Reshape of the Bunch-by-bunch BPM Signal to a Turn-by-turn Matrix during the Fast RF Frequency-sweeping Time in Booster

The bunch-by-bunch BPM signal array has to be reshaped into a turn-by-turn (TBT) matrix in order to make the TBT beam position information of a single bunch available for further data analysis, such as via the Fourier transform to obtain the synchrotron tune and betatron tune, etc. Since the RF frequency sweeps more than 10 MHz in the first 8 ms of a Booster cycle, the revolution time decreases more than 20%. The number of data points for each Booster turn (BT) should be varied in the same pace with the revolution time since the sampling rate of a digital oscilloscope is usually fixed. And this can be done by pre-determining the relationship between the RF frequency and the time in a cycle via the curve fit.