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# ECE 3323 Principles of Communication Systems - PowerPoint PPT Presentation

ECE 3323 Principles of Communication Systems. Section 3.3 Fourier Transform Pairs. 1. Fourier Transform of a Constant. Fourier Transform of a Constant. Fourier Transform of a Constant. 2. Fourier Transform of a Unit Impulse. Fourier Transform of a Unit Impulse. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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1. ECE 3323Principles of Communication Systems Section 3.3 Fourier Transform Pairs

2. 1. Fourier Transform of a Constant

3. Fourier Transform of a Constant

4. Fourier Transform of a Constant

5. 2. Fourier Transform of a Unit Impulse

6. Fourier Transform of a Unit Impulse

7. Fourier Transform of a Unit Impulse

8. 1 . . . . . . 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 t 3. Fourier Transform of The Sampling Function

9. Fourier Transform of The Sampling Function

10. Fourier Transform of The Sampling Function

11. Fourier Transform of The Sampling Function

12. 1 . . . . . . 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 t 1 . . . . . . 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 f Fourier Transform of The Sampling Function

13. 1 . . . . . . -3 T -2 T -1 T 0 T 2 T 3 T t s s s s s s Fourier Transform of The Sampling Function

14. Fourier Transform of The Sampling Function

15. Fourier Transform of The Sampling Function

16. 1 . . . . . . -3 T -2 T -1 T 0 T 2 T 3 T t s s s s s s f s . . . . . . f -3 f -2 f -1 f 0 f 2 f 3 f s s s s s s Fourier Transform of The Sampling Function

17. 4. Fourier Transform of rect(t)

18. Fourier Transform of rect(t)

19. Fourier Transform of rect(t)

20. Fourier Transform of rect(t)

21. Fourier Transform of rect(t)

22. 5. Fourier Transform of tri(t)

23. Fourier Transform of tri(t)

24. Fourier Transform of tri(t)

25. Fourier Transform of tri(t)

26. Fourier Transform of tri(t)

27. Fourier Transform of tri(t)

28. Fourier Transform of tri(t)

29. Fourier Transform of tri(t)

30. Fourier Transform of tri(t)

31. Fourier Transform of tri(t)

32. 6. Fourier Transform of exp(– t)u(t)

33. Fourier Transform of exp(– t)u(t)

34. Fourier Transform of exp(– t)u(t)

35. Fourier Transform of exp(– t)u(t)

36. Fourier Transform of exp(– t)u(t)

37. 7. Fourier Transform of exp( j2π f0 t)

38. Fourier Transform of exp( j2π f0 t)

39. Fourier Transform of exp( j2π f0 t)

40. Fourier Transform of exp( j2π f0 t)

41. Fourier Transform of exp( j2π f0 t)

42. Fourier Transform of exp( j2π f0 t)

43. Fourier Transform of exp( j2π f0 t)

44. 8. Fourier Transform of cos(2π f0 t)

45. Fourier Transform of cos(2π f0 t)

46. Fourier Transform of cos(2π f0 t)

47. Fourier Transform of cos(2π f0 t)

48. Fourier Transform of cos(2π f0 t)