Re: [Discuss-gnuradio] sending single tone Am modulated using usrp1+wbx

[José María Valencia]

I will write my “theory” about usrp working and some math in Am modulation, because I want to be sure before continuing:

If I want to modulate in DSB amplitude a carrier of saying 1GHz ,with a m(t) signal (in this case a simple 1kHz cosine tone) the carrier is sourcing by USRP module, and I have to set up the freq of usrp in 1GHz and based on Leon Couch Book the complex envelope for DSB AM should   be I=Ac(1+m(t))   Q=0. (In my case Ac=1).

This is equivalent to  (1+m(t))(e^0)      eq.1

I and Q are a complex signal that I connect to the usrp sink.

Internally the usrp  multiplies   eq.1 by e^(2*pi*1GHz*t) resulting  (1+m(t))e^(2*pi*1GHz*t)     eq.2

Eq2. “travels by the air” to the receiver.

In the USRP receiver, Eq. 2 is multiplied by  e^-(2*pi*1GHz*t) resulting (1+m(t))(e^0)  whose I and Q components are   1+m(t)   and 0 respectively , and I can obtain the magnitude with a complex to magnitude block, this magnitude is 1+m(t).

This my “theory” and I want to be sure if this is correct…….

Thanks.