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

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

Summary of Phasor Addition

Sinusoids Phasor Addition Rule: Example (2-6.3)

Spectral Representation Chapter 3 Spectral Representation

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.

Sinusoidal Signals of Different Frequencies

Frequency Diagram

Plot Amplitude and Phase

Inverse Euler’s Formula

Interpretation of Spectrum

Spectrum of a Sine

General Form

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