1. 1 Lecture 06 EEE 341 Introduction to Communication Engineering

2. 2 Selected Properties of the Fourier Transform: Linear Combination If Then Proof:

3. 3 Selected Properties of the Fourier Transform: Symmetry / Duality If Then Proof:

4. 4 Symmetry / Duality Property: Example If Then If Then

5. 5 Symmetry / Duality Property: Example If Then If Then

6. 6 Selected Properties of the Fourier Transform: Scaling If Then Proof:

7. 7 Selected Properties of the Fourier Transform: Time-Shifting If Then Proof:

8. 8 Selected Properties of the Fourier Transform: Frequency-Shifting If Then Proof:

9. 9 Selected Properties of the Fourier Transform: Convolution If Then Proof: 

10. 10 Fourier Transform Example exp(jω 0 t) is not real, hence frequency shift usually performed by multiplying with a cos function: Let f 1 (t) be a sinc function. Then F 2 (ω) is ?

11. 11 Exercise HW2  Q1  Q2

12. 12 Notices Reading:  Lathi, Ch 3.3