1. Dr. Michael Nasief Digital Signal Processing Lec 7 1

2. DFT 2 Chapter [6]

3. THE DISCRETE-TIME FOURIER TRANSFORM 3 The discrete-time Fourier transform (DTFT) of a sequence, x(n), is defined as s Remember

4. The DFT 4 DTFT: continuous variable “w” DFS: discrete Fourier Series for Periodic sequence DFT: for non periodic finite sequence

5. DFS : Discrete Fourier Series 5

6. Example 6

7. W N Notation 7

8. DFS Properties 8 Linearity Shift

9. Periodic Convolution 9

10. Example 10

11. 11

12. Solution 12

13. Discrete Fourier Transform DFT 13

14. DFT PROPERTIES 14

15. Circular Shift 15

16. Circular Shift 16

17. Circular Shift 17

18. Circular Shift 18

19. Circular Convolution 19

20. Example 20

21. 21

22. 22 Note