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Blind Pulsar frequency measurement in the frequency domain

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Dave Robinson
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I have been working on a methodology for automatically checking if a signal contains a Pulsar, and if so accurately measuring its repeat period. Although this work is far from complete, I have developed an algorithm which was able to determine the period of the Pulsar in the B0324+54 files to within 0.002% accuracy. I have written a report outlining the method, and included some Matlab/Octave files which will allow experimentation on the technique. This information can be downloaded from here

drop.io/Dave_Robinson_PulsarRate

As the report indicates there are several places where I would welcome some bright ideas, allowing me to reach the next stage. I am currently suffering from a failure of imagination.

Looking forward to some feedback

Regards

Dave Robinson

sigblips
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I have a couple questions: *

I have a couple questions:

* What is a Setisec?

* What filter type and size did you use to low pass filter?

* What factor did you decimate by?

Dave Robinson
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Sorry I hadn't made it

Sorry I hadn't made it clearer in the report, all the details regarding the definition of Setisec, the type of filter and decimation rate were given in my previous document which can be found here

drop.io/Dave_Robinson_Filter

and also discussed briefly in the adjacent thread initiated by Anders "Filtering out simple signals"

Basically I redefined time in terms of a unit I called a Setisecond which is a period of time consisting of 2^23 samples of data  taken on the standard sample rate used to produce the data stored in the cloud (approximately 0.96 seconds). I have then broken the data down into Setisec chunks of data, and stored these on my machine. Matlab/Origin can handle this size of file without hitting an "out of memory" error. Selecting a nice 2^n length of data makes for efficient FFT processing, and allows the use of Wavelet transforms.

I used a Low-Pass filter with a cut off frequency of 128 cycles/Setisec whose impulse response was designed using the Host Window methodology, check out my previous document. However it is relatively academic how you design this filter, and even its cut off frequency is relatively unimportant. Its sole purpose was to allow me to see the pulses in the time domain. (After playing about with the signals for several weeks, and not actually seeing any pulses, I began to doubt they were actually there;-)
I used this filter and a sequential access to my Setisec blocks using an Overlap Save methodology to low-pass filter the time domain data, and then I decimated the data to 4096 samples/Setisec. Still wildly oversampled, but seemed a nice number - maintaining the 2^n theme.

Hope that answers your questions, if anything else puzzles you don't hesitate to come back - and any ideas for improvements will be gratefully received.

Regards

Dave Robinson

sigblips
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Summerized answers:* So a

Summerized answers:

* So a Setisec is 0.96 seconds which I'm going to round up to 1 second for discussion purposes here.

* You LPF'd with a cutoff at 128 Hz.

* You decimated to a 4096 sample/sec rate but you could of decimated to 256 sample/sec due to your LPF and Nyquist. This works out to a decimation ratio of 2048 and 32K respectively.

* Your Robinson_Filter link takes me to http://drop.io/Dave_Robinson_PulsarRate so I can't determine your filter size. It sounds like you did FFT convolution. What size FFT did you use?  Assuming the Host Window method is somewhat ideal I can then have a good visual how sharp the cutoff is.

 

Dave Robinson
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Draft Paper now in Wiki

I have placed a draft paper describing measuring  the pulsar period using the Frequency Domain representation of the Pulsar signal in the Library section of the Wiki - if anyone is interested.

Regards

Dave Robinson

Anders Feder
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Great, Dave. I've moved it

Great, Dave. I've moved it into the 'Astronomy' section. I'll see if I can adjust the formatting to better line up with your original document later.

jill
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your pulsar detection method

i thought you might like to know that PSR B0329 + 54 may have a planet in orbit around it.  the paper is ApJ, 453: 779-782, 1995.  /sites/default/files/files/B0329-planet-1995ApJ___453__779S(4).pdf

the dispersion measure of that pulsar is reported to be 26.833 parsecs/cm^3.  /sites/default/files/files/DM-B0329-J01-P_2(0045).pdf

jill tarter

Dave Robinson
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Hi Jill Thanks for the links

Hi Jill

Thanks for the links to the papers. Its amazing that the Pulsar could actually have a planet. Its hard to believe there was sufficient hard stuff left after the supernova explosion to form another planetary system, one would have imagined that any debris left over from a planetary system prior to the supernova would have been pushed further into interstellar space on a non-return trajectory, and the thought of a planet remainining intact after its mother star exploded seems very unlikely. it seems that planets aren't the rarity that I was brought up to believe - they form wherever they possibly can, an encouraging train of thought.

I would have thought that the algorithm that I outlined in my Wiki article, and the more detailed paper found on the Drop.IO page I referenced elsewhere in this thread would make the basis for an ideal tool for checking out the long term period for a given Pulsar. As the papers show, even with a short data acquisition time of about 120 seconds, the spikes stand well proud of the background noise, and the measured pulse period is remarkably accurate. By extending the observation time, we gain on 2 fronts. We improve the signal to noise ratio, which for this Pulsar won't help much, we can see the signal loud and clear. However more importantly the accuracy that we can obtain for the repeat period improves as the longer observation time provides a much better frequency domain resolution. The algorithm is readily adapted for fully automatic operation. What needs to be done is to compute the length of time we need to observe the pulsar for, in order to get a resolution as fine as is needed to provide the repeat period measurement with sufficient accuracy to be able to determine the tiny shift of frequency such that the modulation can be quantified to show the long term repeat pattern shown in your referenced paper.

Regards

Dave Robinson