If and the amplitude of the carrier signal is varied (amplitude modulated) by the information signal (), then the expression for the amplitude modulated (AM) wave (VAM) can be written as: = [ + sin(2 + )][ sin(2 + )]. = 10 = 5 Assuming C = 0 and i = 0, , VAM becomes: = [10 + 5 sin(2)] [ sin(2)] = 10sin(2) + 5 sin(2) *( sin(2))

We can use the following table of Trigonometric identities to determine the upper and lower sidebands of the amplitude modulates signal.

= 1/2[( ) ( + )]. From the above table we have: = 2 and = 2fi t, = 10 sin(2) + 5 (12) [(2( ) cos 2( + )] , With is the lower side band, and + where is the upper side band. = 100 and = 10

Assume that, use a calculator to develop the equation for the composite modulated signal VAM = ______________.

To generate the time-domain representation of the composite modulated signal, use the "Desmos" graphing tool at https://www.desmos.com/calculator.

The equation used to generate the sample graph below is: Y = 10*sin(628319x) + 2.5*(cos(565487x) -cos(691150x))