# Spectral output vs Dshift parameter

# 10oct07

The pdev
spectrometer dshift parameter (see layout of spectrometer
scaling) down shifts the output of the power
computation before accumulating the spectral values in the 40 bit
accumulators. It allows longer integrations before overflowing the 40
bit accumulator. As an example: a 1 second integrations at 170
MHz with: (A/D=48,pshift=0x1555, dshift=0,ashift=0) has LO
feedthrough birdies close to 1.5e9. The maximum allowed value is 4e9.
Setting dshift would allow 1 second integrations without rfi
overflowing. The maximum allowable downshift value is set by the
requirement that you leave enough bits on the noise.
For a single spectral estimate, the amplitude
of this noise is comparable to the mean value of the power
spectrum.

The allowable range for dshift had been computed
from the spectral mean with dshift = 0 (see page 2 of the plots). It showed
that you would have about 4% of the channels with an rms < 40 counts
with dshift=15, pshift=0x1555 and aToD Rms=48 counts.

On 08oct07 data was taken with different dshifts to
verify that the actual settings matched the computed values.

The datataking setup was:

- The red noise generator was used for input to box 103 band 0.

- The input signal rms had 48 counts at the digitizer.
- Pshift=0x1555, pfbgain=.838
- fftlen=8192, bandwidth 170 MHz.

- 300 seconds of data was taken with .1 second integrations
(FCNT=2075).
- Data was taken with dshift set to: 0,8,12,15.

The plots show the results for
various values of dshift (.ps) (.pdf):

- Page 1 Avg spectrum.

- The .1 second spectra have been averaged for 300 seconds.

- The 4 plots are dshift:0,8,12,15 (divide by 1,256,4096,32768).
- The average spectral value for a single dump (.1/2075=
25usecs):
- dshift=0 : 5.4e6
- dshift=8 : 2.1e4
- dshift=12: 1.3e3
- dshift=15: 166

- The mean value decreased by 2^dshift until dshift=15 where is
increased more rapidly.

- Page 2: 300 second average spectra band pass corrected to the
dshift=0 spectra and then normalized to the mean value.

- The top is polA and the bottom is polB.

- The colors are: black-dshift=8, red dshift=12, green dshift=15.
- The edges of the bandpass do not divide out with dshift=15.

- Page 3. Rms/Mean along each frequency channel for
dshift=0,8,12,15.
- The rms/mean was computed for the 300 seconds of data along
each frequency channel for each dshift.
- Colors specify different dshifts.
- Plots 1,3 are the full scale polA and polB. Plots 2,4 are
blowups of the left edge showing where the bandpass falls off.
- For dshift=15 the rms/mean differs from the expected value for
about 2%*2 of the bandpass. This agrees with the computed value using a
single dshift.

### Conclusions:

- For pshift=0x1555, a/d sig=48 counts,

- Dshift = 0 to 8 the noise statistics for the bandpass is
unchanged.
- Dshift=12 the noise statistics starts to fall off in < 1% of
the channels
- Dshift=15 about 4% of the channels have a modified noise
statistic.

- We should be able to use a Dshift of 8 or 10 all the time (with
32 bit sampling, 8k xform) and not have any trouble with the noise
statistics.

processing: x101/071008/tstdshift.pro

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