[hpsdr] Infinite precision, phased arrays,and us

[Bob McGwier]

Alberto I2PHD wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
> 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>
>   

Neat!
> 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.
>   
In a fixed direction antenna,  if we consider only the relative phase 
differences between elements need to aim the phased array,  the phase 
DIFFERENCES are DC complex constants.  I just throw this in to make sure 
it is understood.
> 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.
>   

Right.    M(t) * exp(j wt  + phi)  is the complex phasor way of 
representing ANY system we might care to discuss.   Remember M(t) can 
complex.

>   
>> 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.
>   
Amen Brother Alberto!
> 73  Alberto  I2PHD
>   
Bob
N4HY

-- 
Robert W. McGwier, Ph.D.
Center for Communications Research
805 Bunn Drive
Princeton, NJ 08540
(609)-924-4600
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