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Design and performance of fast transient detectors
Cathryn Trott, Nathan Clarke, J-P Macquart ICRAR Curtin University


Outline
The incoherent detector · The classical matched filter ­ pros and cons · Degrading effects ­ scattering, inaccurate de-dispersion, trial templates · Performance for high DM events, at different frequencies How to design a better detector? · CRAFT detector ­ working with the dynamic spectrum · Fitting into the hierarchy and implementation · Asymptotic performance


Fast transient source detection
Fast transient pipeline
"Matched filter" on time series (boxcar)

Data product (voltages)

Channelize and square (autocorrelations)

Incoherent de-disperse

Combine antennas RFI excision: choose antennas to include

Detection?

TBB: retain a few seconds of raw data

Off-line follow-up

Coherent dedisperse


The Matched Filter
> Optimal detector for a known signal in known Gaussian noise > Matches expected signal shape (template, h) to data (s), and sums

> Pros: optimal for a given Gaussian dataset > Cons: requires full signal knowledge, not "blind" to signal shape > Performance: signal-to-noise ratios
Template matched to signal, s Template (h) and signal (s) mis-matched


Time series MF implementation
De-disperse Frequency Sum over channels Apply filter Compute detection test statistic

Matched filter

Boxcar: width 2

1



Test s ta ti s ti c

Boxcar: width 2

2

Data Time
Boxcar: width 2
3

Dynamic spectrum

Time series


Degrading factors
> Intrinsic - Scatter broadening due to ISM multi-path > Extrinsic - Incorrect dispersion measure - Finite temporal/spectral sampling - Finite temporal window - Mis-matched/approximate templates


Degrading factors: ISM scattering
Characteristic scattering timescale:

Cordes & Lazio (2002)

DM=1000 DM=300 DM=700

ASKAP parameters: W = 1 ms = 1 GHz

DM=500


Impact of degrading factors: Galactic lines-of-sight
Relative detection performance for identical source at different DMs:


Impact of degrading factors: Frequency dependence
Relative detection performance for identical source at different DMs:


Hierarchy of signal knowledge
Dynamic spectrum power samples Matched filter Full signal knowledge required: temporal and spectral Optimized boxcar templates Partially blind: trial pulse widths, potentially trial spectral index

Time series power (summed over spectral channels) Matched filter Full time domain signal knowledge required Boxcar templates Blind: coarse trial of pulse widths


Hierarchy of signal knowledge
Dynamic spectrum power samples Matched filter Full signal knowledge required: temporal and spectral Optimized boxcar templates Partially blind: trial pulse widths, potentially trial spectral index

Time series power (summed over spectral channels) Matched filter Full time domain signal knowledge required Boxcar templates Blind: coarse trial of pulse widths


Hierarchy of signal knowledge
Dynamic spectrum power samples Matched filter Full signal knowledge required: temporal and spectral Optimized boxcar templates Partially blind: trial pulse widths, potentially trial spectral index

Time series power (summed over spectral channels) Matched filter Full time domain signal knowledge required Boxcar templates Blind: coarse trial of pulse widths


Dynamic spectrum detection
· Design of fast transient detector for CRAFT, using FPGAs to implement de-dispersion and detection algorithm · Works directly with dynamic spectrum power samples from spectrometer · Detector: · Choose samples according to expected power for a given DM: set spectral index (0), pulse width · Average power in a sample calculated analytically · Choose set of samples that maximises signal-to-noise ratio · "Sample-optimised" boxcar template
Clarke et al. (2011, in prep)


Dynamic spectrum detection

Inclusion criterion:

Clarke et al. (2011, in prep)


Asymptotic performance

/ . /


Performance comparison

DM=120 =1MHz W=1ms ASKAP parameters: = [1.0,1.3] GHz TOT = 300 MHz

.

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Summary
> High DM detections difficult, particularly at low frequencies > Optimal matched filter rarely achievable smart boxcar template applied to dynamic spectrum dataset can recover some lost performance > Working directly with dynamic spectrum samples retains signal power, while minimising noise power boxcar template can achieve improved performance Next steps: > Balance combination of DM steps / spectral index steps / pulse width steps for optimal detection with a given FPGA design and architecture > Compare performance with other FT experiments (e.g., VFASTR)


Performance comparison


Performance comparison