Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays) - PowerPoint PPT Presentation

Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays) KSETA Workshop Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin | 17.10.2013 K ARLSRUHE I NSTITUTE OF T ECHNOLOGY (KIT) 80 channel 1 60 channel 2 40 Signal ( µ V) 20 0 -20 -40 -60 -80 0 1000 2000 3000 4000 5000 Time (ns) www.kit.edu KIT – University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association

Cosmic Rays T. Huege Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 2/9

Cosmic Rays What are they made of? 87 % protons 12 % He nuclei 1 % heavy nuclei Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 3/9

Cosmic Rays RADIO R. Engel Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 4/9

Cosmic Rays Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 5/9

Cosmic Rays Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 6/9

Radio Emission Prototypes at Auger LOPES 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 … … YAKUTSK TREND CODALEMA [T. Huege] Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 7/9

Radio Emission Tunka-REX AERA 2010 2011 2012 2013 LOFAR [T. Huege] Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 8/9

Radio emission from air showers Coherent emission at MHz frequencies Two relevant emission mechanisms: Geomagnetic effect Askaryan effect H. Schoorlemmer K.D. de Vries Induction of time-varying current Time-varying net charge of shower Dominant process Relative strength: 14 % Cosmic Rays Radio Emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital Signal Processing for Radio Detection (e.g. of Cosmic Rays)17.10.2013 9/9

Propagation and detection of radio emission Tim Huege Vertical 10 17 eV proton-induced air shower at the site of the Pierre Auger Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Propagation and detection of radio emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Propagation and detection of radio emission Auger Youngsters Meeting 2013, Kathrin Reibelt Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Propagation and detection of radio emission Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform Forward Discrete Fourier Transform: 1 N   2 / [ ] [ ]    i kn N X k x i e  0 n Inverse Discrete Fourier Transform: 1 1 N   2 / [ ] [ ]   i kn N x n X k e N  0 k Amplitude and phase respectively are: 2  [ ] / Re( [ ]) Im( [ ]) 2 ) /  X k N X k X k N Im [ ]   X k arg( [ ]) arctan    X k   Re [ ] X k   Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Fourier transform The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Roman Hiller, Olga Kambeitz, Dmitriy Kostunin, Dmytro Rogozin – Digital signal processing for Radio Detetction - e.g.of Cosmic Rays 17.10.2013

Hardware response Oct. 17th 2012 –

Description Linearity f ( x + y ) = f ( x ) + f ( y ) and f ( ax ) = a · f ( x ) → f ( sin ( ω t )) = α · sin ( ω t + ϕ ) S 21 = α · e i ϕ e.g. from network analyzer 40 20 0 G (dB) − 20 − 40 − 60 − 80 0 20 40 60 80 100 120 f (MHz) Oct. 17th 2012 –

Pulse response f(MHz) f(MHz) Oct. 17th 2012 –

Deconvolution Linearity → uniqueness Convolution theorem f ADC ( t ) = f in ( t ) ∗ g filter ( t ) f ADC ( t ) ∗ f ( t ) = F − 1 ( f ADC ( ν ) · g filter ( ν )) reality: cut attenuation region, f real = f in + f N 0 . 10 0 . 05 0 . 05 S(V) S(V) 0 . 00 0 . 00 − 0 . 05 − 0 . 05 − 0 . 10 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 1 . 6 1 . 8 2 . 0 2 . 2 2 . 4 t(ns) × 10 3 t(ns) × 10 3 Oct. 17th 2012 –

Digital filtering

Raw data channel 1 Signal ( µ V/MHz) channel 2 10 1 0.1 30 40 50 60 70 80 Frequency (MHz) channel 1 200 channel 2 Signal ( µ V) 100 0 -100 -200 0 1000 2000 3000 4000 5000 Time (ns)

Median filter channel 1 Signal ( µ V/MHz) channel 2 10 1 0.1 30 40 50 60 70 80 Frequency (MHz) channel 1 200 channel 2 Signal ( µ V) 100 0 -100 -200 0 1000 2000 3000 4000 5000 Time (ns)

Bandstop filter channel 1 Signal ( µ V/MHz) channel 2 10 1 0.1 30 40 50 60 70 80 Frequency (MHz) channel 1 200 SNR=12.8 !!! channel 2 Signal ( µ V) 100 0 -100 -200 0 1000 2000 3000 4000 5000 Time (ns)

Exercise 1 Draw a Low Pass Filter in frequency and time domain. Explain how it works in frequency/time domain? Oct. 17th 2012 –

Exercise 1 0.08 a . Low-pa ss 0.06 passband plitude transition Amplitude band 0.04 Am 0.02 stopband 0.00 Fre que ncy -0.02 0 10 20 30 Sample number S Oct. 17th 2012 –

Exercise 2 Draw a High Pass filter in frequency and time domain. Tipp: For the time domain use the linearity of the fourier transform to derive the high pass from known spectra (low pass and ?). Explain how it works in frequency/time domain? Oct. 17th 2012 –

Exercise 2 1.25 b. High-pa ss 1.00 plitude Amplitude 0.75 0.50 Am 0.25 0.00 Fre que ncy -0.25 0 10 20 30 Sample number S Oct. 17th 2012 –

Exercise 3 Explain, why both signals have the same spectrum. 0.08 0.5 0.06 0.4 0.04 0.3 0.02 0.2 0.00 0.02 0.1 0.04 0.0 0.06 0.1 0.08 0.10 0.2 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 t(ns) t(ns) FFT 2 10 1 10 0 10 -1 10 -2 10 -3 10 0 20 40 60 80 100 f(MHz) Oct. 17th 2012 –