RFI Subtraction with a reference horn… F. Briggs & M. Kesteven illustrations from Parkes Telescope… (Jon Bell et al.) origins in Int-Mit group at CSIRO – ATNF

RxRx gASgAS S I + g 1 I I g3Ig3I - g 1 I Signal Processing  gASgAS g1g1 g3g3 X Cross Correlation

R F I

Reference Antenna I I(t) =   h  (t) * i o (t    Impulse Response h(t) for each path  Convolution operator Signal radiated by transmitter … with DELAY  

= G(f) I o (f) I (f) = (   G  (f) e - i 2    f ) I o (f) Reference Antenna I Time Domain Frequency Domain I(t) =   h  (t) * i o (t    

Cross correlation: single polarization feed with 2 reference signals 1. Pol A 3. Ref 1 4. Ref 2 …G 1 G 4 * | I o 2 | G 3 G 4 * | I o 2 | ?? G1G1 G3G3 = G 1 G 4 * | I o 2 | G 3 G 4 * | I o 2 | G1G1 G3G3

Cross correlation: single polarization feed with 2 reference signals 1. Pol A 3. Ref 1 4. Ref 2 …G 1 G 4 * | I o 2 | G 3 G 4 * | I o 2 | G1G1 G3G3 = G 1 G 4 * | I o 2 | G 3 G 4 * | I o 2 | = C 14 (f) C 34 (f) = C 14 = C 34

Practical Application: Auto-Correlation Spectrometer |gA2||S2||gA2||S2| S I A/C spectrometer + | g 1 2 | |I 2 | | g 1 2 | |I 2 | = Power Spectrum P(f) g 1 g 3 * |I 2 | g 4 g 1 * |I 2 | g 4 g 3 * |I 2 | = C 13 (f) C 14 * (f) C 34 * (f) Advantage: Cross Correlation Spectra  NO BIAS due to NOISE power

Cross correlation: single polarization feed with 2 reference signals 1. Pol A 3. Ref 1 4. Ref 2 G 1 G 3 * | I o 2 | G 1 G 4 * | I o 2 | G 3 G 4 * | I o 2 | = C 14 = C 34 | g 1 2 | |I 2 | = C 13 (f) C 14 * (f) C 34 * (f) = C 13 A/C Spectrum Contamination

Cross correlation: dual polarization feed with 2 reference signals 1. Pol A 2. Pol B 3. Ref 1 4. Ref 2 G 1 G 3 * | I o 2 | G 1 G 4 * | I o 2 | G 2 G 3 * | I o 2 | G 2 G 4 * | I o 2 | G 3 G 4 * | I o 2 | = C 13 = C 34 = C 14 = C 23 = C 24

Duration 56 s with 0.1 s steps Bandwidth 5 MHz Raw Dynamic Spectra: Time Pol A Pol B frequency

Pol A Pol B frequency Canceled Dynamic Spectra: Time RFI not in reference horn NOT is NOT subtracted ! Non-Toxic to celestial signals

VOLTAGE Spectral Domain Contamination: the VOLTAGE spectrum Estimate { g 1 (f) I (f) } = X 13 (f) g 3 (f) I (f) C 14 (f) C 34 (f) stable on 0.1 second time scale Update every second 1  f Time Domain Contamination: Estimate { g  I(t) } =  x  (t) * g  I (t  Ref Horn FIR filter Effectively… FIR filter coefficients

Time 0.1 sec steps FIR Coefficients + Delay 0.1  s steps

Pol APol B using Ref. “3” using Ref. “4”

Phase Dynamic Pulsar Spectra Pol. A Pol. B Average Spectra Frequency

Phase Dynamic Pulsar Spectra Pol. A Pol. B Frequency Average Spectra Cancellation Applied

Pulse Phase SNR RAW Self-Norm 1 Cancelled2 Cancelled INTEGRATED PULSE PROFILES uncorrected cancelled self- normalized

Phase Dynamic Pulsar Spectra Pol. A Pol. B Average Spectra Frequency Self-Normalized by Total Power Spectra

VLBI

Westerbork Jodrell Bank

Power Spectrum at 840 MHz at Jodrell Bank nearby TV station Cross Correlation Spectrum Jodrell Bank x Westerbork HI absorption z =

VLBI recorder VLBI recorder Celestial Signal RFI off-line correlation + post- correlation processing ….

Conclusions complications of multi-path are contained in complex gains G(f) adaptive filtering with correlation functions preserves phase information…. … equivalent to subtraction of the voltage waveform