Marek GASIOR - Home page

Home >> Professional >> 3D-BBQ >> SPS Results >> Fixed target #1

The measurement was done on 10/09/04 at about 14h45 on the SPS fixed target beam. The beam was only listened to (no excitation, or better, no explicit excitation). The figures below are related to one of many measurements I did with different settings of the 3D Front-End box. Other measurements gave similar results. I picked-up one which did not saturate the sound card to have nice tune sounds.

All processing was done on the samples from the .wav file acquired with an external USB sound card Sound Blaster Audigy 2 NX, giving samples with the maximum resolution of 24 bits and the maximum rate of 96 kHz. I used the maximum rate to get as many samples as possible, but, since I had some software problems when dealing with 24-bit samples, I stored 16-bit samples only. I believe that this had no or only little effect on the results quality, since the signals had their own noise, present already on a few 16-bit sample bits. I checked and, as far as noise and interference are concerned, the card gives PERFECT 16-bit samples; no noise, no interference at all!

Below is a link to the recorded .wav file from which I took the samples, which were processed off-line with Mathematica. The left (L) channel contains a record of the signal of the Horizontal (H) plane of the BBQ system and the right (R) channel - of the Vertical (V) plane.
In the foreground you will hear tones corresponding to the synchrotron motion of the beam and in the background - low whistling of the beam betatron motion. Since the betatron frequencies are above 15 kHz, they cannot be heard easily in the original record. For this reason I prepared versions of the record, which are stretched in time 4 times to reduce all frequencies by the same factor. The longer machine cycle helps also to follow what happens with the synchrotron frequencies.
Headphones help a lot to resolve different components.

Original .wav file (≈ 1.6 MB, 16-bit, 96 kS/s, ≈ 425 kS, 4.4 s)
4-times stretched time scale - H plane (≈ 1.6 MB, 24 kS/s)
4-times stretched time scale - V plane (≈ 1.6 MB, 24 kS/s)

Below are the signal waveforms: the left and right plots correspond to the BBQ H plane (L channel) and V plane (R channel), respectively.

Fig. 1H. H plane (L channel) signal.

Fig. 1V. V plane (R channel) signal.

Samples of the signal of each channel, sampled with the frequency of fs = 96000 Hz, were divided into segments N = 9600 long ( t = N / fs = 0.1 s ), with offset m = 4800 samples ( t = m / fs = 0.05 s ), so each two adjacent sections overlap by 50 %. If each signal is L = 424683 samples long, there are s = Floor( (L-(N-m)) / m ) = 87 full segments. Samples of each segment were (Hanning) windowed and then it was calculated the Discrete Fourier Transform (DFT) of the windowed sample sequences to yield their discrete magnitude spectra. The bin spacing of the discrete spectra is df = fs / N = 10 Hz. The values of N and m were chosen to get the clearest tune paths.
Magnitude spectra of H (left) and V (right) signals are shown below for frequencies 0 - 20 kHz. Below I will show low frequency regions with the synchrotron sidebands magnified and, separately, high frequency parts with the tune paths magnified. The plots are normalized to the highest bin in the spectra of all signal segments and the vertical axis is cut at the top at an arbitrary level to decrease the height of spectra at injections.

Fig. 2H. H plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.

Fig. 2V. V plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.

The spectra in the figures below are similar to the ones in Fig. 1H and 1V. The only difference is that now each segment spectrum is normalized separately.

Fig. 3H. H plane magnitude spectra. Each section spectrum is normalized separately.

Fig. 3V. V plane magnitude spectra. Each section spectrum is normalized separately.

The figures below show contour plots corresponding to the spectra in Fig. 2H and 2V.

Fig. 4H. Contour plot of H plane magnitude spectra of Fig. 2H

Fig. 4V. Contour plot of V plane magnitude spectra of Fig. 2V

The figures below show contour plots corresponding to the spectra in Fig. 3H and 3V.

Fig. 5H. Contour plot of H plane magnitude spectra of Fig. 3H

Fig. 5V. Contour plot of V plane magnitude spectra of Fig. 3V

The figures below show contour plots corresponding to the spectra in Fig. 3H and 3V.

Fig. 6H. H spectra at the time points specified on the plots.
They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 3H).
Note the linear vertical scale.

Fig. 6V. V spectra at the time points specified on the plots.
They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 3V).
Note the linear vertical scale.

Synchrotron sidebands are magnified in the following figures. The figures are low frequency regions of the figures shown already above.
Revolution frequency spectral lines are accompanied by synchrotron sidebands. Since the diodes switch at the revolution frequency, the synchrotron sidebands are downmixed to the vicinity of DC. The front-end used had low-frequency cut-off about 2 kHz, and all components below this frequency got lost. This is why the synchrotron sidebands do not start from DC.

Fig. 7H. H plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.		Fig. 7V. V plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.
Fig. 8H. H plane magnitude spectra. Each section spectrum is normalized separately.		Fig. 8V. V plane magnitude spectra. Each section spectrum is normalized separately.
Fig. 9H. Contour plot of H plane magnitude spectra of Fig. 12H		Fig. 9V. Contour plot of V plane magnitude spectra of Fig. 12V
Fig. 10H. Contour plot of H plane magnitude spectra of Fig. 13H		Fig. 10V. Contour plot of V plane magnitude spectra of Fig. 13V
Fig. 11H. H spectra at the time points specified on the plots. They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 13H). Note the linear vertical scale.		Fig. 11V. V spectra at the time points specified on the plots. They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 13V). Note the linear vertical scale.

Tune paths are magnified in the following figures. The figures are high frequency regions of the figures shown already above.

Fig. 12H. H plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.		Fig. 12V. V plane magnitude spectra. There are 20 spectra per second. Bin spacing is 10 Hz.
Fig. 13H. H plane magnitude spectra. Each section spectrum is normalized separately.		Fig. 13V. V plane magnitude spectra. Each section spectrum is normalized separately.
Fig. 14H. Contour plot of H plane magnitude spectra of Fig. 22H		Fig. 14V. Contour plot of V plane magnitude spectra of Fig. 22V
Fig. 15H. Contour plot of H plane magnitude spectra of Fig. 23H		Fig. 15V. Contour plot of V plane magnitude spectra of Fig. 23V
Fig. 16H. H spectra at the time points specified on the plots. They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 23H). Note the linear vertical scale.		Fig. 16V. V spectra at the time points specified on the plots. They correspond to cross-sections of the tune paths on spectra slices normalized within each slice separately (Fig. 23V). Note the linear vertical scale.