[hpsdr] Infinite precision, phased arrays,and us

[Murray Lang]

At 09:50 PM 8/09/2006, 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>
>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.

This is good food for my efforts to understand what's going on - thanks. It 
raises questions which are motivating me to re-read a few of the papers 
that are out there. I knew about the rotating phasor but didn't realise 
that it actually rotated all the time even without modulation.


> > 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.

It's probably somewhat of a furphy anyway because a float implementation is 
generally going to have 32 bits at least. Once you go to double precision 
or use the native 10 byte X87 representation then you're not going to lose 
much.  Once I get around to looking at some source code I'll be interested 
to see if the sample values are normalised to 1.0 or something.

Thanks again Alberto.

Murray
VK6HL


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