J. Kissel, S. Koehlenbeck

Executive Summary: as an initial guess -- we chose DEMOD parameters as follows:
    . SIG Bank = NO pre-demodulation filtering (just frequency-independent calibration)
    . I & Q Banks = a comb of notch filters at 4096 Hz (the 1f DEMOD frequency), and 8192 Hz (the 2f DEMOD frequency) and a super simple single-pole 200 Hz low-pass.
as the DEMOD filters for the demodulation of signals from the SPI pathfinder's IFO PDs.

I now have a user interface (LHO:90006) to the SPI pathfinder front-end model infrastructure (LHO:89777), so we're now thinking about filling in that infrastructure with real science (or at least real digital signal processing). 

SIG filters
One of the core principles of the SPI pathfinder's longitudinal degree of freedom is demodulating the 4096 Hz between note between the MEAS and REF beam. We only expect to use the SPI up to ~10-50 Hz, as the demodulated interferometer PDs noise floor begin to be limited by ADC noise ~5 Hz -- see LHO:83412 and detailed noise budget in Figure 1bii.1 in T2400145. Of course, it remains to be seen how much displacement signal we see above this noise floor.

Traditionally when demodulating nowadays, we're looking for the amplitude and phase of the excitation line we inject among surrounding noise that we don't want (think ADS lines, calibration lines, violin mode and PI damping, etc). In that case it makes sense to band-pass the raw signal pre-demodulation -- this is why you see narrow band-passes in many SIG banks. However, in the case of the SPI IFOs and other heterodyne IFOs, we're actually quite interested in the "noise" -- the "excitation line" is instead the carrier frequency, and the "noise" is the phase signal that we then interpret as differential displacement. As such, the design of the SIG, I and Q filters has an entirely different mentality:
    - in the "find the amplitude and phase" mentality, you want a tight band pass on the excitation frequency in the SIG bank, and then as low-a-frequency low-pass filter that you're patience allows.
    - in the "measure the sideband noise out to 100 Hz or so" mentality, you want as little filtering magnitude / phase distortion as possible from any filtering while sill removing any noise above the band of interest from the signal, post demodulation -- which is typically down-conversion from the 2f signal.

So -- we want *no* filtering in the SIG bank prior to demodulation, and a low-pass that has minimal in-band magnitude ripple and minimal in-band phase loss.

Attached is a trade study of filters that show the magnitude, phase, and step response for several options. All these options are installed in the MEAS A and B and REF A and B I and Q filters, but we've turned only the comb and single pole.