• The if2 noise source used as input.
• The spectrometer was configured for 8192 channels, 300 1 second integrations, polA,B.
• Decimation (filtering of ) 1..20 was done. For each decimation, the input rms levels was to so that 30 counts=1 sigma.
• The entire 300 second integration was then averaged for each decimation.
• The mock setup software was using 12  - sqrt(dec) for the number of up shifts in the low pass filter.
  

• Overplot the 20 bandpasses normalized to 1 sec (.ps) (.pdf):
• The decimations and bandwidths are listed at the bottom.
• The vertical scale is log10(spectrometer counts)*10. These are for a 1 second integration.
• The number of accumulations in 1 second differs as (1/bw)*fftlen since the time duration of each fft is different.
• Overplot the 20 bandpasses normalized to 1 fft accumulation (.ps) (.pdf):
• The  spectra are now normalized to a single fft accumulation.
  
• The power differences result from the lpf accumulations and the lpf down shifting.
• Mean power, voltage, and spectral jumps vs decimation (.ps) (.pdf):
• Page 1: mean power,voltage
• Top mean power vs decimation normalized to the mean power with no decimation (dec=1).
• The power  decreases because of the hrshift in the lpf. The slow rise is the sqrt(dec)  increase of the noise power from the lpf accumulations.
• Bottom: mean rmsV vs decimation (normalized to dec=1).
• This is the sqrt of the previous plot.
  
• The black line shows the rmsvolts vs decimation
• the green line shows where the lpf performed a down shift (in voltage) ..divide by 2.
• The red line show the product of the lpf down shift and the rms voltage increase from the lpf additions.
• The  change in the rms volts follows the expected value (red line).
• Page 2: counts at input to the fft butterfly stages. adjpwr=30 counts at a/d.
  
• Top: the rms voltage counts at the input to the fft butterfly (12bits).
• This was back computed from the output spectruam (pdevlevels.pro).
• Bottom: actual rms counts after 1st pshift down shift.
• The down shift is done before the butterfly multipley, add stage. This shows the upper 12 bits of the 16 bit register.
  
• Since the down shift is done in a 16 bit register,  this should notmake any difference since no data is lost.
• Page 3: size of spectral jumps vs decimation.
• The spectrometer shows jumps in the spectra at 2^n spacing. This plot shows the jump at channel 2048 vs decimation.
  
• The black trace shows the difference of 20 channels averaged on the left and right of channel 2048. It is normalized to the average counts in these 40 channels.
• The red line (from page 1 top) shows the relative variation of the power level over the entire band vs decimation.
  
• The increases in the jump size correlate with the decrease in the power level.
• Band pass shape (falloff) vs decimation (.ps) (.pdf):
• The 20 bandpasses are overplotted using a db scale.
• The horizontal scale is +/- .5 *nyquist frequency.
• The spectra have been normalized to unity Near DC.
• No decimation
  
• This shows a large fall off with little aliasing
• Decimation 2 to 20.
• The edge of the bandpass is only  3db down. There must be a lot of aliased power folding back in.

Conclusions:

• The lpf power levels changes by up to a factor of 3 relative to no filtering.
• This change follows from the hrshift down shift and the  sqrt(dec) increase caused by the lpf accumulations.
•  The bandpass shape for decimation is 3db down at the edge of the band.
  

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