Hi Patrick, > So the working must be something close to: > * analytic mixing of I (with cos(wt) and sin(wt)) > * analytic mixing of Q (with cos(wt) and sin(wt)), > At this level there are 4 components. > * sum et difference of components (I don't go into > details) will give two new components in quadrature I' and Q', with > two major frequencies (the base band (around w=0) and the > image band (around -2w). > > At this level, either you do a FFT or you do a > decimation. In the second case, you must apply two > low pass filters (one for I' and for Q') before the > decimation and the FFT.
No, it is easier:-) Your hardware supplies I and Q and for the moment we assume that there is only one signal present at the angular frequency w. I(rf)=cos(wt) Q(rf)=sin(wt) Now, we have an NCO at an angular frequency v (close to w.) This means: I(nco)=cos(vt) Q(nco=sin(vt) Frequency mixing means multiplication: I(if)= I(rf)*I(nco)+Q(rf)*Q(nco) Q(rf)=-I(rf)*Q(nco)+Q(rf)*I(nco) If we do the algebra (for I only) we get: I(if)=cos(wt)*cos(vt)+sin(wt)*sin(vt)= =0.5*[cos(wt+vt)+cos(wt-vt)-cos(wt+vt)+cos(wt-vt)]= =cos(wt-vt) Standard formulae: cos(a)*cos(b)=0.5*[cos(a+b)+cos(a-b)] sin(a)*sin(b)=0.5*[cos(a-b)-cos(a+b)] Complex mixing gives only one frequency! It can be the sum or the difference frequency according to your choice of sign for Q(nco) It all works also for analog circuits. Phasing SSB transmitters do the above. 73 Leif / SM5BSZ > > 73 > Patrick > > > > > ----- Original Message ----- > From: i2phd > To: [email protected] > Sent: Sunday, August 26, 2007 1:08 AM > Subject: [soft_radio] Re: Mix the time domain Q & I signal with a NCO to > make a near to zero signal > > > > --- In [email protected], "Leon" <[EMAIL PROTECTED]> wrote: > > > >> Hello Fred, Alberto and all, > >> > > > I'm investing an interesting time in the SdR theory. One particular > message of this group makes me problem. > >> > >> The problematic sentence is the following: > >> "1° Mix the time domain Q & I signal with a NCO to make a near to zero > signal"(this before the FFT) > >> It seems that the "NCO" must mean something as "numerical oscillator". I > don't suppose that it is an analytic oscillator > >> (cos wot / sin wot) but a simple oscillator (cos wot). This simple > oscillator applies to I and Q. > > > > > > An NCO (numerically-controlled oscillator) is the same as a DDS. > > > > 'I' means 'in-phase' and 'Q' means 'quadrature'. > > > > Leon > > > > Yes, correct, the NCO in Winrad is a numerically controlled oscillator > that mimics the working of a DDS, and that generates two components, sin(wt) > and cos(wt), which are then used for the full complex mixer that brings to > zero IF the signal. > > 73 Alberto I2PHD > > >
