1. SIGNAL AND SYSTEM CT Fourier Transform

2. Fourier’s Derivation of the CT Fourier Transform x(t) -an aperiodic signal -view it as the limit of a periodic signal as T→ ∞ For a periodic signal, the harmonic components are spaced ω0= 2π/T apart... As T→ ∞, ω0→0, and harmonic components are spaced closer and closer in frequency ⇓ Fourier series Fourier integral

3. Motivating Example: Square wave

4. Derivation

5. Derivation(continued)

7. For what kind of signals we do this

8. Example

9. CT Fourier Transforms of Periodic Signals

10. Example

11. Properties

12. Properties(continued)

14. 5.Differentiation and Integration 6.Duality

15. Properties(continued) 7.Parseval’s Relation 8.Multiplication Property 9.Convolution Property

16. LTI System characterized by Differential Equations (Some slides are referred from MIT )