One Rotating PhasorHere is single phasor rotating. Notice that the phasor is red and its projection on the real axis is green. The green real part is also plotted vs. time on the lower plot. The length of the green phasor traces out a cosine wave versus time. The accompanying movie shows the phasor rotating and the sinusoidal wave being traced out in time. 

Positive & Negative Frequency PhasorsThis shows how a single frequency cosine is composed of the sum two phasors: one with positive frequency the other with negative frequency. The positive frequency phasor is red (rotating counterclockwise), and the negative frequency phasor is blue (rotating clockwise). The vector sum of the two is the green phasor which is the real part. 

Two PhasorsThis movie shows two phasors at different frequencies. One is four times the frequency of the other, but its amplitude is half as big. The green one is rotating faster than the blue one. The red vector is the sum of the two, and the violet one its real part. 

Beats: Closely Spaced FrequenciesHere are two more phasors at different frequencies, but this time the ratio of the two frequencies is 1.15. Since the two frequencies are nearly the same, the resulting time waveform exhibits the characteristic shape of a "beat frequency." The blue and green vectors are rotating at nearly the same speed. Their sum is the erratically rotating red vector, whose projection onto the real axis is the violet line. Hear the beats here. Use MATLAB to play with beats here. Use LabVIEW to play with beats here. 
Home
McClellan, Schafer, and Yoder, Signal Processing First, ISBN 0130655627.
Prentice Hall, Upper Saddle River, NJ 07458.
© 2012 Pearson Education, Inc.