[hpsdr] Infinite precision, phased arrays,and us

[Alberto I2PHD]

Murray Lang wrote:

>> Picture in your mind the signal produced by the sound card as a rotating 
>> phasor, described by the two I and Q
>> components. Then the instantaneous phase, phi(t), is described by
>>
>>    phi(t) = atan(Q(t) / I(t))
> 
> OK, so I keep I fixed (but not at 0!) and swing Q up and down with the 
> modulating signal. A fixed phase shift is DC.

  Well, you cannot keep it fixed. I is a function of time, and together with Q they describe the rotating phasor that is 
the signal being generated. Click on this URL :
<http://ptolemy.eecs.berkeley.edu/eecs20/berkeley/phasors/demo/phasors.html>
then click on the button labeled "One". At this point you will see (if Java is enabled on your PC), a yellow rotating 
phasor that represents your signal, and a red projection of it on the X axis which is the I component. You have just to 
make a little imagination effort, and add with your mind the projection on the Y axis, which is the Q component.

You can see that both I and Q are continuously changing in value, describing the projections on the two axes of the 
analytical signal. A signal with a given phase offset from it will have both I and Q also delayed (or advanced) in phase.

Imposing a modulation (whatever it is) on this signal means perturbating (sp?) the rotation of I and Q so to produce a 
vectorial combination that represents the wanted modulated analytical signal.

> Actually, it will be an integer by the time it gets to the D/A but the same 
> holds. I wonder if it would be better to work with integers in some cases 
> since the numbers that can be precisely represented by floats are 
> concentrated around 0 and get more sparse as you move out.

Well, this is just an implementation detail, best left to the engineers.. :-)
Seriously, IMHO the answer is application dependent, there could be cases where integers would do better than floats.

> So, the next question is: Why muck around with PLLs to shift the clocks 
> when it can be done in software?

Again IMHO, that is the gist of SDR. Never do in hardware what can be done in software.

73  Alberto  I2PHD

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