What does folding mean in pulsar radio astronony signal processing?

What Does Folding Mean in Pulsar Radio Astronomy?

In pulsar radio astronomy, FOLDING is a signal-processing technique that allows us to detect extremely weak, periodic pulses from a pulsar by repeatedly adding together successive rotations of the pulsar.

It is one of the most important techniques in pulsar detection.

1. The Basic Principle

A pulsar emits radio pulses at remarkably regular intervals.

For example, imagine a pulsar with a rotation period of exactly 1 second.

Your radio telescope records a continuous stream of data:

Time (seconds)

  0       1       2       3       4       5
  |       |       |       |       |       |
  /\      /\      /\      /\      /\      /\
 /  \    /  \    /  \    /  \    /  \    /  \

The problem is that individual pulses may be buried in receiver noise. A single pulse might be almost impossible to distinguish from the background.

However, because the pulsar repeats its pulse every second, we can exploit that periodicity.

2. How Folding Works

Imagine collecting 100 seconds of observations from a pulsar with a period of exactly 1 second.

We divide the data into 100 consecutive sections, each one second long.

We then:

• Take the first second of data.
• Take the second second and add it to the first.
• Take the third second and add it to the accumulated data.
• Continue for all 100 seconds.

The important point is that the pulses occur at the same position in every section.

When the sections are added together, the pulses reinforce one another, while random noise tends to average out.

Conceptually:

Pulse 1:  ----*-------------------
Pulse 2:  ----*-------------------
Pulse 3:  ----*-------------------
Pulse 4:  ----*-------------------
Pulse 5:  ----*-------------------
           |
           +-- Pulses align here

After folding:

          *
          *
          *
          *
          *

3. Why Folding Improves Signal-to-Noise Ratio

Suppose we fold 100 pulses.

• The pulsar signal adds coherently: amplitude increases approximately 100-fold.
• Random noise increases approximately 10-fold.
• The resulting signal-to-noise ratio improves approximately 10-fold.

The general relationship is:

SNR improvement = sqrt(N)

Where N is the number of pulses folded.

This assumes independent random noise and that the pulses are correctly aligned.

4. What Happens If the Pulsar Period Is Not Known?

This is where pulsar searching becomes interesting.

Software searches through possible combinations of:

• Pulse period (rotation frequency).
• Period derivative (how quickly the pulsar is slowing down).
• Dispersion measure (DM), accounting for frequency-dependent delays as radio waves travel through the interstellar medium.

For each trial period, the software folds the observations and looks for a strong, statistically significant pulse profile.

The correct period should produce a recognisable pulse profile with a high signal-to-noise ratio.

5. What Does the Final Result Look Like?

The resulting graph is called an INTEGRATED PULSE PROFILE.

It normally has:

• Horizontal axis: pulse phase (0 to 360 degrees, or 0 to 1 rotation).
• Vertical axis: average radio intensity.
• Peaks: positions where the pulsar emits most of its detectable radio energy.

The profile can contain several peaks, reflecting the pulsar’s radio emission geometry.

6. Relevance to Amateur Radio Astronomy

For an amateur observatory such as Lichfield Radio Observatory, folding is particularly interesting because it allows detection of signals that are individually too weak to see.

A typical processing chain might be:

RADIO TELESCOPE AND RECEIVER
             |
             v
         DIGITISATION
       (SDR and sampling)
             |
             v
         DEDISPERSION
 (Correct frequency-dependent
       arrival delays)
             |
             v
           FOLDING
  (Align and accumulate successive
          pulsar rotations)
             |
             v
    INTEGRATED PULSE PROFILE
             |
             v
       PULSAR DETECTION

One important distinction:

Folding does not actually create a stronger radio signal. It increases our ability to distinguish the periodic signal from random receiver noise.

7. An Interesting Project for LRO

You could use your SDR equipment and GNU Radio to capture pulsar observations and then write a Python program to perform folding and produce integrated pulse profiles.

The program would:

• Read the recorded SDR data.
• Apply any necessary frequency-channel corrections.
• Apply dedispersion.
• Divide the observation into pulse-period intervals.
• Align and accumulate successive periods.
• Plot the resulting integrated pulse profile.
• Calculate the signal-to-noise ratio.

This might make make a fascinating practical pulsar astronomy project for us to consider doing at Lichfield Radio Observatory.