[Difx-users] Reg. Fringe Rotation in general..

[Adam Deller]

Hi Manikantan,

On 20 February 2018 at 14:11, Manikantan Ramadas <mramadas at gmail.com> wrote:

> Hi Adam,
>
> Thanks for the response! Please find my replies inline.
>
>
>> 1.The delay in the fringeRotationVal should be T, not T'.
>>
>>
>  So, I should use the accurate delay value estimate T instead of the
> rounded-off value T'? OK can do. But my logic was that this error is what I
> am correcting in Fractional sample correction, and I should be doing
> fringe-rotation for the same delay d that I am using in delay-tracking of
> the other station's data stream.
>

There are two corrections being made: delay and phase.  Delay is made up of
integer sample delay and fractional sample delay, to get to the ideal delay
correction.  Phase can be corrected exactly in one step with simply the
ideal delay times the LO.

So fractional sample correction has nothing to do with fringe rotation (you
would need to do it even if you had no frequency conversion, in which case
no fringe rotation would be needed, but delay still would be).

If you were doing fringe rotation with the integer sample delay, you'd only
ever be shifting the phase by multiples of 250ns * Vlo, which given your LO
of 2300 MHz would always be an integer number of turns of phase, which
means your fringe rotation is basically doing nothing and hence the fringe
is entirely washed out.


>
> Also, fractional sample correction is normally done differently in a
>> baseline based correlator, but the scheme you describe of going into the
>> frequency domain, correcting, and then back should work (albeit somewhat
>> computationally expensively).  However, you have either a typo or an error
>> in your equation: the phasor exponent should be -i*2*PI*channelfreq*Tfc,
>> not -i*2*PI*Vlo*Tf.  Channelfreq is the frequency of the channel, which
>> would range from 0 to 4 MHz (for upper sideband data), -4 to 0 MHz (for
>> lower sideband data), or -2 to 2 MHz (if this complex subband really has
>> been mixed down to be centred on 0 Hz - see next point).  So the frequency
>> you are multiplying by is not fixed (otherwise what would be the point of
>> going to the frequency domain?), it is a ramp across the band.  If this is
>> really an error and not a typo, then this is certainly destroying your
>> fringes!
>>
>
> This is a typo! I am using channelfreq as you have mentioned. This is a
> complex sub-band varying from -2 MHz to 2 MHz and centered at 0. In sky
> freq-range, our central channel is centred on 2.3 GHz varying from 2.298
> GHz (-2MHz) to 2.302 (+2MHz). The channelfreq that I am using in fractional
> bit-shift correction is 0 for the central 2.3 GHz sub-channel, +2MHz at the
> upper-end of the band, -2 MHz at the lower-end of the band and channel freq
> steps of 4 MHz/64 in between range (FFT size is 64).
>
>
>> Finally, Vlo (the local oscillator frequency) should be the signed sum of
>> the effective LO, which is likely at the edge of the 4 MHz band, not in the
>> middle.  If you have this wrong, you'll then have a residual fringe rate of
>> half your bandwidth, or 2 MHz in this case.
>>
>> By "signed sum of the effective LO", you mean the LO values set at each
> stage if I am doing it at multiple stages, right? In this case, it is a
> single step conversion from RF to IF (70MHz).
> In my complex sub-band (mixed to be centred at 0 Hz), I am using the
> central local oscillator frequency - 2.3 GHz (for my central channel). This
> is OK right? I am doing same way for other channels as well.
>

Any implicit frequency conversion which is done by channelisation at the
intermediate frequency counts towards to the LO sum.  Imagine you're
observing at 1500-1516 MHz, and you set the LO to be 1400 MHz.  So your
band of interest is now mixed down to 100-116 MHz.  Now you sample it at
256 Msamples/s with a real sampler, giving you the range 0-128 MHz, and
then you use a digital downconverter to bandpass filter and shift down the
frequency range 100-116 MHz by 100 MHz, so your subband is now at 0-16
MHz.  The signed sum of the LOs in this case would be 1400+100=1500 MHz.

If your digital downconversion from the IF really does center your band of
interest on DC (so it has both positive and negative frequencies), then
indeed the LO would be as you describe.

Cheers,
Adam


>
>
>
>> Don't worry about the interpolators in DiFX: they are just down-sampling
>> the 5th order polynomial which is valid for 120 seconds to a 1st or 2nd
>> order polynomial which is valid for of order a few microseconds, for
>> computational efficiency.
>>
>> Thanks for clarifying that!
>
>
>> Note that autocorrelations are never really a great test, since they are
>> insensitive to the phase, which is where almost every mistake is made :)
>>
>
> Yeah, right! :-)
>
>
>>
>> 2.  The fractional bandwidth is irrelevant for fringe rotation: you can
>> think of the chunk of spectrum as having been shifted in frequency by Vlo
>> in the downconversion process.  That holds true for every frequency within
>> the downconverted subband: assuming upper sideband data, then the lowest
>> band edge has been shifted down from Vlo Hz to 0 Hz, and the upper band
>> edge has been shifted down from Vlo + B Hz to B Hz.  Hence they've all been
>> shifted by Vlo, and that single correction is good for all of the
>> frequencies within the subband.
>>
>> OK!
>
> - Manikantan.
>
> --
> "By being pleasant always and smiling, it takes you nearer to God, nearer
> than any prayer." - Sri Ramakrishna Paramahamsa
> ------------------------------------------------------------------
>



-- 
!=============================================================!
Dr. Adam Deller
ARC Future Fellow, Senior Lecturer
Centre for Astrophysics & Supercomputing
Swinburne University of Technology
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phone: +61 3 9214 5307
fax: +61 3 9214 8797

office days (usually): Mon-Thu
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