Optimal periodicity searching: Revisiting the Fast Folding Algorithm for large-scale pulsar surveys

Abstract

The Fast Folding Algorithm (FFA) is a phase-coherent search technique for periodic signals. It has rarely been used in radio pulsar searches, having been historically supplanted by the less computationally expensive Fast Fourier Transform (FFT) with incoherent harmonic summing (IHS). Here we derive from first principles that an FFA search closely approaches the theoretical optimum sensitivity to all periodic signals; it is analytically shown to be significantly more sensitive than the standard FFT+IHS method, regardless of pulse period and duty cycle. A portion of the pulsar phase space has thus been systematically under-explored for decades; pulsar surveys aiming to fully sample the pulsar population should include an FFA search as part of their data analysis. We have developed an FFA software package, riptide, fast enough to process radio observations on a large scale; riptide has already discovered sources undetectable using existing FFT+IHS implementations. Our sensitivity comparison between search techniques also shows that a more realistic radiometer equation is needed, which includes an additional term: the search efficiency. We derive the theoretical efficiencies of both the FFA and the FFT+IHS methods and discuss how excluding this term has consequences for pulsar population synthesis studies.

Accepted for publication in MNRAS, 20 pages, 9 figures. Minor corrections and improved clarity throughout

References in corpus (29)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• The ATNF Pulsar Catalogue
• The ATNF Pulsar Catalogue
• PSRCHIVE and PSRFITS An Open Approach to Radio Pulsar Data Storage and Analysis
• The Parkes Multibeam Pulsar Survey: I. Observing and Data Analysis Systems, Discovery and Timing of 100 Pulsars
• Fourier Techniques for Very Long Astrophysical Time Series Analysis
• The High Time Resolution Universe Pulsar Survey I: System configuration and initial discoveries
• The repeating Fast Radio Burst FRB 121102: Multi-wavelength observations and additional bursts
• Searches for Fast Radio Transients
• Arecibo Pulsar Survey Using ALFA. I. Survey Strategy and First Discoveries
• A Plateau in the Planet Population Below Twice the Size of Earth
• Fifty Years of Pulsar Candidate Selection: From simple filters to a new principled real-time classification approach
• The Parkes Multibeam Pulsar Survey: V. Finding binary and millisecond pulsars
• Arecibo Pulsar Survey Using ALFA. IV. Mock Spectrometer Data Analysis, Survey Sensitivity, and the Discovery of 41 Pulsars
• Searches for Giant Pulses from Extragalactic Pulsars
• LOFAR discovery of a 23.5-second radio pulsar
• A new technique for the detection of periodic signals in ``coloured'' power spectra
• The SUrvey for Pulsars and Extragalactic Radio Bursts I: Survey Description and Overview
• The LOFAR Tied-Array All-Sky Survey (LOTAAS): Survey overview and initial pulsar discoveries
• New Limits on Radio Emission from X-ray Dim Isolated Neutron Stars
• On Computing Upper Limits to Source Intensities
• An investigation of pulsar searching techniques with the Fast Folding Algorithm
• The SUrvey for Pulsars and Extragalactic Radio Bursts IV: Discovery and polarimetry of a 12.1-second radio pulsar
• The implementation of a Fast-Folding pipeline for long-period pulsar searching in the PALFA survey
• A Framework for Assessing the Performance of Pulsar Search Pipelines
• Targeted search for young radio pulsars in the SMC: Discovery of two new pulsars
• The SUrvey for Pulsars and Extragalactic Radio Bursts V: Recent Discoveries and Full Timing Solutions
• Upper Limits on Pulsed Radio Emission from the 6.85 s X-ray Pulsar XTE J0103-728 in the Small Magellanic Cloud
• Harmonic Summing Improves Pulsar Detection Sensitivity: A Probability Analysis

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