1. A-A+ B-B+ C-C+ F

2. Week 11. Chapter 10 Fourier Transforms 1.The Four Fourier transforms CTFT DTFT FS DFT/S 2.Relationships 3.Important properties

3. 1.The Four Fourier transforms The signal spaces The transform definitions 2.Relationships 3.Important properties

4. The 4 Signal Spaces CTFT is defined for ContSignals DTFT is defined for DiscSignals FS is defined for ContPeriodic p DFT (DFS) defined for DiscPeriodic p

5. CTFT

6. CTFT Intuition

7. Properties 1 Sinusoids

8. Example FS & FT of periodic signals

9. Properties 2 Time change

10. Example

11. Properties 3 Symmetry

12. Properties 4 More symmetry

13. Example

15. Properties 5 Duality

16. Example

18. Properties 6 Convolution

20. Properties 7Delay

21. Properties 8Modulation

22. Discrete-time Fourier Transform (DTFT)

23. Example Rectangle

24. Example Upsampling

25. Fourier series 012 1

26. Discrete Fourier Transform (DFT) 07 1

27. Fourier series and DTFT

28. SummaryDefinitions CTFT InvCTFT DTFT InvDTFT

29. FS InvFS DFT InvDFT

30. Properties for CTFT Linearity Symmetry Duality Convolution Time-scale Multiplication Modulation Delay

31. Properties for DTFT Periodic Convolution Multiplication Delay Modulation Upsampling

32. Important signals Delta Complex exponentials, sinusoids Rectangular pulse, sinc Exponentials