Signal processing with heterogeneous digital filterbanks: lessons - - PowerPoint PPT Presentation

Signal processing with heterogeneous digital filterbanks: lessons from the MWA and EDA

Randall Wayth – ICRAR/Curtin University with Marcin Sokolowski, Cathryn Trott

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Outline

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Goal: Ingest digital data from EDA into MWA correlator to measure the SEFD of EDA

"Holy grail of CASPER system is multi-user system” Jack H on Monday

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Perth ~200 km Geraldt

• n

41,000 sq. km = The Netherlands

MRO (operated by CSIRO) Pawsey Centre 20 PB storage for MWA On site: data rate into central building ~60 Gbps Ofg site: data rate into science archive ~3 Gbps

Antenna tiles: 4x4 array of dual pol dipoles

Beamformer

Receivers:

• Each receiver services 8 tiles
• Sky signal is digitised and sent to central

processing facility Receivers:

• Each receiver services 8 tiles
• Sky signal is digitised and sent to central

processing facility

• Visibilities integrated to ~1s time resolution

Central Signal Processing:

• 128 dual pol tiles
• 30.72 MHz bandwidth, 10 kHz spectral resolution
• 8128 baselines

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MWA digital signal path

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Tremblay et al, 2015

24 x 1.28 MHz coarse

• channels. 8-tap PFB

10 kHz fjne channels 12(?) tap PFB 10G ethernet Software correlator

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Engineering Development Array (EDA)

Signatec PX-1500 GTX 750

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MWA correlator inputs

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MWA:

• Sample rate 655.36 Msamp/sec
• 8-tap critically sampled PFB for

coarse channels (1.28 MHz)

• 12-tap critically sampled PFB for

fine channels (10 kHz)

EDA:

• Sample rate 655.36 Msamp/sec

– Uses MWA clock

• Do 65536-sample FFT to directly

transform to 10 kHz channels (easy on GPU)

Result:

• Brute-force fringe search using Sun as source
• Clear lag, but at equal magnitude for 5 and 6 samples
• SNR of cross-correlation at either lag is lower than expected, but roughly equal
• WTF?

Analysis

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Consider weighted-overlap-add model of a PFB

• Each chunk of signal appears in the window n_taps

times

• For even-sized PFB, signal appears twice with equal

power (but mirror reflected weights) with largest weights For FFT-based spectrometer, signal from any block of input samples only appears in output once.

From Crochiere & Rabiner, 1983 “Multirate digital signal processing”

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Analysis

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• The correlator works on the fjne

channels out of the DFT

• Fine channels will correlate ifg the same

(broadband) signal went into the fjlterbank at time t.

• Obvious from inspection that signal

contributing to time t in PFB also contributes to time t+1.

• If we lag correlate fjne channel time

series from FFT and PFB we would expect equal amplitude for times t and t+1.

• BUT, for a given lag, more than 50% of

DFT output will not correlate. -> Low SNR

FFT only Coarse chan data Fine chan data

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Analysis

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+ +

DFT DFT DFT DFT

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Analysis

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+ +

DFT DFT DFT DFT

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Analysis

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+ +

DFT DFT DFT DFT

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Analysis

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DFT DFT DFT DFT

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Analysis

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DFT DFT DFT DFT

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Analysis

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DFT DFT DFT DFT

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Simulation summary

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d1 d1 d2 d2

10% common signal power

FFT direct to fjne chans FFT direct to fjne chans PFB to coarse chans. Select 1 PFB to coarse chans. Select 1

Noise data streams

FFT to fjne chans FFT to fjne chans Odd PFB to fjne chans Odd PFB to fjne chans Even PFB to fjne chans Even PFB to fjne chans

Fine chan data streams “EDA” “MWA”

Simulation – even sized PFB

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Generate noise time series

• Channelise to coarse channels

using PFB

• Fine channelise using

– Even-sized PFB and – FFT

• Find lag in fine channel time

series

• Equal lag magnitude and t=0

and t=1

Simulation – odd sized PFB

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Generate noise time series

• Channelise to coarse channels

using PFB

• Fine channelise using

– Odd-sized PFB and – FFT

• Find lag in fine channel time series
• Significant lag only at t=0

Inspecting time series of fine channels, the effect is obvious.

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By eye comparison of odd vs even vs fft

Simulation - SNR

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Simulate MWA/EDA system:

• PFB for coarse chans,

then fine channelisation

• FFT x FFT (ideal case)
• FFT x (…options)

Results:

• method of coarse

channelisation not important

• Odd-sized PFB better

SNR than even sized PFB when correlated with FFT fine channels Stddev in phase = proxy for SNR

0.033 0.033 0.054 0.084

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Proof of the pudding… EDA into MWA

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EDA sensitivity (via SEFD) as measured by noise in calibrated visibilities

• All data correlated

in MWA correlator

• Calibration via

normal MWA calibration on strong compact source

• Using 4-tap PFB in

EDA improves SNR by 2x vs straight FFT

Summary – heterogeneous filterbanks

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• Odd and even-sized filterbanks do not

play nice when correlated

• There is no fundamental reason why an

even or power-of-two number of taps is required in a PFB

• Odd-sized number of taps gives

closer representation to intuitive FFT result

• SNR of correlated data is affected by

match (or mismatch) in PFB window used

Jobs@ICRAR

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