2.1-AM Wave : The mathematical expression of the AM wave is given by :


By using and manipulating few trigonometric identities, we reduce the AM equation into a form containing a sum of three different signals at 3 different frequencies : {f_c, with an amplitude equals to V_c,max}, {(f_c-f_i), with an amplitude of mV_c,max/2} and {(f_c+f_i), with an amplitude of mV_c,max/2} where m is called the percent modulation of the AM signal and is equal to V_i,max/V_c,max. The figure below shows us the spectrum of an AM signal.


2.1.1 Analysis : The three impulses delimits the regions occupied by an AM signal, the regions are named : USB or Upper Side Band and the LSB or the Lower Side Band . The USB and the LSB are equidistant to the carrier frequency f_c. Note that both LSB and USB impulses carry an equal amoint of power and we simply refer to it as P_SB.
2.1.2 Bandwidth : This is one of the most important parameter in telecommunication. It determines the amount of space needed to transmit an intelligent signal. In the case of AM modulated signals the needed bandwidth is equal to 2f_i. In order to assign a carrier frequency and a bandwidth for emitters we need to fix the maximum transmitted intelligent frequency or f_i,max. In Canada, the government ministry responsible for allocating frequencies and bandwidth is Industry Canada