1. Lecture 7: Spectral Representation
Signals and Systems
Lecture 7:
Spectral Representation

2. Example 3-5: Amplitude Modulation
Find the spectral components of x(t)
x(t)= [5 + 4cos(40πt)] cos(400πt)

3. Figure 3.7: Spectrum of AM signal
x(t)= cos (2π(20)t) cos (2π(200)t)

4. Periodic Signals
f0 = gcd (fk)

5. Harmonic Signal Spectrum

6. Define Fundamental Frequency

7. Harmonic Signal (3 frequencies)

8. Periodic Signals

9. Period of Complex Exponential

10. Harmonic Signal (3 frequencies)

11. Another Spectrum

12. Examples Harmonic Signal
xh(t)= 2cos (20πt) – 2/3 cos (20π(3)t) + 2/5 cos (20π(5)t)
Non-Harmonic Signal
x2(t)= 2cos (20πt)– 2/3 cos (20π(8)1/2t) + 2/5cos (20π(27) 1/2t)

13. Irrational Spectrum

14. xh(t)= 2cos (20 πt) – 2/3 cos (20π(3)t) + 2/5 cos (20π(5)t)
Harmonic Signal

15. Non-Harmonic Signal
x2(t)= 2cos (20πt)– 2/3 cos (20π(8)1/2t) + 2/5cos (20π(27) 1/2t)

16. Example: Synthetic Vowel

17. Spectrum of a Vowel

18. Spectrum of a Vowel

19. Vowel Waveform