How to find period of a pulsar from a given time sampled voltage data?

Question

I've a data file with 2 columns, each containing time sampled voltage output (a sequence of real numbers) from a radio telescope, so there is a pair of telescope which are measuring the signal here. The source of the data is a pulsar and I've to find its period and dispersion measure.

I'm an amateur trying to understand what is really happening in the method. The data is time sampled at the Nyquist sampling frequency (2B) and the signal is measured at central frequency f and broadband B.

I studied the cross correlation between the two voltages V1 and V2 from essential radio astronomy, but didn't quite understand the method. Do we have to evaluate the cross correlation function of each reading and then plot it with time to get the pulse profile? Or do we have to take fourier transform of each pair of voltage(how?) and then plot it to get the pulse profile? We find period of a pulsar from its average pulse profile, right?

It is also written that to find pulsar timing, we've to fold data from many pulses modulo instantaneous pulse period (how can we do that if we don't know the pulse period in the first place?). This sentence is everywhere and I'm not able to understand it each time.

I'm confused about the appropriate series of steps to be done here to get the pulsar period and dispersion measure. Could you give me some insight?

Thanks.

Answer 1

To understand the basics of algorithms like that, I find it's often best to look at what amateur practicioners are writing (as opposed to diving directly into scientific papers). The description of the folding algorithm at joataman.net is thorough and pragmatic.

A great in-depth book on the topic is Lorimer/Kramer: Handbook of Pulsar Astronomy, Oxford University Press.

For the actual work, I would suggest the sigproc package by Duncan Lorimer. Its home is at Sourceforge, but there are forks all over the place because the original software is a bit quirky when run on modern Linuxes.

Answer 2

The problem you are trying to solve is one generally known as spectral estimation. In addition to the practical references provided by jstarek, I suggest you also read some fundamentals.

The book by S.M.Kay Modern Spectral Estimation, although almost 20 years old, is totally up to date and is a very well explained (easy to read) introduction.

You will see that the folding algorithm is just a flavour of the Welch periodogram, and that your cross-correlation approach fits as an MLE estimation scheme (nowadays also known as signal subspace techniques).