1. Digital Signal Processing Lecture 4 DTFT
add slide for format types , d , f, c etc
Dr. Shoab Khan

2. Complex Exp Input Signal

3. The Frequency Response

4. Delay and First Difference

5. More on the Ideal Delay

6. Discrete Time Fourier Transform

7. Fourier with DTFT Mag-Phase

8. Properties

9. Properties…(cont)

10. Symmetric Properties
DTFT Properties:

11. Consequences of Hermitian SymmetryIf
then
And
symmetry

12. DTFT- Sinusoids

13. DTFT of Unit Impulse

14. Ideal Lowpass Filter

15. Example

16. Magnitude and Angle Form

17. Magnitude and Angle Plot

18. Example

19. Real and Even ( Zero Phase)
Consider an LTI system with an even unit sample response
DTFT is = e 2 j w + 3 -
cos( ) 4

20. Real & Even (Zero Phase)
Frequency response is real, so system has “zero” phase shift
This is to be expected since unit sample response is real and even.

21. Linear Phase
symmetryLP

22. Useful DTFT Pairs

23. Convolution Theorem

24. Linear Phase… ( cont.)

25. freqfilter

26. Frequency Response of DE

27. Matlab

28. Example

29. Ideal Filters

30. Ideal Filters

31. Ideal Lowpass Filter

32. h[n] of ideal filter

33. Approximations

34. Freq Axis

35. Inverse System