1. Lecture 5: Phasor Addition & Spectral Representation
Signals and Systems
Lecture 5:
Phasor Addition
&
Spectral Representation

2. Today's lecture Chapter 2: Phasor Addition Example
Chapter 3: Definition of Spectrum
Spectrum of a Sinusoid
Graphical Spectrum
Amplitude Modulation
Periodic and Non-Periodic Signals

3. Summary of Phasor Addition

4. Sinusoids
Phasor Addition Rule: Example (2-6.3)

5. Spectral Representation
Chapter 3
Spectral Representation

6. Concept of the Spectrum
Complicated waveforms can be constructed as sums of sinusoidal signals of different amplitudes, phases and frequencies,
Spectrum simply shows the relationship between frequency ,phase and amplitude.

7. Sinusoidal Signals of Different Frequencies

8. Frequency Diagram

9. Plot Amplitude and Phase

10. Inverse Euler’s Formula

11. Interpretation of Spectrum

12. Spectrum of a Sine

13. General Form

14. Definition of Spectrum
Can be expresses as set of pairs
{ (0,X0), (f1,1/2 X1), (-f1,1/2 X*1),
……(fk,1/2 Xk), (-fk,1/2 X*k)}
Each pair of (fk,1/2 Xk) indicates the complex amplitude of the sinusoidal component at the frequency fk
Spectrum is the frequency domain representation of a signal
Up-till now we have seen the time-domain representation of signals