Pulsar Analytics Kit: A Toolkit for Pulsar Signal Processing and Analysis#

Key Characteristics#

• Spin Period ($P$): Time interval between successive pulses.
• Dispersion Measure (DM): A measure of electron column density along the line of sight.

Dispersion Delay Equation:#

$\Delta t = 4.15 \times 10^3 \cdot \text{DM} \left( \frac{1}{f_1^2} - \frac{1}{f_2^2} \right) \text{ ms}$

Where:

• $\Delta t$ = time delay between two frequencies
• DM = Dispersion Measure (pc/cm(^3))
• $f_1, f_2$ = frequencies in MHz

Purpose of Dedispersion: To correct this delay and align the pulse across all frequency channels.

Dynamic Spectrum#

A 2D plot of signal intensity as a function of time and frequency. This is the primary data format analyzed in this software.

Construction:#

• The raw voltage data is divided into blocks.
• Each block is Fourier transformed.
• Spectral power is averaged over blocks.

Spectrogram Equation:#

$S(f, t) = |\text{FFT}[x(t)]|^2$

Where:

• $x(t)$ = time series voltage
• $S(f, t)$ = spectral power at frequency $f$ and time $t$

Method 1: Autocorrelation#

Compute the autocorrelation of the dedispersed time series:

$R(\tau) = \frac{1}{N} \sum_{t=0}^{N-\tau} x(t) x(t + \tau)$

Periodic spikes in $R(\tau)$ indicate possible pulse periods.

Method 2: Fourier Domain#

Use FFT to locate periodicities:

• Look for peaks and their harmonics.
• Use highest S/N frequency as the inverse of pulse period.

$P = \frac{1}{f_{peak}}$

Folded Profile:#

$F(n) = \sum_{i=0}^{M} x(iT + n)$

Where:

• $x(t)$ = signal
• $T$ = period
• $n$ = bin index
• $F(n)$ = average pulse profile

Grid Search for DM#

A brute-force method to find optimal DM by:

1. Dedispersing data at trial DMs
2. Folding at known period
3. Scoring pulse sharpness (e.g., via S/N or Gaussian sharpness)
4. Fitting a Gaussian to the score-DM curve

Sharpness Scoring:#

Can use standard deviation, kurtosis, or Gaussian peak fitting.

RFI Identification Techniques:#

• Median Absolute Deviation (MAD)
• Channel-wise standard deviation thresholding
• Sigma-clipping

Channel Efficiency Metric:#

$\epsilon = \frac{\mu}{\sigma \sqrt{\text{TBP}}}$

Where:

• $\mu$ = mean intensity
• $\sigma$ = standard deviation
• TBP = time-bandwidth product

Channels with $\epsilon$ significantly deviating from 1 are flagged.

Modular Components:#

• pulsar_analysis.py — core processing class
• functions.py — utility methods (FFT, dedispersion, autocorrelation, etc.)
• gui.py — PyQt5-based multi-tab GUI
• plotting.py — matplotlib-based visualization toolkit
• updater.py — auto-update script via GitHub

Key Features#

• Interactive GUI for non-programmers
• Multi-format data support: ASCII, binary, SIGPROC .fil
• Dynamic spectrum visualization
• Dedispersion and folding tools
• Auto-period detection and DM optimization
• RFI mitigation techniques