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Published byLee Maxwell Modified over 8 years ago
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Short Time Fourier Transform-based method for fast transients detection Centre for eResearch, University of Auckland, New Zealand, g.soudlenkov@auckland.ac.nz g.soudlenkov@auckland.ac.nz International Centre for Radio Austronomy Research, the University of Western Australia, slava.kitaeff@icrar.org
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Fast transients search Lack of regularity/periodicity Lack of regularity/periodicity Frequency evolution and integrated pulse shape of the radio burst. The survey data, collected on 24 August 2001, are shown here as a two-dimensional “waterfall plot” of intensity as a function of radio frequency versus time. The dispersion is clearly seen as a quadratic sweep across the frequency band, with broadening toward lower frequencies. (Lorimer, 2007)
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Fast transients search Lack of regularity/periodicity Lack of regularity/periodicity Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation
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Fast transients search Lack of regularity/periodicity Lack of regularity/periodicity Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation The solution is to be scalable The solution is to be scalable
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Fast transients search Lack of regularity/periodicity Lack of regularity/periodicity Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation Multiplicity of sources – Cerenkov emission, gamma-ray bursts, RRATs, synchrotron radiation The solution is to be scalable The solution is to be scalable The solution must be computationally inexpensive The solution must be computationally inexpensive
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Jean B. Joseph Fourier (1768-1830) “ An arbitrary function, continuous or with discontinuities, defined in a finite interval by an arbitrarily capricious graph can always be expressed as a sum of sinusoids ” J.B.J. Fourier
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Dennis Gabor (1900-1979) Nobel Prize in Physics, 1971, inventor of holography – and the one who introduced time/frequency transforms (paper on Gabor transform published in 1946)
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Signal assumed stationary within short window Signal assumed stationary within short window
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Short Time Fourier Transform Spectrograms © 2009 National Instruments Corporation. All rights reserved.
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Signal assumed stationary within short window Signal assumed stationary within short window Maps signal into two-dimensional function in time/frequency plane Maps signal into two-dimensional function in time/frequency plane
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Signal assumed stationary within short window Signal assumed stationary within short window Maps signal into two-dimensional function in time/frequency plane Maps signal into two-dimensional function in time/frequency plane Algorithm has relatively low computational complexity and provides good ground for parallelized solution Algorithm has relatively low computational complexity and provides good ground for parallelized solution
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Short Time Fourier Transform Transforms from time to join time/frequency domain Transforms from time to join time/frequency domain Signal assumed stationary within short window Signal assumed stationary within short window Maps signal into two-dimensional function in time/frequency plane Maps signal into two-dimensional function in time/frequency plane Algorithm has relatively low computational complexity and provides good ground for parallelized solution Algorithm has relatively low computational complexity and provides good ground for parallelized solution Disadvantage: difficulty in obtaining satisfactory resolution in both domains (Fourier uncertainty principle) Disadvantage: difficulty in obtaining satisfactory resolution in both domains (Fourier uncertainty principle)
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STFT is a drawing board - over noise background Noise is considered to be normal Noise is considered to be normal Zero mean Zero mean Constant variance Constant variance Zero correlation Zero correlation Spectrum is approximately exponential Spectrum is approximately exponential Cox-Box transform can make spectrum sequences to be approximately Gaussian AR(1) process Cox-Box transform can make spectrum sequences to be approximately Gaussian AR(1) process Local signal can now be detected as a series of outliers in frequency bands Local signal can now be detected as a series of outliers in frequency bands
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Cells scoring – stage 1 Mean frequency band - MFB Mean frequency band - MFB Mean power in MFB Mean power in MFB Cells – windows with regular time width Cells – windows with regular time width
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Cells scoring – stage 1 Mean frequency band - MFB Mean frequency band - MFB Mean power in MFB Mean power in MFB Cells – windows with regular time width Cells – windows with regular time width Use of centralized cells reduces negative impact of edge effect Use of centralized cells reduces negative impact of edge effect
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Cells scoring – stage 1 Mean frequency band - MFB Mean frequency band - MFB Mean power in MFB Mean power in MFB Cells – windows with regular time width Cells – windows with regular time width Use of centralized cells reduces negative impact of edge effect Use of centralized cells reduces negative impact of edge effect Each cell is assigned a score Each cell is assigned a score
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Cells scoring – stage 1
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Cells scoring – stage 2 Cells are sorted in score descending order Cells are sorted in score descending order Identify signal-bearing cells Identify signal-bearing cells Make sure this signals are of interest Make sure this signals are of interest
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Cells scoring – stage 2 Identify signal-bearing cells Identify signal-bearing cells Make sure this signals are of interest Make sure this signals are of interest Implementation solution uses outliers trains counting in frequency bins Implementation solution uses outliers trains counting in frequency bins
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Cells scoring – stage 2 Identify signal-bearing cells Identify signal-bearing cells Make sure this signals are of interest Make sure this signals are of interest Proposed implementation uses outliers trains counting in frequency bins Proposed implementation uses outliers trains counting in frequency bins Other methods can use statistical properties of STFT- transformed noise Other methods can use statistical properties of STFT- transformed noise
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Cells scoring – stage 2 Candidate cells marked for further investigation have identified dispersion measure Candidate cells marked for further investigation have identified dispersion measure Incoherent de-dispersion is easy and computationally inexpensive Incoherent de-dispersion is easy and computationally inexpensive Coherent de-dispersion can be done if full content of the original Fourier transform remains (real and imaginary parts) Coherent de-dispersion can be done if full content of the original Fourier transform remains (real and imaginary parts)
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Vela (PSR J0835-4510)
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Observed in 1968 Observed in 1968 Period of 89 ms Period of 89 ms Dispersion measure 68 pc*cm^-3 Dispersion measure 68 pc*cm^-3
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Vela (PSR J0835- 4510)Detector results … Pos: 79, sec: 0.632000 * Pos: 80, sec: 0.640000 Pos: 90, sec: 0.720000 * Pos: 101, sec: 0.808000 * Pos: 112, sec: 0.896000 * Pos: 123, sec: 0.984000 * Pos: 134, sec: 1.072000 * Pos: 144, sec: 1.152000 * Pos: 145, sec: 1.160000 Pos: 156, sec: 1.248000 * Pos: 166, sec: 1.328000 * Pos: 167, sec: 1.336000 … Stable period of 88 ms is visible now
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Vela (PSR J0835-4510) Time/frequency representation of pulsar J0835 − 4510, observed at Parks telescope, central frequency 1416 MHz, bandwidth 64 MHz, recorded with 2-bit VLBI recorder. Recording started at 2009.12.10 − 17 : 25 : 51UTC. Single pulse
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Vela (PSR J0835-4510) Portion of the spectrum stripe with detected and de-dispersed pulses Single pulse – de-dispersed
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Acknowledgments We would like to thank Dr. Aidan Hotan of Curtin Institute of Radioastronomy, Dr. Joeri van Leeuwen from Astron, Dr. Duncan Lorimer from West Virginia University for the data been made available.
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