[Discuss-gnuradio] USRP phase to sample index relation in the DDC/DUC chain

[Nicolas GALLAND]

Hello everyone,

I am using a USRP X310 with basic RX and basic TX daughterboards and I 
would like to know the exact relation between the number I enter as a 
parameter for the central frequency in the UHD USRP sink/source block 
(which is a real number) and the actual phase per each sample.

As a matter of facts, if the DDC/DUC chains were using a DDS, the 
relation would be pretty straightforward (knowing the control word of 
the DDS and the number of bits of the phase accumulator...). However, as 
I understand, the FPGA design uses a CORDIC for the DDC/DUC chain, for 
which the exact correspondence between sample index and phase is not as 
straight forward to derive. I am sorry if this is textbook material for 
CORDIC specialists (which I am not...), but I am wondering if someone 
could point me to the exact formula of phase vs sample index that I 
could use to very accurately know what is going on in the DDC/DUC chain. 
The bottom line is that I need to be sure of what is happening at the 
nrad level for MHz-ish input/output and mod/demod frequency, and the 
intricacies of the CORDIC behavior is - to my best understanding - 
playing a major role at this level.

Any help would be greatly appreciated.

Best regards,

    Nicolas