒏𝑻 + 𝝉 = 𝒙[𝒏𝑻]
𝟎 ≤ 𝝉 ≤ 𝑻 𝒏 = 𝟎, 𝟏, 𝟐, …
•
•
•

31. 𝒚 𝒕 𝒚[𝒏]
↓ 𝑻

33. • 𝒙(𝒕)
•
𝒚(𝒕)

34. •
•

35. •
𝚫𝒕 → 𝟎
𝒕 = 𝒏𝑻
𝒚 𝒏 = 𝒚 𝒕 𝜹[𝒕 − 𝒏𝑻]
𝜹[𝒕 − 𝒏𝑻]
•

36. 𝒚 𝒏
𝒚 𝒏 = 𝒚 𝟎 + 𝒚 𝟏 + 𝒚 𝟐 + ⋯
𝒚 𝒏 = 𝒚 𝟎 𝜹[𝒕] + 𝒚[𝟏] 𝜹[𝒕 − 𝑻] + 𝒚[𝟏]𝜹[𝒕 − 𝟐𝑻] + ⋯
𝒚 𝒏 = ෍
𝒌=𝟎
∞
𝒚 𝒏𝑻 𝜹[𝒕 − 𝒏𝑻]

37. 𝑻
𝒖 𝒏 = 𝒖 𝟎 + 𝒖 𝟏 + 𝒖 𝟐 + ⋯
𝒖[𝒕] = 𝒖[𝟎]𝜹[𝒕] + 𝒖[𝟏]𝜹[𝒕 − 𝑻] + 𝐮[𝟏]𝜹[𝒕 − 𝟐𝑻] + ⋯
𝒖(𝒕) = ෍
𝒏=𝟎
∞
𝒖[𝒏𝑻] 𝟏 𝒕 − 𝒏𝑻 − 𝟏(𝒏 − 𝒏 + 𝟏 𝑻

38. 𝓛 𝟏 𝒕 − 𝒏𝑻 =
𝒆−𝒏𝑻𝒔
𝒔
𝒖(𝒕)
𝓛{𝒖(𝒕)} = 𝓛 ෍
𝑛=𝟎
∞
𝒖(𝒏𝑻) 𝟏 𝒕 − 𝑛𝑻 − 𝟏(𝒕 − 𝒏 + 𝟏 𝑻
𝑼 𝒔 =
𝟏 − 𝒆−𝒏𝑻𝒔
𝒔
෍
𝒏=𝟎
∞
𝒖[𝒏𝑻]𝒆−𝒏𝑻𝒔

39. 𝒁𝑶𝑯 𝒔 =
𝟏 − 𝒆−𝑻𝒔
𝒔

40. t
T
1 t T
1 t T
1 T
5
𝒖(𝒕)

41. t
T
1 t T
1 T
4 T
5 T
6
𝒖(𝒕)

42. 𝑻
𝒖 𝒕 = 𝒖 𝒏𝑻 +
𝒖[𝒏𝑻] − 𝒖[ 𝒏 − 𝟏 𝑻]
𝑻
[𝒕 − 𝒏𝑻]
𝒏𝑻 ≤ 𝒕 ≤ 𝒏 + 𝟏 𝑻 𝒏 = 𝟐, 𝟑, 𝟒, …

43. 𝑭𝑶𝑯 =
𝟏 + 𝒔𝑻
𝑻
𝟏 − 𝒆−𝒔𝑻
𝒔
𝟐
1
1
2
T 2T
-1

44. 0 1T 3T 5T 7T t
𝑢(𝑡)
0 1T 3T 5T 7T t
𝑢(𝑡)
0 1T 3T 5T 7T t
𝑢[𝑛𝑇]

45. 0 2T 4T 6T 8T 10T t
𝒖[𝒏𝑻]
0 2T 4T 6T 8T 10T t
𝒖(𝒕)
0 2T 4T 6T 8T 10T t
𝒖(𝒕)