The goal of this exercise is to establish if there is a correlation between correlated pedestal noise and 60 Hz power line.

Method:

• pick single channel (or group of channels)
• build table raw ADC (or ADC sum) vs. 48-bit bXing
• do Furrier analysis

Implementation:

I decided to use all events from a single muDst from the highest luminosity run

st_physics_9069005_raw_1010002.MuDst.root

and pick BTOW towers which are on the floor of WAH, close to the STAR magnet  power lines (I know it is DC current). If there is another more noisy location let me know.

Selected:

• ADC from 2 BTOW towers: softID 3382, 3392
• ADC sum from 160 towers in BTOW crate 0x08, softID[3381-3540]
• ADC sum for 140 towers from the same carte, rejecting 20 largest ADCs , should have less physics background.

Fig 0. Pedestal spectra. Left: single channels, right : summed spectra, arbitrary constance subtracted from the sums. Assuming single pedestal with of 1.0 ADC  the sum of 160 uncorrelated ADCs should have width of ~13 instead of ~76.

Fourier decomposition.

We start with the set of pairs {T,ADC} where T is event time recorded very precise (106ns Clock) but at random time values. Most of Fourier commonly available  transform tools  (e.g. FFT.C in CENR root) do not work with such randomized time data because they assume signal is sampled with equal intervals in time: T(i)=i*delT. This is not the case for STAR events.

Fortunately Mathematica contains Discrete cosine transform (DCT) which accepts sparse vector as input.

 For the purpose of DCT True event time  recorded as 48-bit bXing was expressed in mili seconds and converted to integers. There is ~75K of events recorded in this run over a period of ~1000 seconds. We have 75 measurements of ADC per seconds. Therefore sparse array time step of 1 mili seconds was filled only in 8%.

Example of distribution ADC(time) is shown in fig 4 (sorry for the order of figures).

In order to test DCT works I have added artificial periodic signal to the data with frequency of 80 Hz and amplitude of 20 (comparable to raw ADC itself because noise level was high).

Fig 2 shows spectrum of amplitudes (frequency) with well visible peak at 80 Hz.

Fig 1. shows amplitudes (frequency) for single ADC (softID=3382),   the same data as in fig 1. Now you can see  increased amplitudes at ~45..55 Hz (I have no clue why not at 60 Hz). There is a hint of next peak at ~110 Hz - the second harmonic.

Fig 3 shows Fourier transform of "truncated sum of 140 ADCs". Here one sees ~50 Hz, 120 Hz , perhaps also  enhancement at 180 Hz.

Conclusions:

• BTOW pedestals are modulated with frequency of the power grid
• one could think to correct event by event raw ADC using cos(60Hz) correction factor. Not sure if benefits justify the effort, but this Fourier transform technique allows to verify if pedestal correction is correct.

For the record the following files are attached:

* event file for run 9069005, format { eveID, time(sec), ADC1, ADC2, sumADC, truncated sumADC}

* PDF with computation from Mathematica for "truncated sumADC"