# Question reg. Amplitude Modulation

1. Nov 27, 2008

### gh0st

Given m(t) = 25cos(2*pi*1000t) and sc(t) = 75cos(2*pi*150000t), hence the AM signal equation is 75[1+0.333cos(2*pi*1000t)]cos(2*pi*150000t).

Expanding it will yield 75cos(2*pi*150000t) + 12.5cos(2*pi*149000t) + 12.5cos(2*pi*151000t) and proceeding with Fourier Transform, i got delta functions of amplitude 37.5 at f=+/-150kHz (carrier) and 6.25 at f=+/-151kHz & +/-149kHz. (sidebands).

From the frequency translation/modulation theorem property, 12.5cos(2*pi*fc*t) <---> 0.5*[12.5delta(f-fc) + 12.5delta(f+fc)] = 6.25[delta(f-fc) +delta(f+fc)]. The answer provided, however says that the amplitude for the sidebands are 12.5 instead of 6.25. Is there anywhere i went wrong?

Another example i found on googlebooks : http://img88.imageshack.us/my.php?image=70822797oa6.jpg

Shouldn't the amplitude for the sidebands in time domain be 1.25? Using the trigonometry identity of cosAcosB=1/2[cos(A+B) + cos(A-B)] ? In the example itself wrong or did i missed out something as well?

Last edited: Nov 28, 2008