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baudline analysis of PSR B0329+54

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sigblips
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I did a detailed signal analysis of the Pulsar PSR B0329+54 data file and posted it to my baudline blog. Lots of drifting-random-walking signals, some demodulation, no pulses, more elephants, and a filter extraction.

http://baudline.blogspot.com/2010/06/setiquest-pulsar-psr-b032954.html

Q: Is the sample rate 8738133 samples/sec?
Q: What is the base frequency?

robackrman
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Very nice analysis. I have

Very nice analysis. I have been told the 25600 Hz artifacts seen in the data match the switching frequency associated with a signal processing room power supply. I am encouraged to read in your analysis, verification that the largest artifacts (elephants) are gone.

The sample rate is 8738133 and 1/3 s^-1

The observation center frequency for the pulsar data is 1420.0 MHz

The "5-lobed shape" shown in your spectrum is the hydrogen line Doppler-spread by various velocities along the line-of-sight. You should not refer to it as "the pulsar" in your analysis. The actual pulsar emission is very weak and extremely wide-band - detectable over a frequency range of tens of MHz to tens of GHz.

The B0329+54 DM is small enough that it is not necessary to compensate for dispersion over the ~ 6.5 MHz observation bandwidth. It is also not necessary to compensate for pulsar period +/- dilation due to Doppler shift from Earth rotation because the S/N is large enough to see the pulsar in less than a minute of data.

I think It is more interesting to see the distinctive pulsar profile in the time-series rather than its spectrum. One way to do this is to square the samples (convert to power) and then fold the power values, adding them, at the same rate as the pulsar period. You should see the profile clearly, at the S/N of the recently published observation, within ~ 100 folds.

robackrman
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Sample strong pulsar

Sample strong pulsar detection code (normalize, adjust range for contrast, and then plot variable "pwr" as image):


width = 512;
height = 512;
smplrate = 8738133 + 1.0/3.0;
period = 0.714519; # pulsar B0329+54
folds = 100;
colintvl = period/width;
t = 0.0;
deltat = height/smplrate;
pwr = zeros(height, width);
fd = fopen(filename);
while (1)
  coeffs = fread(fd, height*2, "int8");
  cmplx(1:height) = coeffs(1:2:height*2) +
     coeffs(2:2:height*2) * i;
  index = floor(t/colintvl);
  if (!((index/width) < folds))
    break;
  endif
  foldedindex = mod(index, width);
  pwr(1:height, foldedindex+1) .+=
     transpose(abs(fftshift(fft(cmplx))).^2);
  t = t + deltat;
endwhile
fclose(fd);

Dave Robinson
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Have you tried to use

Have you tried to use averaged Cepstrum in order to detect the repeat period of the Pulsar, then use this to define the time domain frame time to undertake averaging?

I have just started to download the first chunk of the Pulsar data set in order to try this out. Should there be enough elapsed time in the one segment to pull the pulsar signal out - my IP provider gets cross if I down load too much a month :-(

Regards

Dave Robinson

robackrman
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No, we have not tried that.

No, we have not tried that. Very interesting idea. Please share with us the result of your detection of the pulsar period using this method.

Yes, the first chunk of data is more than enough data to detect the pulsar. 8738133 * 2 * 60s ~= 1GB should be plenty.

Dave Robinson
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Sad to report that simply

Sad to report that simply using one block of data, I was unable to extract the repeat period of the Pulsar, using Cepstrum. Although there appeared to be a spike at the pulse time, it wasn't of sufficient amplitude to distinguish it from equally impressive spikes at other periods, which I assume is down to noise.

I might repeat the experiment when I have down loaded the rest of the pulsar signal, where a longer sample may supress the spurious spikes and allow automatic pulse rate detection.

Can anyone give me a clue regarding the pulse width of the signal that I should be expecting to see. It could be that when I resample my data signal I am severely attenuating the signal that I am searching for during the antialiasing low pass filter operation prior to the sample rate reduction

Regards

Dave Robinson.

robackrman
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Please consider giving it

Please consider giving it another go. I am looking forward to a pulsar detection in this forum.

The B0329+54 pulsar profile width is approximately 1/12 of the ~ 0.714519s period. See this image.

Did you analyze the complex voltage samples or the power values? If not the latter, compute (real^2+imag^2) for each complex sample pair and feed that as a time-series into the front FFT in your analysis.

Dave Robinson
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I haven't given up on

I haven't given up on automatic pulse frequency detection yet, I still have several other techniques I want to try, for example autocorrelation and Wavelet analysis techniques, but as soon as I get the rest of the data downloaded I will give the Cepstrum another go.

I had used Power (I multiplied the Complex data by its complex conjugate) like you suggested. Thanks for the Pulsar plots, these are wide enough for them to get through the antialiasing filter (albiet smeared somewhat) prior to the resample, so I am surprised that I didn't get some indication of its existance.

I will report back on further results.

Regards

Dave Robinson

sigblips
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What rate are you decimating

What rate are you decimating down to? The dirac deltas should have no problem getting through your anti-alias filter.

I've tried multiple sample rates all the way down to 8 samples/sec. I see the periodicities with the Fourier and Autocorrelation transforms where I expect the 0.71452s period pulsar to be but they are not even one sigma above the noise floor. So there is something there but it is not enough to even remotely claim it to be a signal.

I recommend running some test signals through your code to verify your methods. I built a basic pulsar simulator using baudline and besides verifying my code it gave me an incredible amount of insight into pulse trains and noise. Other than finding that they are very difficult weak signals to detect I've discovered all sorts of pulse train bandwidth equivalence relationships that I've never seen in books or papers before. I probably should write up a blog post about this.

robackrman
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S/N is reduced by decimation

S/N is reduced by decimation and filtering in this case. The pulsar power is distributed evenly over the entire observation bandwidth. The pulse signal occupies only a portion of the time dimension and is only affected by the noise power during that time if the analysis is done in a way to take advantage of that.

It is not necessary for this observation data to correct for dispersion, so here is the simplest Octave/MATLAB code I could think of that will detect the B0329+54 pulsar (requires ~ 200MB of observation data):


fd = fopen("2010-05-07-psrb0329+54-8bit-1-of-5.dat","r");
N = 87381;
# for 1000 times, sum power into 10ms bins
for k = 1:1000
  coeffs = fread(fd,(N*2),"schar");
  cmplx(1:N) = coeffs(1:2:(N*2)) + coeffs(2:2:(N*2)) * i;
  pwrsum = sum(abs(cmplx).^2)/N;
  pwrseries(k) = pwrsum;
endfor
fclose(fd);
plot(pwrseries)
title "2010-05-07-psrb0329+54-8bit-1-of-5.dat"
xlabel "10ms per count"
ylabel "power (uncal.)"

Here is the resulting plot.

14 pulses can be seen in the plot over 10 seconds which is consistent with the known ~ 0.714519s period of pulsar B0329+54.

Most pulsars are too weak to be detected this way.

More sophisticated analysis, which I hope will happen here in the forum, is required to build up and plot a detailed pulse profile.

sigblips
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Thanks, I can see it now in

Thanks, I can see it now in baudline's Waveform window when I zoom out to 65536X. The key was using sum() instead of the min(), max() operations I was using. I will need to rethink how timebase zooming is done in the waveform window, summing could be a useful option to add.

Re: S/N is reduced by decimation and filtering in this case.

That statement is not completely correct. Here is my logic:

* You basically are decimating and filtering in your Matlab code example. The sum() operator is a poor quality low pass filter and the decimation by N=87381 is being done by the fread().

* Tests with the pulsar simulator I made show that decimation does increase the SNR. Roughly +3 dB per decimate by factor of 2.

* A dirac delta impulse response has infinite bandwidth and passes through filters and tuners just fine.

* True, decimating a single pulse does not improve the SNR. But if the pulses are periodic then decimating by 2 now puts twice as many pulses in the same number of samples as before. The Fourier domain likes this and sees it as an SNR gain.

Now I believe all of these statements to be true but obviously they didn't help me see these periodic pulses so there must be a flaw in my logic or I'm not thinking of something important. My simple folding algorithm didn't work either, hmmm, I have more testing and thinking to do.

robackrman
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I agree that the sample code

I agree that the sample code can be considered to be decimating and low-pass filtering the power envelope. It also can be considered lag-zero autocorrelation over successive windows, which offers a potential idea for where this method of detection might be best integrated into baudline. I was suggesting in my previous post, based on your discussion with Dave that mentioned an anti-aliasing filter, that better success might be had, given no need in this case to compensate for dispersion, by not removing spectrum and associated pulsar signal power from the observation data.

sigblips
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An important point about

An important point about autocorrelation is that white noise and a single impulse look identical (flat with a spike at time zero). So it wouldn't be too interesting looking in baudline unless I just plotted the magnitude of time zero. Is that the sort of thing that you were suggesting? Or were you suggesting the autocorrelation of multiple impulses?

You mention "by not removing spectrum" but the sum() operation is a low pass filter and it is removing spectrum. If you make the sum() filter/decimator shorter than N=87381 in the Matlab code example then the 60 Hz bleed-in will become visible and the pulsar will be more difficult to distinguish.

robackrman
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No spectrum is removed. See

No spectrum is removed. See "discrete Fourier transform" at bottom of "Applications" section of the Wikepedia entry on Parseval's Theorem.

Gerry posted Crab Pulsar observation data today of which no analysis has been done by SETI Institute staff.

I had previously checked the B0329+54 data we have been analyzing in this thread. Here is a plot of the pulsar detected using the Octave code I posted 06/02/2010. The power in time (horizontal) over a range of frequency bins (vertical) is summed incoherently into a pulse profile at the bottom with the hydrogen band omitted. There was no appreciable dispersion.

I am hoping Dave will weigh in with a report on some of his alternative detection ideas whether or not they are successful.

sigblips
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That's not exactly what

That's not exactly what Parseval's Theorem says. It's basically saying that the sum of the energy in the time domain is equal to the sum of the energy in frequency domain. So you're not removing spectrum when you are summing but you are when you are decimating (plotting). What has me thinking is why this works as well as it does? I suspect it has to do with exploiting the width of the pulsar impulse. If N is too small then you'll be swamped by 60 Hz+noise and if N is too large then the impulse will be down -3 dB for each doubling of N. It seems like a delicate balance.

Now what they call the inner form:

integral( x(t) y*(t) dt ) = integral( X(f) Y*(f) df )

Looks very interesting, sort of autocorrelation-like when y=x. I'm assuming the complex conjugate y*(t) is time reversal in the time domain. It is unfortunate that Oppenheim & Schafer just glosses over it in an exercise. Do you know of a better informational source? Wikipedia and the other sources on-line are very weak.

jpsd0510
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Some S/N reduction using data summation

I obtain a slight increase of S/N ratio using your Octave code on a file obtained by summation of values from complex voltage in the first chunk of data (1.9 GB) from PSRB0329+54-8bit. I do summation over 2.8581 sec (4 pulsar periods) on approx 115 sec of data. Each data of the first 2.8581 sec are summed with the corresponding data in next 2.8581 sec intervals up to 115 sec (40X summation on each data over the 2.8581 sec interval). Next, i use your code with absolute values of complex voltage instead of absolute squares (power) and with k=1:250 (2.5 sec) to obtain graph versus time of the signal. Three pulses are clearly visible. I will eventually check this method (or an improved method) with data from Crab nebula.

I am a French speaking people so excuse my English...

sigblips
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So the 5-lobed shape is

So the 5-lobed shape is Hydrogen and not the Pulsar? OK, I'm embarrassed, I expected the strongest visible pulsar from Earth to be, well, strong.

The spectral width, strength, and shape of this hydrogen really threw me. Previous hydrogens had a spectral width of about 200 kHz and a strength of about 0.5 dB above the noise floor. The hydrogen in this PSR 0329+54 data has a spectral width of about 500 kHz and a strength of 3.8 dB above the noise floor and it has 5 lobes. So does each lobe center represent a different Doppler shift? That would explain why it is spectrally wider but why 3.4 dB stronger? That seems like a lot.

Thanks for pointing this out. I'm fixing my blog post now.

robackrman
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No person in this forum

No person in this forum should feel embarrassed! BTW, the first pulsar was detected by Jocelyn Bell at much lower frequency where pulsars are generally much stronger.

See chapter 8, pages 87-100, "Radio Astronomy, 2nd edition, Kraus" and elsewhere for a description of the hydrogen profile which varies in intensity and shape as observations move in-and-out of the galactic plane and within the galactic plane.

Each lobe of the hydrogen profile in your analysis represents a region of space along the line-of-sight moving at a different velocity with respect to the observatory.

Some of the intensity difference might also be attributed to changes in the instrument (ATA) between observations: a different number of antennas may have been involved and the delay and phase calibration of the beamformer may have been different.

gerryharp
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HI and pulsar

Hi again

The pulsar is a broadband signal that shows up in the time domain only. The hydrogen (HI) you see in the frequency spectrum is not from the pulsar but in the foreground and background of the pulsar, dispersed through the galaxy.

Occasionally you can see HI _absorption_ when looking at strong continuum sources such as CasA. So a dip in the middle of an HI spectrum might be cause by this. (What is being absorbed is the strong emission by the foreground HI.)

The HI content is highest in the galactic plane (where most pulsars are found). So you can expect strong HI in the vicinity of most pulsars. Compared to e.g. exoplanets, which are anywhere in the sky, the HI flux may fluctuate by a couple orders of magnitude.

Besides absorption, since you are looking through the entire galaxy, some hydrogen is moving towards you and some is moving away. You can sometimes observe HI =above= its laboratory frequency when it is blueshifted, and below when redshifted. Since you may see several clumps of hydrogen along any particular lines of sight, you can see several bumps.

Gerry

sigblips
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You mentioned that a power

You mentioned that a power supply switching frequency matches that of the 25600 Hz artifacts. Is this power supply at all related to the clock frequency used by the ATA's ADC?

I just added two paragraphs to my PSR 329+54 blog post about 25600 Hz and its harmonics. Excerpt:

"I carefully measured 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."

and

"In my previous Exoplanet 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."

What exactly was fixed to make the large elephants go away? It would be helpful to know this since the 25600 Hz sidebands also went away but the root quadrature magnitude 25600 Hz and harmonics remain. I suspect that artifacts from the 25600 Hz are responsible for the signal rich environment, I just haven't been able to make a mathematical connection, yet.

gerryharp
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25600 Hz artifact

Well, we have 25 kHz switching power supplies (not all identical or synched) in the signal processing room. If you're seeing something that is exactly a power of 2 from the sampling frequency, it might be coming from the "Walsh" function generator. The frequencies of our Walsh functions are: 100 Hz, 200 Hz, 400, 800, 1600, 3200, 6400, 12800 Hz. There could be an artifact from, say, the highest frequency Walsh function if there were a glitch every time the Walsh function switches from 0 to 180 degrees.

I'll leave it to Billy Barott (who may log in soon) to describe Walsh'ing and the potential origins of a sample-frequency related artifact.

Gerry

billy
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25.6 KHz, Walshing, and Packets

Hi all-
Jumping in here at Gerry's suggestion:
First of all, great data analysis, sigblips - I always enjoy.

Now - the rate of 25.6 KHz, phase-locked to the sampling clock, is special in a few ways. First, the packet generator that feeds setiQuest operates at a packet rate of 51.2 KHz. Any artifacts at a rate of once-every-two-packets would produce a 25.6 KHz artifact. While possible, I don't think that this is very likely with the current packet generator.

A second potential source for these artifacts is the walsh functions that Gerry mentioned. In the ATA back end, we modulate our last analog local oscillator by a square wave prior to mixing with the RF signal. This introduces a phase flip to the RF data-- e.g., when the modulating signal is +1, data are in phase, when the modulating signal is -1, output data are 180 degrees out of phase from their original data. The phase switching is undone in our digital electronics.

So - why do this - We have 8 unique walsh functions (at the rates 100 Hz... 12.8 KHz), and ensure that, where there is a potential for cross-talk in the analog system, neighboring signals have different walsh functions. The short of it is that cross-talk signals don't get properly "decoded", and tend to integrate away. This is great in a correlator (for imaging), but can leave artifacts in the beamformed data - first and foremost in that any cross-talk signals can be seen - if we look hard enough - as very weak tone sidebands.

You might already have noticed that the analog "walshing" is probably not exactly 0/180 degrees, and this can indeed introduce artifacts (e.g., if the analog is 0/179, and the digital is 0/180, we'll end up with a 0/1 degree phase modulation in the resulting beamformed data). This leads to many (weak!) sidebands at the harmonic rates of each walsh function. Further, if the analog "walshing" and digital "unwalshing" are not very-well aligned in time, we'll get artifacts at the transition edges of the walsh square wave. This will tend to create artifacts at 2x the walsh rate and up - once more, 25.6 KHz comes up as the 2x rate of 12.8 KHz.

I've started (but am not far into) my own analysis of this data set to better understand the artifacts that you've identified.

Billy Barott (ATA)

sigblips
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The 100 Hz Walsh rate could

The 100 Hz Walsh rate could explain the oddball 50 Hz sidebands I saw in the B0329+54 data. The 12800, 25600, 51200 Hz sidebands/harmonics I've seen in the different data sets could also be explained by this but most data sets have multiple error modes.

I've never heard of a Walsh function generator before. It sounds a bit like "differential signaling" where the noise affects both differential channels and is subtracted away. With Walsh signaling though it seems that the crosstalk noise is randomized, so like you mentioned, it integrates away. Is that the general idea? If so, then even if the analog-digital sides are perfectly aligned it seems that any crosstalk would create a variety of mixing products.

Is the Walsh frequency a universal rate that all the antennas use? Or does each antenna use a different rate?

Would it be possible to turn off the Walsh function generator and see if this problem goes away?

You could use baudline as a real-time tool to detect and debug this. A command line something like:

realtime_ata_feed | baudline -stdin -format s8 -channels 2 -samplerate 8738133 -operation magnitude -overlap 100 -fftsize 16384 -average

will make it very quick and easy to see the 1/3, 2/3 elephants along with their 25600 Hz sidebands in real-time. Then you can adjust the Walsh generator knobs/switches and immediately see the effects.

billy
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More walsh details

I haven't given too much thought as to whether the walshing would produce the 50 Hz sidebands. I haven't seen sidebands at 50 Hz other observations that I've analyzed in detail, but I'm now motivated to take a closer look.

I wouldn't say that the walshing randomizes cross-talk, but more that it balances it (somewhat like using a twisted pair, where interfering flux cancels on consecutive loops). If we look at the cross-correlation products resulting from cross-talk signal over one fundamental period of the walsh system, half of the cross-correlation will be in-phase, and half will be out-of-phase, so the signal cancels.

You're absolutely right - in the SETI back ends, the walshing actually hurts us a bit with cross-talk rather than helping, because any cross talk will get unswitched at a different rate than it was switched, creating lots of sidebands (though hopefully at a low level relative to the tone).

We know very well that many of these artifacts are due to the walshing, and would expect them to go away if we turned off the walsh system -- this is something that is possible, but not convenient, to do (maybe we'll do it on some future data set, though, as a point of comparison?). I should point out that although the sidebands impact our spectral analysis, the walshing is very useful to our calibration process -- just like the imaging correlator, the ATA beamformer uses cross-correlation products to calibrate, and so walshing mitigates the effects of cross talk during calibration.

In answer to your other question: There are 8 unique walsh functions at the ATA, and they are phase-locked with our master clock. We wire our system so that each ADC unit (which accepts 4 analog inputs) has inputs that are on unique walsh functions. If it helps your analysis, the X-polarization antpols use 100 * 2^ functions, for exponents 1,3,5,7, and the Y-polarization antpols use 100*2^, for exponents 0,2,4,6. As I recall, most of the data sets that have been posted are for X-pol beams.

Billy

sigblips
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Thank you for explaining how

Thank you for explaining how this Walsh coding works. It is all very interesting but unfortunately it brings up even more questions. (:

What are the exact Walsh waveform bit streams? The reason I'm curious is if I know the exact waveform then I might be able to predict distortion products. I've found this http://mathworld.wolfram.com/WalshFunction.html reference, so are you using the W(3,x) sequences?

You mentioned 100 * 2^x where x = { 0 .. 7 }, so is it correct to assume that the multiplication by 100 extends each Walsh bit { +1, -1 } by 100 Hz or something else? I'm trying to understand how this translates to a range of 100 Hz ... 12800 Hz?

Since the Walshing / un-Walshing is a mixed analog-digital domain operation, how accurate is the alignment? This relates to the 0/179 degrees phase example you mentioned earlier. I suspect even a 0.001 degree phase error would produce artifacts. What sort of phase accuracy do you expect the analog-digital Walshing system to have?

billy
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The sequeces

The sequences are pretty simple. They are square waves {+1, -1} with the rate mentioned, zero DC offset.
EG, for an antpol with a 100 Hz walsh function, the function spends 5ms at +1, then transitions and spends the next 5ms at -1, etc.
The 200 Hz walsh function is just another square wave. In that same 10ms (one period of 100 Hz), the 200 Hz function goes:
0..2.5ms: +1
2.5..5ms: -1
5..7.5ms: +1
7.5..10ms: -1

And so on for the other functions.
The alignment in time between walshing and unwalshing is very good.
The analog system is not perfect, as mentioned, and might implement: exp(j*pi/180 * 179) and (exp(j*pi/180*0)) instead of -1/+1, e.g. a degree of phase error in the modulation. We'll see this in the data - CW tones will retain a small residual phase modulation, and you might see artifacts at the walsh function frequencies, but these should typically be low (-20dBc at the largest given our accuracies, iirc). A small error of 0.001 degrees won't be visible except with the strongest tones or longest integrations. The sideband level is easily calculated.

Billy

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So the Walsh waveforms you

So the Walsh waveforms you use are just square waves and not bit sequences like the MathWorld page mentions? That makes it a lot easier to model. How are the square waves synchronized relative to each other? At phase = zero or do they all have different phase offsets?

Artifacts at -20 dB doesn't seem that low. How high is the cross-talk to begin with?

billy
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Alignment

The walsh functions are just analog square waves that drive a mixer, yes. They are all synchronized to each-other on an edge of the 100 Hz wave and phase locked to our master timing system.

I don't have exact numbers for the cross talk, but you have to remember that -20dBc artifacts on a single-antenna really aren't that bad: the artifacts won't be evident in the radio astronomy data (since our channels are usually much wider), and in arrayed SETI data, the artifacts tend to wash out to a certain degree (since the artifacts are not all at the same frequency and tend to have pseudorandom phases after beamforming). Also, the artifacts will be very well-defined relative to a tone present in the data, so somewhat easy to separate from more interesting signals.

sigblips
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At a 8738133 sample rate the

At a 8738133 sample rate the full cycle of a 100 Hz square wave will be 87381 samples. So a 1 degree error will be 243 samples and a 0.01 degree error will be 2 samples. I'm building a Walsh test bench from several of baudline's tone generators to get a feel for this phase error and any other potential error modes. Maybe I'll blog about it.

I agree that for noise-like radio astronomy data these artifacts won't be much of an issue. Anything periodic though is a different matter. Multiple channel summing of the artifacts could be viewed as a "washing out" and it could also be viewed as a spreading out. Depending on the math, some inter-mixing could be going on too. Add in any aliasing or quantization and the Walshing artifacts could become very difficult to separate.

What I do know is that I've seen a wealth of interesting signals in each of the setiQuest data sets. This Walshing phase error is a potential source but the shear number of signals makes me believe that there are multiple error sources.

sigblips
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For continuation of this

For continuation of this sub-thread a description of the Walshing system was wiki-fied here:

http://setiquest.org/forum/topic/walsh-system

billy
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25.6 KHz, revisited

Sigblips (and all)-
I have reviewed the observation notes in a little more detail and compared to some engineering data, and it is very likely that the 25.6 KHz tone is coming from one particular antpol (antenna-polarization, our slang) used in this observation. This artifact does appear to originate in the analog walshing system described in the other post. I'll take a closer look at the hardware-in-question shortly.

Billy

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I just added a section called

I just added a section called Side Skirting to my blog B0239+54 blog post. I take a look at a couple of signals in the filter roll-off skirts that I previously ignored. A bunch of whole number frequency ratios, odd power fluctuations, and phase discontinuities are discovered. I also found a signal that has an extremely unusual fractal-like structure to it. I believe that this signal could be the source for all of the distortion products I'm seeing.

4096 is looking more and more special. So is 50 Hz and 120 Hz. The ATA is not in Europe and I just said 50 Hz. It gets even stranger.

gerryharp
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sampling rate is ~8.7381

Hi

I'm not sure how you derived the repeating digits after the "1," perhaps someone else told you. In my header information I'm recording only to the nearest 100 Hz.

Gerry

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I'm confused as to what you

I'm confused as to what you are referring to. Which digits? Which 1? Are you saying that the sample rate is not 8738133.333_ but it is instead 8738100.000 ?