Yes Patrick, I agree with your explanation. That was succinct and easy to understand. Thanks.
On Tue, May 31, 2011 at 4:55 PM, Patrick Sisterhen <[email protected] > wrote: > John, > > Typo in my equations, should have been: > > y_q = (x_i * sin(phi)) - (x_q * cos(phi)) > > Patrick Sisterhen > National Instruments > > > > From: John Andrews <[email protected]> > To: Patrick Sisterhen <[email protected]> > Cc: [email protected] > Date: 05/31/2011 02:08 PM > Subject: Re: [Discuss-gnuradio] Signal coming from the USRP to the > computer > ------------------------------ > > > > Thanks Patrick. I was concerned with the received signal path. Suppose, I > have the receiver tuned to, let's say, GPS signal. What will the received > signal look like. Considering the GPS message signal is m(t), then what > would equation would best describe the received signal. > > If 'f_c' is the carrier frequency then the signal coming over the USB bus > on to the computer for baseband processing will be, > inphase(t) = m(t) cos(phi) > quadrature(t) = m(t)sin(phi) > > where, 'phi' is the instantaneous offset. Remember, phi here is a broad > term which includes all kinds of offsets(frequency, phase etc). > > On Tue, May 31, 2011 at 11:47 AM, Patrick Sisterhen <* > [email protected]* <[email protected]>> wrote: > 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 > _______________________________________________ > Discuss-gnuradio mailing list* > **[email protected]* <[email protected]>* > **https://lists.gnu.org/mailman/listinfo/discuss-gnuradio*<https://lists.gnu.org/mailman/listinfo/discuss-gnuradio> > > >
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