Tuesday, June 01, 2010

setiQuest Pulsar PSR B0329+54

The baudline signal analyzer was used to analyze the setiQuest pulsar PSR B0329+54 data file. he following command line was used to stream the pulsar data file into baudline:

cat 2010-05-07-psrb0329+54-8bit-*.dat | baudline -session setiquest -stdin -format s8 -channels 2 -quadrature -flipcomplex -samplerate 8738133 -fftsize 65536 -pause -utc 0

The quadrature data has a sample rate of 8738133.333 samples/second and a base frequency of 1420.0 MHz. The roughly 9 GB of data is 8 minutes and 40 seconds in duration. Decimation by 4 was used with a 65536 point FFT for a 66.67 Hz/bin resolution to create the image below.

The 5 lobed shape of roughly 500 kHz bandwidth in the center is hydrogen. The shape of interstellar hydrogen is spread out due to Doppler shift because it is undergoing a number of different velocities along its path to Earth. The midpoint of each of the lobes was measured to be:
  • +376533 Hz
  • +424000 Hz
  • +451200 Hz
  • +527467 Hz
  • +732267 Hz

Hydrogen has Sidebands
The strongest peak of hydrogen (+527 kHz) is in the center of the Average display below:

It looks like the strongest peak of hydrogen is directly in between the sideband-like tones. Let us verify this with some measurements and calculations. Baudline's primary Hz and fundamental Hz windows were used to perform some extremely accurate measurements.

Features of interest:
  • 44468.190 Hz (lower sideband tone)
  • 527467 Hz (strongest peak of hydrogen) estimated error = ±700 Hz
  • 1008467.116 Hz (upper sideband tone)
Some math:
  • (1008467.116 - 44468.190) / 2 = 481999.463 Hz (sideband delta)
  • (1008467.116 + 44468.190) / 2 = 526467.653 Hz (midpoint)
  • 527467 - 526468 = 999 Hz (center offset)
So the center offset between the sidebands' midpoint and the strongest peak of hydrogen is 999 Hz which is slightly more than the estimated error for this difficult measurement. That sideband delta Hz value looks very suspicious at being almost 482000 Hz. This number factors to 2^4 * 5^3 * 241 which doesn't seem to have any relationship to the base ATA's 2^20 *100 sample rate or its decimate by 12 rate. So maybe its value doesn't have any importance but the fact the sidebands are almost perfectly centered is important.

Exploring the Sidebands
Decimation by 256 for a 1.0417 Hz/bin resolution was used to create the lower sideband image below:

Twelve narrowband signals are visible in this "signal nursery." Baudline's Auto Drift algorithm was used in both the Average and Spectrogram displays above. The shape and the height of the Auto Drift curve can give some insight into a signal's drifting characteristics. The green dots represent stationary signals while the purple dots drifting signals. Both types will be investigated in more detail below.

I call the area just to the left of hydrogen a signal nursery because large numbers of interesting features have been found in this location. For example; the drifting FSK signal in the Kepler Exo-4 data and the 15 signals in the Exoplanet 060 data. Why the concentration of signals to the left of the main feature? There is no logical reason why this location is special so it could be a clue to an error in the ATA's digital signal processing chain.

We will now explore these green and purple dot signals of interest by using decimation of 4096 with a 65536 point FFT for a 0.0651 Hz/bin resolution.

+30628 Hz
A drifting-random-walk with a +2.15 Hz / 520 seconds = +0.00413 Hz/sec drift rate.

+31553 Hz
A drifting-random-walk that has a large negative curvature with a -1.63 Hz / 520 seconds = -0.0313 Hz/sec drift rate.

+32971 Hz
A fast drifting-random-walk with a -106.12 Hz / 520 seconds = -0.2041 Hz/sec drift rate. Note that the horizontal zoom was set to Hz=2X so the signal drift is comparatively twice as wide as it appears in the spectrogram below.

+35267 Hz
Another drifting-random-walk. The Auto Drift rate measurement reports that this signal is drifting at a +0.1144 Hz/sec rate. Note that horizontal zoom was changed to Hz=2X so the wide frequency drift would fit on the screen.

The signal starts at +35242 Hz, wiggles for about 100 seconds, and then begins a fast +65.89 Hz / 360 seconds = +0.1830 Hz/sec drift rate. The drift rate undergoes multiple acceleration changes The discrepancy with the auto drift rate measurement window is because Auto Drift calculated its highest energy drift at one of the slower linear sections. The Auto Drift algorithm is designed to work with constant drift rates but it works surprisingly well with a signal that undergoes multiple rate changes.

+36680 Hz
A drifting-random-walk with a -5.53 Hz / 520 seconds = -0.0106 Hz/sec drift rate.

+37186 Hz
A drifting-random-walk with a +26.30 Hz / 520 seconds = +0.05058 Hz/sec drift rate.

+38746 Hz "sisters"
It looks like these two drifting-random-walking sisters cross over each other, it is difficult to discern, but it could of been a random-walk "bounce." Assuming a cross-over, they are moving at -23.89 Hz / 520 seconds = -0.04594 Hz/sec and +27.08 Hz / 520 seconds = +0.05208 Hz/sec drift rates. Very similar drift rates but in opposite directions.

It is difficult to tell with this low SNR but it looks like the right sister near the bottom undergoes a bifurcation to 2 and then back to 1. These sisters share what appears to be several minor feature wiggles in a mirror reflection symmetry. So they are related tightly in frequency and loosely in distinctive characteristics. This is a significant find and might have importance in determining what sort of mixing is causing all of these drifting random walks.

+39190 Hz
A strong drifting-random-walk with a -9.96 Hz / 520 seconds = -0.0192 Hz/sec drift rate.

+39623 Hz
A weak wildly drifting-random-walk with a -9.64 Hz / 520 seconds = -0.0185 Hz/sec drift rate. The Auto Drift algorithm was used for a little additional extraction of this weak signal.

+40212 Hz
A drifting-random-walk with a -7.42 Hz / 520 seconds = -0.0143 Hz/sec drift rate.

+44492 Hz
A strong drifting-random-walk that has a very large negative curvature with a +4.62 Hz / 520 seconds = +0.00888 Hz/sec drift rate.

+45504 Hz
A drifting-random-walk with a +12.70 Hz / 520 seconds = +0.02442 Hz/sec drift rate.

The discontinuous jumps make this signal interesting. It almost looks like FSK with a 1.4 Hz mark-space spread and 17.391 second cycle (0.0575 baud) rate. Measurements were make with baudline's click-shift-drag mechanism and periodicity bars. Here is a quick and likely very error prone demodulation:


Where the symbols {-, 0, +} are deltas that denote a negative, a zero, or a positive jump in frequency. Starting at 6 that delta stream translates to:


This likely has a lot of errors but the information that should be extracted here are the single bit transitions and the runs of 2 or 3 consecutive bits and whether they are caused by a negative or a positive frequency transition.

Demodulating a weak and drifting random wiggling signal is very difficult. If you would like to take a crack at it then click on the small image on the right that already has the periodicity bars overlaid. Good luck.

+1008460 Hz
This interesting signal is of hydrogen's upper sideband. Note the horizontal zoom has been change to Hz=2X so that the signal fits on the screen. It looks like two groups of 7 Hz wide noise that are drifting at different rates. The first has a +38.8 Hz / 144 seconds = +0.269 Hz/sec drift rate. The second has a + 65.6 Hz / 169 seconds = +0.388 Hz/sec drift rate.

It also looks like the start of each group consists of three distinct pulses separated by brief pauses. Both signals start with a 40 second pulse, a 10 second pause, a strong middle section, and then a fading tail.

Side Skirting
I usually ignore signals located in the ADC or quadrature filter roll-offs (side skirts) because they are in a section of spectrum that was meant to be filtered away. Signals in the side skirts are usually weaker and they may be due to out-of-band signal leakage. But these side skirting signals are interesting and they may be important in solving the mystery of the rich signal nursery. Here is a full width Average spectrum of the entire bandwidth:

Of interest are the three signals that are in the side skirts that are underneath the green dots. They will each be decimated by 4096 for a 0.0651 Hz/bin resolution and investigated in more detail below.

-3321665 Hz
A drifting wideband noise signal that looks like it is in the same family as the +1008460 Hz signal. The signal is drifting at -65.6 Hz / 520 seconds = -0.126 Hz/sec drift rate. Note that the horizontal zoom is set to Hz=2X.

This looks like 8 pulses that are spaced about 61 seconds apart from each other.

+3469083 Hz
Another drifting wideband noise signal. This signal is drifting at +157.0 Hz / 520 seconds = +0.302 Hz/sec drift rate. Note that this signal is drifting so fast that the horizontal zoom had to be set to Hz=8X so that it would all fit on the screen.

+4315733 Hz
This far right skirt section is 5 dB down from the main flat part of the spectrum near Hydrogen. Using baudline's fundamental Hz window this very strong stationary tone was accurately measured to be 4315733.185 Hz. This number is interesting because 4315733.185 / 8738133 * 4096 = 2023.0000076 which is very close to the whole number 2023. Note that 2^12 = 4096 and it will also be derived below in the Quadrature Magnitude section in relation to 25600 Hz. Nothing is special about the number 2023 but I suspect that it is somehow important to the ATA's beamformer-decimator DSP code or filter banks.

Below is an annotated Average spectrum view that has been zoomed in and centered at the strong 4315733.185 Hz tone.

The blue sidebands were accurately measured to be ±120.009 Hz from the center carrier frequency. The yellow sidebands are ±50.004 Hz away from the center. The green dot peak is +76.631 Hz from the center frequency. It is interesting that there is no sign of 60 Hz sidebands despite the presence of strong 120 Hz sidebands.

So what is the significance of these sideband delta Hz numbers? I'm not sure but there are a number of unique whole number ratios. Such as 120 / 50 * 100 / 12 = 20. Note that the raw ATA sample rate is 100 * 2 ^ 20 which is then decimated by 12. Also 76.631 / (120 - 50) * 1024 = 1121.002 which is the whole number 1121 when accounting for Hz measurement error. Again, the whole numbers 20 and 1121 have no particular significance other than probably being deeply embedded in the ATA's DSP code.

This waveform plot shows how the energy of this slice of spectrum varies over time (from left to right). The magnitude time domain operation along with the Waveform window's new prototype sum() option were used to create this plot.

These energy fluctuations in the waveform view have some unusual periodic humps and discontinuities. Here is a zoomed in spectrogram of main center tone:

A nice strong stationary tone. The fluctuations of the center tone match what was seen in the Waveform window. Let us take a look at the phase of this tone with the blip Fourier transform. Click on the image below for a more detailed view.

Notice that the phase slowly rolls and then an abrupt phase shift occurs. These discontinuities happen about five different times. This is extremely unusual for a constant stationary tone.

Next let us take a look at the -120 Hz sideband tone by zooming in on the Average display.

That looks like two tones that are very close together. What is going on here? We need to explore this further. Let us zoom in a bit more by decimating by an additional factor of 8 for a 0.00814 Hz/bin resolution.

Now it's three tones! This is getting stranger and stranger. The spacing between those three tones is 0.18170 Hz and 0.09534 Hz.

Next, let us move the down mixer back to the center carrier frequency at 4315733.185 Hz and see what is going on there.

That doesn't look like a single distinct carrier tone anymore. There are four tones in there. Let's dive deeper still, decimate by an additional factor of 8, and zoom in for a 0.00102 Hz/bin resolution which is approximately the spectral limit for this amount of data.

Now the center carrier consists of 8 tones! This looks like a narrower version of the modulated signal seen in the Exoplanet 060 analysis. Too bad we can't zoom in anymore because this fractal-like structure is becoming extremely fascinating. What we saw above as power fluctuations of the main carrier tone were actually beat frequencies. One way to create a structure like this is to sum together a number of pure tones that are slightly offset in frequency. Could a beam former that is steering the delays of 42 different antennas create something like this?

Seeing the Pulses
Visualizing the pulsar's pulses defied traditional signal analysis techniques. No hint of the pulses were visible in the frequency domain, instead a time domain technique was required. Here were the steps. Decimation by 4 with the down mixer moved to a clean chunk of spectrum to the left of Hydrogen. Then the down-mixed quadrature data had the magnitude operation applied in the time domain. Finally the Waveform display used a prototype summing feature with a timebase zoom of 32768X.

There are 19+ pulses visible in the above Waveform display. Baudline's periodic bars measured the pulse periodicity to be 0.71455 seconds which is fairly close to the published 0.714519 second value. The accuracy of this measurement is impressive considering only 17 seconds of data were used.

Quadrature Magnitude
Baudline's Input Mapping time domain operation was set to quadrature magnitude to see the Fourier power envelope. Gone are the large elephants that were at 1/3, 2/3, and 3/3 Nyquist in the Exoplanet 060 data. This Average spectral plot was done with no decimation.

Notice the strong tone at 25600 Hz and 9 of its harmonics. Using the Average window, the fundamental Hz measurement display, and a higher order harmonic the frequency was carefully measured to be 25600.0 Hz with an error of less than ±0.1 Hz. The ATA's ADC sample rate 100 * 2^20 / 25600 Hz = 4096. This suspicious power of 2 number suggests that these distortion products are related to the ADC or its follow on processing prior to and including the decimation by 12 stage.

When baudline's decimation is set to 2 and the down mixer is moved the 25600 Hz tone and harmonics remain stationary. This is just like the elephant polka music on every radio channel analogy mentioned in the Exoplanet 060 data analysis. In that same 060 analysis the cyan, magenta, yellow, and orange tones had sidebands with delta offsets of 25600 Hz. Since that time something in the ATA was fixed and those sidebands are missing in this 0329+54 data.

Next, a look at 60 Hz by using the quadrature magnitude operation with the Fourier transform and decimating by 256 for a 0.5208 Hz/bin resolution.

The exact frequency is 59.930 Hz and 8 harmonics are visible. These tones also remain stationary when the down mixer tuning frequency is adjusted. The 60 Hz tone is doing something else interesting as a function of time. Below is the accompanying spectrogram display:

Baudline's periodicity bars measured the 60 Hz pulsing to be at a roughly 21 - 22 second period. The 120 Hz tone is undergoing its own pulsing at an unrelated and somewhat random period. The pulsing period is different enough from the baud rate seen in the FSK signal at +45504 Hz that it is not likely related.

Filter Extraction
The impulse response transform was used to compare the I and Q channels. It should be noted that because of the stimulus source being very white noise-like the cross-correlation produces a similar image. Also note that the horizontal axis should be time lag (not Hz) and the vertical axis should be a linear scale (not dB).

This very unusual shape has an inverse symmetry for negative and positive lag. It also doesn't have any hints of being a Hilbert filter which is unusual for quadrature of a noise source. In the next image a Hilbert filter was applied to the I channel prior to calculating the impulse response. This effectively undoes quadrature.

This looks like a low pass filter (LPF) with a sharp even-odd notching in the center.

The hydrogen has sidebands with a delta of 482 kHz which could be caused by signal distortion or by erroneous DSP error mixing products. Located at or near these sidebands are a large number of weak signals that have a wealth of unique characteristics. Some of these signals are worth further study and some effort will be required to successfully demodulate one of them. It is becoming apparent that a signal "nursery" to the left of the main feature seems to be a common theme in the setiQuest ATA signal data. The cause of this left-side preference is unknown.

Baudline's Auto Drift algorithm found a couple of drifting signals that would of been missed in the standard analysis pass. The more experience we gain with the tools, the more it will allow us to refine our analysis technique and find more weak signals.

The quadrature magnitude technique was used again and it found fairly strong 25600 Hz and 60 Hz elements that are omnipresent phase distortion products. It is possible that many of the interesting weak signals seen here have been caused by the mixing of these distortion products. The shear number and uniqueness of the weak signals suggest that this is not the sole cause though. This is an improvement from the previous Exoplanet 060 data file which had slightly more weak signals but those signal characteristics also had more symmetry.

An extremely unusual fractal-like carrier tone was discovered in the side skirts that had 50 Hz and 120 Hz sidebands. Where did the 50 Hz come from? The 4096 buffer size pops up again.

So we have a signal rich environment. It is like the haystack is made of needles, the problem of SETI is not finding the drifting weak signals but determining which ones are truly extraterrestrial and which ones are just local interference or internal noise. Some people have suggested constructing an EMI database as a tool to distinguish false signals. From what I have seen this approach will not work because the signals are everywhere and they seem to have an infinite variety of characteristics and behaviors. Possibly the multi-beam nulling method will prove to be a powerful discriminating tool. It should work well for local interference but internal DSP noise is a different animal. So it is possible that many of these weak signals will be unique to specific beams which would render this technique null. It would be extremely interesting to test this theory with a future ATA data set that contains multiple symmetrically nulled beams.

[Note: Baudline can only handle 4 quadrature channels at a time, so no more than 4 complex beams per data file would be preferred.]


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