[hpsdr] Infinite precision, phased arrays,and us

[Murray Lang]

Hi Alberto

At 10:35 PM 7/09/2006, Alberto I2PHD wrote:
>***** High Performance Software Defined Radio Discussion List *****
>[snip]
>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.


>So far, I am sure you will agree. Now, suppose you want to generate a 
>second signal with a given phase shift wrt the
>previous one. It will have an instantaneous phase given by :
>
>    phi(t) + delta = atan(Q'(t) / I'(t))
>
>You just solve the above to find, given Q(t) and I(t), what Q'(t) and 
>I'(t) should be to satisfy it.

Understood.

>As I and Q are described by floating point numbers, with 138 dB of dynamic 
>range as written by Bob, the granularity of
>the solution is much more finer than needed.

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.


>Consider then that the phase shift is preserved when upconverting to the 
>final RF frequency, and this should clear any
>residual doubts. Or not ? Sorry if I added to the confusion.

No it's good. I think others have been trying to say the same things to me 
but it takes a while to leech in.
So, the next question is: Why muck around with PLLs to shift the clocks 
when it can be done in software?

Many thanks for taking the time.
Murray
VK6HL




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