Re: [Discuss-gnuradio] Signal coming from the USRP to the computer

[Patrick Sisterhen]

I think a little more detailed precise
answer to John's question might help:

John Andrews wrote:

> each complex sample that enters the
> USB bus is the following,
> 
> x[i] = (inphase_component) + j (quadrature_component), and
> x[i] = m(t)cos( 2*pi*FREQ_OFFSET*t + PHI ) + jm(t)sin( 2*pi*FREQ_OFFSET*t
+
> PHI ), where m(t), is the actual message signal, FREQ_OFFSET is the
> frequency offset, and PHI is the phase.
> 
> Is that correct?

I think you're confusing the baseband
and passband signals a little, and the equations aren't quite right.

The complex-baseband signal (your message)
is the data that is transferred across the USB channel.
x[i] = (in-phase) + j*(quadrature)
       = (x_i) +
j*(x_q)

These are samples of your message signal,
after modulation (mapping to a complex QAM-constellation, for example),
coding, pulse-shaping, etc.

The signal is up/down converted on the
USRP device such that the transmitted RF signal is

r(t) = x_i*cos(2*pi*f_c) - (x_q)*sin(2*pi*f_c)

(where f_c is your RF carrier frequency,
and I'm ignoring phase offsets and noise)

Notice the subtraction there (which
comes from the trig identities) and that all the terms are real (it's a
real passband signal).

Hope that helps a little.

Patrick Sisterhen
National Instruments