1. 1 Review of Continuous-Time Fourier Series

2. 2 Example 3.5 T/2 T1T1 -T/2 -T 1 This periodic signal x(t) repeats every T seconds. x(t)=1, for |t|<T 1, and x(t)=0, for T 1 <|t|< T/2 Fundamental period= T, Fundamental frequency    Choosing the period of integration to be between -T/2 and +T/2. Use eqn 3.39 to get at Fourier Series Coefficients.

3. 3 Example 3.5 continued

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8. 8 Continuous-Time Fourier Transform

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10. 10 Continuous-Time Fourier Transform

11. 11 Continuous-Time Fourier Transform

12. 12 Continuous-Time Fourier Transform Pair Equation

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15. 15 An exponential time function and its Fourier Transform

16. 16 Bode Plot representation of the Fourier Transform of an exponential time function

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21. 21 Properties of Fourier Transform Linearity Time Shifting Conjugation Differentiation in the time-domain Integration in the time-domain Time and Frequency Scaling. Duality Parseval’s Relation Convolution Multiplication

22. 22 FT Property associated with Linearity

23. 23 FT Properties associated with Time shifting & Conjugation

24. 24 FT Properties associated with Differentiation & Integration in Time Domian

25. 25 FT Properties associated with Time & Frequency Scaling.

26. 26 FT Properties associated with Duality

27. 27 FT Properties –Duality continued.

28. 28 FT Properties – Duality continued.

29. 29 FT Properties-Duality continued

30. 30 FT Properties- Duality continued

31. 31 FT Property associated with Convolution in time domain

32. 32 FT Property associated with Multiplication in time domain