This note describes the figures in the accompanying postscript files, which are also part of this document. The data used in these plots was obtained using a scope towards the end of August or early September 2003. The files I am looking were obtained from Jim Steimel: Single_Proton_Store/sing_bunch_coal_250Ms_wfilt_A15_Ch1.mat Single_Proton_Store/sing_bunch_coal_250Ms_wfilt_A15_Ch2.mat The Ch1 file contains data from the proton end cable on the A plate and Ch2 cotnains data from the proton end cable on the B plate. The data comes from BPM A15 and were sent through a low pass filter before reaching the scope. The data were digitized with an 8 bit ADC at a rate of 250 MHz. There are just under 4x10^6 data points in each file. This corresponds to about 763 turns. The conditions were a single coalseced bunch of protons at 150 GeV. Page 1. The first plot show the time series of the digitized raw data near the time of the single bunch in the first turn. The other plots show the same information for subsequent turns. Note that these plots show about 55 bins out of approximately 5239 bins in a full turn. That is, they represent about 1% of a turn. The vertical red lines show the time interval over which the Fourier transforms (FT) were computed, 35 bins wide. Page 2. Each colored line shows the fourier transform of the time series data from one of the figures on the previous page. The horizontal axis is MHz. Each fourier transform was computed using only the data in a window around the bunch, as indicated by the vertical lines on the previous page. The seven colored lines show seven different turns. Each turn was analyzed indepently. A vertical red line is drawn at the RF frequency. This was estimated by: a) Assume that each time bin is exactly 4 ns wide. b) Find the number of bins between the maximum bin in the first bunch in the time series and the maximum bin in the last bunch in the time series. c) Given this and the harmonic number of 1113, compute the RF frequency. It comes out to 53.10372 MHz. This plot show the FT of the bunch time profile, multiplied by the frequency response of the pickup and the low pass filter. a) If the beam had a gaussian time profile with a sigma of about 2 ns, then its power spectrum would be a gaussian, with a sigma of about 80 MHz. b) Over the frequency range shown here, the pickup plate acts as a high pass filter, cutting off the low frequencies. c) The high frequencies are cut off by a low pass filter between the cable and the scope. d) Because we are looking only at one bunch for one turn, there is no comb structure. Page 3. The same plots as on the previous page, zoomed in around the RF frequency. From this we estimate a signal to noise for just the A signal to be around 50:1. Page 4. This page and the next are an aside on how to get bad signal to noise. The upper left plot shows the Fourier transform for the first full turn of data, including the 35 bins used in the previous few pages plus about 5200 bins of noise. The same gross structure as before is present but it is very noisy. The RF frequency is shown as the vertical red line. The center left plot and the bottom left plot show the same histogram but zoomed in around the RF frequency. The second and third columns show the corresponding information for the second and third turns. Page 5. This shows the same information as the previous page but zoomed in closer to the RF frequency. The 7 colors show 7 different turns. From this we can estimate a signal to noise of about 5:1. So, at least with 8 bits, we clearly need to gate around the bunches to get good signal to noise. Page 6. This plot is a single time series that starts at the upper left and goes to the bottom right. The horizontal axis is turn number within the file and there is one point per turn. The vertical axis is the beam position given as (A-B)/(A+B). To make this plot, A was measured as the magnitude of the FT of the A plate, measured at the RF frequency. Similarly B was measured as the magnitude of the FT on the B plate, measured at the RF frequency. These measurements were made using only the 35 bins in the neighbourhood of the bunch. The horizontal black line is drawn at the mean of the data. There are no trends visible in the data, just scatter about the mean. Page 7. The upper left plot on this page is the same plot which was expanded on the previous page. The upper right plot was made by grouping the data from the upper left plot into independent groups of 8 consecutive bins. Each bin on the right plot corresponds to the average of 8 bins in the left plot. The scatter is reduced. Again there are no trends in the data. The remaining plots on this page show the same exercise, but averaging the turn by turn data in groups of 16, 32 or 64. The scatter is reduced as the number of bins in the average is increased. Page 8. The upper left plot on this page is the projection of the upper left plot of the previous page onto its vertical axis. Presuming that all of this variation is due to noise, rather than to true beam motion, we conclude that the signal to noise for this data is about 10:1. We don't have a calibration for this measurement but a value of 0.14 must be fairly close to the B plate. If it is close to a full scale deflection of 10mm, then the repeatability of the measurement is about at the level of a mm or so. Remember that this data uses an 8 bit ADC. The other plots on this page show the corresponding projections of the plots on the previous page. We can see that the signal to noise improves as the number of turns in the average increases. Page 9. This shows the first step in a study to see if it is possible to reduce noise by using the phase information in the FT. The upper left plot on this page was made but running the fourier transform over 16 turns, but only using the data in the neighbourhood of each bunch. This is different than averaging 16 turns, each FT'ed independently, because, in this method, the phase information is preserved to the end. The plots are shown for the signal on the proton A cable. The RF frequency is shown as the red line, which verifies that the estimate of the RF frequency, described earlier, is good. The 6 plots show the results of the exercise for 6 independent sets of 16 turns each. Page 10. The upper left plot on this page shows a time series of position measurements made using independent groups of 16 runs. For each group of runs, the A and B amplitudes were determined by extracting the point at the RF frequency from a plot like those on the previous page. The position was computed as (A-B)/(A+B). The upper right plot shows the projection of the upper left plot onto the vertical axis. This shows that the measurement is repeatable at the level of about 2%. The lower two plots are just copies of the plots for groups of 16 runs on page 7 and 8. This too has a repeatability of about 2%. So we have not gained anything by preserving the phase to the end. But we have introduced a problem that it is very important to compute the A and B stregths precisely at the RF frequency. <