Digital FIR Filtering Options for CARMA Digitizers 
Kevin P. Rauch 
Astronomy Dept, University of Maryland, College Park 

Design possibilities are examined for the implementation of narrowband CARMA 
spectral-line modes using digital filtering techniques. The model designs are 
based on an analog pre-filter followed by one or more stages of digital 
filtering and decimation that narrow and shape the input analog bandpass to 
create the desired observing window. The pre-filter is the same one used to 
construct the narrowest analog-based spectral-line mode. It is found that for 
a 62~MHz pre-filter, 31~MHz, 8~MHz and 2~MHz observing bands exhibiting 
$<0.5$~dB of passband ripple (peak-to-peak, analog pre-filter excluded), 30~dB
of stopband rejection, and a relative transition width of $\sim$1/64 (per 
edge) require $\approx 50\%$ of the digital logic available in one COBRA 
digitizer FPGA. It is therefore possible to implement the corresponding 
spectral modes using COBRA digitizer cards without resorting to narrowband 
analog filters. Requantization after digital processing is found to reduce 
efficiency by 3-6\%, depending on the number of bits retained between 
decimation stages. Assuming as-is reuse of COBRA hardware, the 31~MHz mode is 
feasible only if digital frequency modulation is used. Spectral bandwidths 
$<2$~MHz are also easily supported in designs based on frequency modulation 
(with small additional reductions in efficiency).