This type of modulation system is referred to as double-sideband amplitude modulation (DSAM).
15.2 Fundamental Principles The radio carrier wave signal onto which the analog amplitude variations are to be impressed is expressed as:
( ) ( )e t A E tc c= cos ω (15.1) Where: e(t) = instantaneous amplitude of carrier wave as a function of time (t) A = a factor of amplitude modulation of the carrier wave ωc = angular frequency of carrier wave (radians per second) Ec = peak amplitude of carrier wave
If A is a constant, the peak amplitude of the carrier wave is constant, and no modulation exists. Periodic modulation of the carrier wave results if the amplitude of A is caused to vary with respect to time, as in the case of a sinusoidal wave:
( ) ( )A tE E mm c= +1 cos ω (15.2) Where: Em/Ec = the ratio of modulation amplitude to carrier amplitude
The foregoing relationship leads to:
( ) ( ) ( ) ( )[ ]e t E t tc E E m cm c= +1 cos cosω ω (15.3) This is the basic equation for periodic (sinusoidal) amplitude modulation. When all multiplications and a simple trigonometric identity are performed, the result is:
( ) ( ) ( ) ( ) ( ) ( )e t E t t t t tc c M c m M c m= + + + −cos cos cosω ω ω ω ω2 2 (15.4) Where: M = the amplitude modulation factor (Em/Ec)
Amplitude modulation is, essentially, a multiplication process in which the time functions that describe the modulating signal and the carrier are multiplied to produce a modulated wave containing intelligence (information or data of some kind). The frequency components of the modulating signal are translated in this process to occupy a different position in the spectrum.