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F. C-C+. B-B+. A-A+. Week 11. Chapter 10 Fourier Transforms The Four Fourier transforms CTFT DTFT FS DFT/S Relationships Important properties. The Four Fourier transforms The signal spaces The transform definitions Relationships Important properties. The 4 Signal Spaces.

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Presentation Transcript

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

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

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

  4. The 4 Signal Spaces CTFT is defined for ContSignals DTFT is defined for DiscSignals FS is defined for ContPeriodicp DFT (DFS) defined for DiscPeriodicp

  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

  14. Example

  15. Properties 5 Duality

  16. Example

  17. Example

  18. Properties 6 Convolution

  19. Properties 7 Delay

  20. Properties 8 Modulation

  21. Discrete-time Fourier Transform (DTFT)

  22. Example Rectangle

  23. Example Upsampling

  24. 1 0 1 2 Fourier series

  25. 1 0 7 Discrete Fourier Transform (DFT)

  26. Fourier series and DTFT

  27. Summary Definitions CTFT InvCTFT DTFT InvDTFT

  28. FS InvFS DFT InvDFT

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

  30. Properties for DTFT Periodic Convolution Multiplication Delay Modulation Upsampling

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

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