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Advanced functionality for radio analysis in the Offline software framework of the PierreAuger Observatory

P. Abreubk, M. Agliettaax, E.J. Ahnbz, I.F.M. Albuquerquen,bz, D. Allardaa, I. Allekottea, J. Allencc, P. Allisonce, J. AlvarezCastillobd, J. Alvarez-Munizbr, M. Ambrosioar, A. Aminaeibe, L. Anchordoquicl, S. Andringabk, T. Anticicv, C. Aramoar,

E. Argandabo, F. Arquerosbo, H. Asoreya, P. Assisbk, J. Aublinac, M. Aveai,ag, M. Avenierad, G. Avilai, T. Backeram, M. Balzerah,K.B. Barberj, A.F. Barbosak, R. Bardenetab, S.L.C. Barrosoq, B. Baughmance, J.J. Beattyce, B.R. Beckercj, K.H. Beckeraf,

J.A. Bellidoj , S. BenZvick, C. Beratad, X. Bertoua, P.L. Biermannaj, P. Billoirac, F. Blancobo, M. Blancobp, C. Bleveaf,H. Blumerai,ag, M. Bohacovax,ch, D. Bonciolias, C. Bonifazit,ac, R. Boninoax, N. Borodaibi, J. Brackbx, P. Brogueirabk,

W.C. Brownby, R. Bruijnbt, P. Buchholzam, A. Buenobq, R.E. Burtonbv, K.S. Caballero-Moraai, L. Carameteaj, R. Carusoat,A. Castellinaax, G. Cataldiaq, L. Cazonbk, R. Cesterau, J. Chauvinad, A. Chiavassaax, J.A. Chinellatoo, A. Choubz,cc, J. Chudobax,R.W. Clayj , M.R. Colucciaaq, R. Conceicaobk, F. Contrerash, H. Cookbt, M.J. Cooperj, J. Coppensbe,bg, A. Cordierab, U. Cottibc,

S. Coutucf, C.E. Covaultbv, A. Creusotaa,bm, A. Crisscf, J. Croninch, A. Curutiuaj, S. Dagoret-Campagneab, R. Dallierae, S. Dassof,d,K. Daumillerag, B.R. Dawsonj, R.M. de Almeidau,o, M. De Domenicoat, C. De Donatobd,ap, S.J. de Jongbe, G. De La Vegag,W.J.M. de Mello Junioro, J.R.T. de Mello Netot, I. De Mitriaq, V. de Souzam, K.D. de Vriesbf, G. Decerpritaa, L. del Peralbp,

O. Delignyz, H. Dembinskiai,ag, A. Denkiewiczb, C. Di Giulioao,as, J.C. Diazcb, M.L. Dıaz Castrol , P.N. Diepcm, C. Dobrigkeito,J.C. D’Olivobd, P.N. Dongcm,z, A. Dorofeevbx, J.C. dos Anjosk, M.T. Dovae, D. D’Ursoar, I. Dutanaj, J. Ebrx, R. Engelag,

M. Erdmannak, C.O. Escobaro, A. Etchegoyenb, P. Facal San Luisch, H. Falckebe,bh, G. Farrarcc, A.C. Fautho, N. Fazzinibz,A.P. Fergusonbv, A. Ferrerob, B. Fickcb, A. Filevichb, A. Filipcicbl,bm, S. Fliescherak, C.E. Fracchiollabx, E.D. Fraenkelbf,

U. Frohlicham, B. Fuchsk, R.F. Gamarrab, S. Gambettaan, B. Garcıag, D. Garcıa Gamezbq, D. Garcia-Pintobo, A. Gasconbq,H. Gemmekeah, K. Gesterlingcj, P.L. Ghiaac,ax, U. Giaccariaq, M. Gillerbj, H. Glassbz, M.S. Goldcj, G. Golupa, F. GomezAlbarracine, M. Gomez Berissoa, P. Goncalvesbk, D. Gonzalezai, J.G. Gonzalezai, B. Gookinbx, D. Goraai,bi, A. Gorgiax,

P. Gouffonn, S.R. Gozzinibt, E. Grashornce, S. Grebebe, N. Griffithce, M. Grigatak, A.F. Grilloay, Y. Guardincerrid, F. Guarinoar,G.P. Guedesp, J.D. Haguecj, P. Hansene, D. Hararia, S. Harmsmabf,bg, J.L. Hartonbx, A. Haungsag, T. Hebbekerak, D. Heckag,

A.E. Hervej, C. Hojvatbz, V.C. Holmesj , P. Homolabi, J.R. Horandelbe, A. Hornefferbe, M. Hrabovskyx,y, T. Huegeag, A. Insoliaat,F. Ionitach, A. Italianoat, S. Jiraskovabe, K. Kadijav, K.H. Kampertaf, P. Karhanw, T. Karovax, P. Kasperbz, B. Keglab,

B. Keilhauerag, A. Keivanica, J.L. Kelleybe, E. Kempo, R.M. Kieckhafercb, H.O. Klagesag, M. Kleifgesah, J. Kleinfellerag,J. Knappbt, D.-H. Koangad, K. Koterach, N. Krohmaf, O. Kromerah, D. Kruppke-Hansenaf, F. Kuehnbz, D. Kuempelaf,

J.K. Kulbartzal, N. Kunkaah, G. La Rosaaw, C. Lachaudaa, P. Lautridouae, M.S.A.B. Leaos, D. Lebrunad, P. Lebrunbz, M.A. Leiguide Oliveiras, A. Lemierez, A. Letessier-Selvonac, I. Lhenry-Yvonz, K. Linkai, R. Lopezba, A. Lopez Aguerabr, K. Louedecab,

J. Lozano Bahilobq, A. Lucerob,ax, M. Ludwigai, H. Lyberisz, C. Macolinoac, S. Malderaax, D. Mandatx, P. Mantschbz,A.G. Mariazzie, V. Marinae, I.C. Marisac, H.R. Marquez Falconbc, G. Marsellaav, D. Martelloaq, L. Martinae, O. Martınez Bravoba,H.J. Mathesag, J. Matthewsca,cg, J.A.J. Matthewscj, G. Matthiaeas, D. Maurizioau, P.O. Mazurbz, G. Medina-Tancobd, M. Melissasai,

D. Melob,au, E. Menichettiau, A. Menshikovah, P. Mertschbs, C. Meurerak, S. Micanovicv, M.I. Michelettib, W. Millercj,L. Miramontiap, S. Molleracha, M. Monasorch, D. Monnier Ragaigneab, F. Montanetad, B. Moralesbd, C. Morelloax, E. Morenoba,

J.C. Morenoe, C. Morrisce, M. Mostafabx, C.A. Moura.s,ar, S. Muellerag, M.A. Mullero, G. Mullerak, M. Munchmeyerac,R. Mussaau, G. Navarraax,1, J.L. Navarrobq, S. Navasbq, P. Necesalx, L. Nellenbd, A. Nellesbe,ak, P.T. Nhungcm, N. Nierstenhoeferaf,

D. Nitzcb, D. Nosekw, L. Nozkax, M. Nyklicekx, J. Oehlschlagerag, A. Olintoch, P. Olivaaf, V.M. Olmos-Gilbajabr, M. Ortizbo,N. Pachecobp, D. Pakk Selmi-Deio, M. Palatkax, J. Pallottac, N. Palmieriai, G. Parentebr, E. Parizotaa, A. Parrabr, J. Parrisiusai,R.D. Parsonsbt, S. Pastorbn, T. Paulcd, M. Pechx, J. Pekalabi, R. Pelayobr, I.M. Peper, L. Perroneav, R. Pescean, E. Petermannci,

S. Petreraao, P. Petrincaas, A. Petrolinian, Y. Petrovbx, J. Petrovicbg, C. Pfendnerck, N. Phancj, R. Piegaiad, T. Pierogag, P. Pieronid,M. Pimentabk, V. Pirronelloat, M. Platinob, V.H. Poncea, M. Pontzam, P. Priviterach, M. Prouzax, E.J. Quelc, J. Rautenbergaf,

O. Ravelae, D. Ravignanib, B. Revenuae, J. Ridkyx, M. Risseam, P. Ristoric, H. Riveraap, C. Rivieread, V. Riziao, C. Robledoba,W. Rodrigues de Carvalhobr,n, G. Rodriguezbr, J. Rodriguez Martinoh,at, J. Rodriguez Rojoh, I. Rodriguez-Cabobr,

M.D. Rodrıguez-Frıasbp, G. Rosbp, J. Rosadobo, T. Rosslery, M. Rothag, B. Rouille-d’Orfeuilch, E. Rouleta, A.C. Roverof,C. Ruhleah, F. Salamidaag,ao, H. Salazarba, G. Salinaas, F. Sanchezb, M. Santanderh, C.E. Santobk, E. Santosbk, E.M. Santost,

F. Sarazinbw, S. Sarkarbs, R. Satoh, N. Scharfak, V. Scheriniap, H. Schielerag, P. Schifferak, A. Schmidtah, F. Schmidtch, T. Schmidtai,O. Scholtenbf, H. Schoorlemmerbe, J. Schovancovax, P. Schovanekx, F. Schroederag, S. Schulteak, D. Schusterbw, S.J. Sciuttoe,

M. Scuderiat, A. Segretoaw, D. Semikozaa, M. Settimoam,aq, A. Shadkamca, R.C. Shellardk,l, I. Sidelnikb, G. Siglal,A. Smiałkowskibj, R. Smıdaag,x, G.R. Snowci, P. Sommerscf, J. Sorokinj, H. Spinkabu,bz, R. Squartinih, J. Stapletonce, J. Stasielakbi,

M. Stephanak, A. Stutzad, F. Suarezb, T. Suomijarviz, A.D. Supanitskyf,bd, T. Susav, M.S. Sutherlandca,ce, J. Swaincd,Z. Szadkowskibj,af, M. Szubaag, A. Tamashirof, A. Tapiab, O. Tascauaf, R. Tcaciucam, D. Tegoloat,az, N.T. Thaocm, D. Thomasbx,

∗Corresponding author: augerpc@fnal.gov1Deceased2at Konan University, Kobe, Japan

Preprint submitted to Nuclear Instruments and Methods in Physics Research, A February 4, 2011

J. Tiffenbergd, C. Timmermansbg,be, D.K. Tiwaribc, W. Tkaczykbj, C.J. Todero Peixotom,s, B. Tomebk, A. Tonachiniau,P. Travnicekx, D.B. Tridapallin, G. Tristramaa, E. Trovatoat, M. Tuerosbr,d, R. Ulrichcf,ag, M. Ungerag, M. Urbanab, J.F. Valdes

Galiciabd, I. Valinobr,ag, L. Valorear, A.M. van den Bergbf, B. Vargas Cardenasbd, J.R. Vazquezbo, R.A. Vazquezbr, D. Vebericbm,bl,V. Verzias, M. Videlag, L. Villasenorbc, H. Wahlberge, P. Wahrlichj , O. Wainbergb, D. Warnerbx, A.A. Watsonbt, M. Weberah,

K. Weidenhauptak, A. Weindlag, S. Westerhoffck, B.J. Whelanj , G. Wieczorekbj, L. Wienckebw, B. Wilczynskabi, H. Wilczynskibi,M. Will ag, C. Williamsch, T. Winchenak, L. Winderscl, M.G. Winnickj, M. Wommerag, B. Wundheilerb, T. Yamamotoch,2,

P. Younkam,bx, G. Yuanca, B. Zamoranobq, E. Zasbr, D. Zavrtanikbm,bl, M. Zavrtanikbl,bm, I. Zawcc, A. Zepedabb, M. Ziolkowskiam

aCentro Atomico Bariloche and Instituto Balseiro (CNEA-UNCuyo-CONICET), San Carlos de Bariloche, ArgentinabCentro Atomico Constituyentes (Comision Nacional deEnergıa Atomica/CONICET/UTN-FRBA), Buenos Aires, Argentina

cCentro de Investigaciones en Laseres y Aplicaciones,CITEFA and CONICET, ArgentinadDepartamento de Fısica, FCEyN, Universidad de BuenosAires y CONICET, Argentina

eIFLP, Universidad Nacional de La Plata and CONICET, LaPlata, ArgentinafInstituto de Astronomıa y Fısica del Espacio (CONICET-UBA), Buenos Aires, Argentina

gNational Technological University, Faculty Mendoza(CONICET/CNEA), Mendoza, ArgentinahPierre Auger Southern Observatory, Malargue, Argentina

iPierre Auger Southern Observatory and Comision Nacionalde Energıa Atomica, Malargue, ArgentinajUniversity of Adelaide, Adelaide, S.A., Australia

kCentro Brasileiro de Pesquisas Fisicas, Rio de Janeiro,RJ,BrazillPontifıcia Universidade Catolica, Rio de Janeiro, RJ,Brazil

mUniversidade de Sao Paulo, Instituto de Fısica, SaoCarlos, SP, BrazilnUniversidade de Sao Paulo, Instituto de Fısica, SaoPaulo, SP, Brazil

oUniversidade Estadual de Campinas, IFGW, Campinas, SP,BrazilpUniversidade Estadual de Feira de Santana, Brazil

qUniversidade Estadual do Sudoeste da Bahia, Vitoria daConquista, BA, BrazilrUniversidade Federal da Bahia, Salvador, BA, Brazil

sUniversidade Federal do ABC, Santo Andre, SP, BraziltUniversidade Federal do Rio de Janeiro, Instituto deFısica, Rio de Janeiro, RJ, Brazil

uUniversidade Federal Fluminense, Instituto de Fisica,Niteroi, RJ, BrazilvRudjer Boskovic Institute, 10000 Zagreb, Croatia

wCharles University, Faculty of Mathematics and Physics,Institute of Particle and Nuclear Physics, Prague, CzechRepublicxInstitute of Physics of the Academy of Sciences of theCzech Republic, Prague, Czech Republic

yPalacky University, RCATM, Olomouc, Czech RepubliczInstitut de Physique Nucleaire d’Orsay (IPNO),Universite Paris 11, CNRS-IN2P3, Orsay, FranceaaLaboratoire AstroParticule et Cosmologie (APC),Universite Paris 7, CNRS-IN2P3, Paris, FranceabLaboratoire de l’Accelerateur Lineaire (LAL),Universite Paris 11, CNRS-IN2P3, Orsay, France

acLaboratoire de Physique Nucleaire et de Hautes Energies(LPNHE), Universites Paris 6 et Paris 7, CNRS-IN2P3, Paris,FranceadLaboratoire de Physique Subatomique et de Cosmologie(LPSC), Universite Joseph Fourier, INPG, CNRS-IN2P3, Grenoble,France

aeSUBATECH, CNRS-IN2P3, Nantes, FranceafBergische Universitat Wuppertal, Wuppertal, Germany

agKarlsruhe Institute of Technology - Campus North -Institutfur Kernphysik, Karlsruhe, GermanyahKarlsruhe Institute of Technology - Campus North -Institutfur Prozessdatenverarbeitung und Elektronik,Karlsruhe, Germany

aiKarlsruhe Institute of Technology - Campus South -Institutfur Experimentelle Kernphysik (IEKP), Karlsruhe,GermanyajMax-Planck-Institut fur Radioastronomie, Bonn, Germany

akRWTH Aachen University, III. Physikalisches Institut A,Aachen, GermanyalUniversitat Hamburg, Hamburg, Germany

amUniversitat Siegen, Siegen, GermanyanDipartimento di Fisica dell’Universita and INFN,Genova,Italy

aoUniversita dell’Aquila and INFN, L’Aquila, ItalyapUniversita di Milano and Sezione INFN, Milan, Italy

aqDipartimento di Fisica dell’Universita del Salento andSezione INFN, Lecce, ItalyarUniversita di Napoli ”Federico II” and Sezione INFN,Napoli, ItalyasUniversita di Roma II ”Tor Vergata” and Sezione INFN,Roma,Italy

atUniversita di Catania and Sezione INFN, Catania, ItalyauUniversita di Torino and Sezione INFN, Torino, Italy

avDipartimento di Ingegneria dell’Innovazionedell’Universita del Salento and Sezione INFN, Lecce, ItalyawIstituto di Astrofisica Spaziale e Fisica Cosmica diPalermo(INAF), Palermo, Italy

axIstituto di Fisica dello Spazio Interplanetario (INAF),Universita di Torino and Sezione INFN, Torino, ItalyayINFN, Laboratori Nazionali del Gran Sasso, Assergi(L’Aquila), Italy

azUniversita di Palermo and Sezione INFN, Catania, ItalybaBenemerita Universidad Autonoma de Puebla, Puebla,Mexico

bbCentro de Investigacion y de Estudios Avanzados del IPN(CINVESTAV), Mexico, D.F., MexicobcUniversidad Michoacana de San Nicolas de Hidalgo,Morelia,Michoacan, Mexico

bdUniversidad Nacional Autonoma de Mexico, Mexico, D.F.,MexicobeIMAPP, Radboud University, Nijmegen, Netherlands

bfKernfysisch Versneller Instituut, University ofGroningen, Groningen, NetherlandsbgNIKHEF, Amsterdam, NetherlandsbhASTRON, Dwingeloo, Netherlands

2

biInstitute of Nuclear Physics PAN, Krakow, PolandbjUniversity of Łodz, Łodz, Poland

bkLIP and Instituto Superior Tecnico, Lisboa, PortugalblJ. Stefan Institute, Ljubljana, Slovenia

bmLaboratory for Astroparticle Physics, University ofNova Gorica, SloveniabnInstituto de Fısica Corpuscular, CSIC-Universitat deValencia, Valencia, Spain

boUniversidad Complutense de Madrid, Madrid, SpainbpUniversidad de Alcala, Alcala de Henares (Madrid),Spain

bqUniversidad de Granada& C.A.F.P.E., Granada, SpainbrUniversidad de Santiago de Compostela, Spain

bsRudolf Peierls Centre for Theoretical Physics,Universityof Oxford, Oxford, United KingdombtSchool of Physics and Astronomy, University of Leeds,United Kingdom

buArgonne National Laboratory, Argonne, IL, USAbvCase Western Reserve University, Cleveland, OH, USA

bwColorado School of Mines, Golden, CO, USAbxColorado State University, Fort Collins, CO, USA

byColorado State University, Pueblo, CO, USAbzFermilab, Batavia, IL, USA

caLouisiana State University, Baton Rouge, LA, USAcbMichigan Technological University, Houghton, MI, USA

ccNew York University, New York, NY, USAcdNortheastern University, Boston, MA, USAceOhio State University, Columbus, OH, USA

cfPennsylvania State University, University Park, PA, USAcgSouthern University, Baton Rouge, LA, USA

chUniversity of Chicago, Enrico Fermi Institute, Chicago,IL, USAciUniversity of Nebraska, Lincoln, NE, USA

cjUniversity of New Mexico, Albuquerque, NM, USAckUniversity of Wisconsin, Madison, WI, USA

clUniversity of Wisconsin, Milwaukee, WI, USAcmInstitute for Nuclear Science and Technology (INST), Hanoi, Vietnam

Abstract

The advent of the Auger Engineering Radio Array (AERA) necessitates the development of a powerful framework for theanalysis of radio measurements of cosmic ray air showers. AsAERA performs “radio-hybrid” measurements of air shower radioemission in coincidence with the surface particle detectors and fluorescence telescopes of the Pierre Auger Observatory, the radioanalysis functionality had to be incorporated in the existing hybrid analysis solutions for fluoresence and surface detector data.This goal has been achieved in a natural way by extending the existing Auger Offline software framework with radio functionality.In this article, we lay out the design, highlights and features of the radio extension implemented in the Auger Offline framework.Its functionality has achieved a high degree of sophistication and offers advanced features such as vectorial reconstruction of theelectric field, advanced signal processing algorithms, a transparent and efficient handling of FFTs, a very detailed simulation ofdetector effects, and the read-in of multiple data formats including data from various radio simulation codes. The source code ofthis radio functionality can be made available to interested parties on request.

Keywords: cosmic rays, radio detection, analysis software, detectorsimulation

1. Introduction

Forty years after the initial discovery of radio emission fromextensive air showers [1], the CODALEMA [2] and LOPES [3]experiments have re-ignited very active research activities in thefield of radio detection of cosmic ray air showers. Nowadays,the field is in a phase of transition from first-generation experi-ments covering an area of less than 0.1 km2 to large-scale arraysof tens of km2. In particular, the Auger Engineering Radio Ar-ray (AERA) [4] will complement the southern site of the PierreAuger Observatory [5] with 161 autonomous radio detector sta-tions covering an area of≈ 20 km2.

One particular merit of the Pierre Auger Observatory is itshybrid mode of observation, which uses coincident detection of

extensive air showers with both optical fluorescence telescopes(FD) and surface particle detectors (SD) to gain in-depth infor-mation on the measured air showers. Consequently, the analysissoftware has to support complete hybrid processing and inter-pretation of the data. This requirement is fulfilled by the AugerOffline software framework [6]. To take full advantage of theradio data taken in the hybrid environment of the Pierre AugerObservatory, it is clear that also radio analysis functionality,which has so far been existing in a separate software package[7], had to be included in this hybrid analysis framework.

In this article, we describe how we have therefore built ad-vanced radio analysis functionality into the Auger Offline soft-ware framework. The general structure of the radio implemen-

3

tation in the Offline framework will be discussed in section 2.A number of innovative features have been realized in this con-text for the very first time. These and other highlights will bediscussed in section 3. Finally, in section 4 we demonstratehow the advanced radio functionality embedded in the Offlineframework can be used to carry out a complete detector simula-tion and event reconstruction on the basis of a simulated radioevent.

2. Embedding radio functionality in the Offline framework

The Offline framework has a clear structure to allow for easymaintenance and ongoing shared development over the wholelife-time of the Pierre Auger Observatory [6]. In particular,there is a clear separation between the internal representationof the Detectorand theEvent. The Detectorprovides accessto all of the relevant detector information such as the positionsof detector stations in the field, the hardware associated withthese stations, etc. TheEventdata structures in contrast holdall of the data applying to a specific event, such as ADC traces,but also reconstructed quantities such as the event geometry.There is no direct connection between these two entities. In-stead, analysisModulesuse the defined interfaces of both theDetectorand Eventdata structures to carry out their specificanalysis tasks. No interface exists either between separate anal-ysis modules, which can only propagate their results throughthe Eventdata structure. This ensures that dependencies be-tween analysis modules are kept to a minimum and facilitatesthe replacement of individual modules with alternative imple-mentations, thereby providing a very high degree of flexibility.

Clearly, the radio analysis functionality had to be imple-mented following the same philosophy. The hierarchical im-plementation of the radio parts of both theDetectorandEventclasses in addition to the existing FD- and SD-specific classesis depicted in Fig. 1. In analogy to the hierarchy ofStationsandPMTs in the SD functionality, the implementation of the radiodata structures has been divided intoStationsandChannels. AStationrepresents one location in the field at which the electricfield of the radio waves is measured. Data stored atStationleveltherefore represents the physical electric field devoid of any de-tector influence except for the location (and limited observingbandwidth) of theStation. In contrast,Channelsrepresent theindividual antenna channels at which the “raw” measurementisperformed by an ADC digitizing voltages. This clear separationbetweenChannelsandStationsis a very powerful concept andis original to the radio implementation in Offline. We will dis-cuss its significance, among other highlights, in the followingsection.

3. Highlights of the radio analysis functionality

The radio functionality in the Offline framework provides anumber of unique features facilitating an advanced radio dataanalysis. In this section, we will describe some of these high-lights.

3.1. Clear separation of Channel- and Station-levels

When analyzing radio data, one is faced with two different“levels”. The Channellevel is defined by the detector chan-nels acquiring the raw data. These data consist of time-seriesof samples digitized with a sampling rate adequate for the fre-quency window of interest. Each sample denotes a scalar quan-tity such as an ADC count recorded by the channel ADC. Low-level detector effects such as the correction for the frequency-dependent response of cables, filters and amplifiers are treatedon this level for eachChannelindividually. Likewise, detector-related studies such as the evaluation of trigger efficiencieswould be typically performed onChannellevel. When read-ing in measured data files, the raw data (ADC counts) are filledinto the appropriateChanneldata structures.

In contrast, theStationlevel is defined by the physical elec-tric field present at a given location in the field, stored as atime-series of three-dimensional vectors. It is onStationlevelthat radio pulses are identified and quantified, before a geom-etry reconstruction of the given event is performed. Once theevent reconstruction has been completed, the data atStationlevel no longer have any dependence on the detector character-istics, except for the location and limited observing bandwidthof the measurement. A reconstruction of the electric field ontheStationlevel is therefore suited best for a comparison of radiomeasurements of different experiments, as well as for the com-parison of radio measurements with corresponding simulations.Since simulated electric field traces provided by radio emissionmodels also represent physical electric fields independentof agiven detector, they are read in on theStationlevel.

Analysis modules in Offline usually work on eitherChannelor Stationlevel, and typically it is very clear which analysis stephas to be performed on which level. The transition between thetwo levels is performed by applying the characteristics of theantennas associated to each of theChannels. This transitioncan be employed in both directions, fromStationto Channelor vice-versa. The transition from aStationto the associatedChannelsis typically performed to calculate the response ofthe individual detectorChannelsto an electric field providedby simulations. The opposite transition is required when re-constructing the three-dimensional electric field vector from thedata recorded by the (typically) two measurement channels inthe field. This reconstruction will be further discussed in sec-tion 3.7.

3.2. Read-in from different data sources

The Event data structures are complemented with readerfunctionality to populate them with data available in one ofseveral file formats for both experimentally measured data andsimulated radio event data. Due to its wealth of supported for-mats and the possibility of easy extension with new formats,the radio functionality in Offline therefore provides very power-ful functionality to compare data and simulations from differentsources, which again is an original feature usually not found inthe analysis software suites developed in the contexts of otherexperiments. At the time of writing, the following data formatsare supported. For experimental data:

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• measurement data from two different prototype setups sit-uated at the Balloon Launching Station of the Pierre AugerObservatory [8, 9]

• measurement data from AERA [4]

For simulation data, the following formats are currently read-able:

• simulation data from MGMR [10]

• simulation data from REAS2 and REAS3 [11, 12]

• simulation data from ReAIRES [13]

3.3. Modular approach

The strict interface design of theDetector, theEventand theanalysis modules allows for a very modular implementation ofradio analysis functionality. As the analysis modules are thepart of the code typically the most exposed to the end-user, theirinterface has been kept relatively simple. End-users developinganalysis functionality for Offline therefore only need relativelybasic proficiency in C++.

An analysis application within Offline is defined through a“module sequence” in XML syntax, an example of which islisted in section 4. In such a module sequence, analysis mod-ules are chained in a meaningful sequence to perform a specificanalysis task. The individual modules do not communicate di-rectly with each other, but only share data through theEventdata structures. Consequently, modules can easily be removed,replaced or rearranged within a module sequence. This does notrequire recompilation of the source code. Additionally, eachmodule can be configured individually through XML files.

3.4. Transparent FFT handling

Radio analyses typically apply algorithms both on time- andfrequency-domain data. As a consequence, they heavily relyon fast Fourier transforms (FFTs). The Offline framework hasthus been extended with FFT functionality based on the FFTWlibrary [14]. A special feature of this implementation is thatFFTs are handled completely transparently in the background.The user does not need to invoke FFTs manually.

This is realized by the use ofFFTDataContainersas illus-trated in Fig. 2. These containers encapsulate both the time- andfrequency-domain representations of radio data on theChannelandStationlevels. The user can access both the time-domainand frequency-domain data at any time. TheFFTDataCon-tainer keeps track of which representation has been changedlast and whether an FFT has to be performed or not before thedata requested by the user are returned. All data are passedby reference and changed in place, so that even traces with anextreme length can be handled efficiently.

As a consequence of this design, the user can simply chainanalysis modules working in any of the two domains withoutworrying which domain has last been worked on. (There isa performance benefit when grouping modules working in thesame domain together, but it is not very significant.)

3.5. Advanced analysis modules

A number of analysis modules performing recurring steps inadvanced radio analysis pipelines are available by default. Theycan easily be included or excluded from module sequences asneeded:

• modules applying bandpass filters to theChannelandSta-tion levels

• a module performing an up-sampling of under-sampleddata

• a module resampling data to a different time-base

• a module suppressing narrow-band radio frequency inter-ference through a “median filter”

• a module performing an enveloping of time traces via aHilbert transform

• a module determining timing differences between differ-ent antenna stations from the reference phases of a beacontransmitter

• modules applying a windowing function (e.g., Hann win-dow) to theChannelandStationlevels

3.6. Detailed simulation of the detector response

When comparing measured data to simulated radio pulsesfrom various models, it is required to perform a detailed simu-lation of the effects introduced by the various detector compo-nents. This encompasses in particular:

• the complex response (impulse response defined by thefrequency-dependent amplitudes and phases3) of all theanalogue components (cables, filters, amplifiers) in eachindividual channel

• the frequency- and direction-dependent complex gain (or“effective antenna height”) of the antenna connected toeach individual channel (cf. Fig. 3)

• effects introduced by the sampling of the data with a givensampling rate

• saturation effects occurring at the ADCs

• effects introduced by the layout of the array, including ge-ometric effects occurring on large scales due to the curva-ture of the Earth

All of this functionality has been implemented in the Offlineframework. At the moment, detector description data are pro-vided as XML files. Later, a transition to MySQL or SQLite

3A full transport matrix representing the transmission in forward direction,transmission in backward direction, as well as the reflections on the input andoutput could be implemented for a more detailed description. For the moment,however, we assume that impedance matching in the experimental setup is suffi-ciently good so that transmission in the forward direction describes the detectorresponse with good precision.

5

E, xN, y

z

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Figure 3: The antenna characteristics are defined in a spherical coordinate sys-tem with the antenna in its center. The effective antenna height~Heff for emis-sion coming from a given arrival direction is decomposed into the componentsalong the unit vectorseθ andeφ. These local (i.e., arrival direction-dependent)unit vectors lie in the plane perpendicular to the Poynting vector, which alignswith the dashed blue line in this figure for the incoming direction defined byθandφ. As electromagnetic waves in air have no electric field component alongthe Poynting vector, this representation is complete. The antenna height itself isa frequency-dependent, complex quantity, the amplitude ofwhich denotes thegain of the antenna, while the phase provides information about signal delaysand dispersion.

databases is foreseen and can be performed transparently. Thecomplex response of individualChannelsis provided via aRe-sponseMapdetailing the hardware elements comprising eachindividual channel. The overall response of each channel isthen calculated on-the-fly from the tabulated responses of eachindividual hardware component listed in theResponseMap. Acaching mechanism ensures that overall responses are only re-calculated when needed.

3.7. Vectorial E-field reconstruction

The physical electric field is a three-dimensional, vectorialquantity. When comparing results from different experimentsor experimental results and radio emission models, the electricfield is the quantity of choice, as in principle it has no depen-dence on the detector (except for the location at which it wasmeasured and the limited observing bandwidth). Most radio de-tectors, however, are only equipped with two channels per po-sition in the field, typically measuring the east-west and north-south linear polarization components. In other words, theyonlymeasure a projection of the three-dimensional electric field tothe horizontal plane. In such a setup, twoChannelsare avail-able at each detector station, one connected with an east-west-aligned antenna and one connected with a north-south-alignedantenna. The (scalar) response of each individual channel to theincoming electric field can be calculated as the dot product be-tween the electric field vector and the vectorial representationof the effective antenna height. The effective antenna height isrelated to the gain of the antenna and depends on the arrivaldirection and frequency (cf. Fig. 3). Consequently, this calcu-lation is best done in the frequency domain.

Figure 4: Hierarchical structure of the radio-related quantities stored in ADSTfiles. The individual classes constitute logical entities present in theEventdatastructures, storing for example information on Monte Carlogenerated quanti-ties inRGenStationand the reconstructed radio lateral distribution functioninRdLDF.

The more difficult problem is the inverse calculation: the re-construction of the three-dimensional electric field vector fromthe two-dimensional measurement. This inversion is possible ifthe arrival direction of the electromagnetic wave is known,be-cause electromagnetic waves in the atmosphere constitute trans-verse waves, the electric field of which lies in a plane perpen-dicular to the direction of propagation.4

The antenna characteristics needed to reconstruct the vecto-rial electric field on theStationlevel depend on the arrival di-rection. This arrival direction, however, is not availableuntilafter the reconstruction on the basis of theStationlevel three-dimensional electric field. Therefore, an iterative approachstarting with a reasonable initial arrival direction is performedin the radio analysis in Offline. The reconstructed arrival direc-tion quickly converges to its final value, and the vertical com-ponent of the electric field can be reconstructed from the two-dimensional measurement (cf. section 4). This reconstructionscheme is truly original to the Offline radio functionality.

3.8. Advanced data output

End-users performing a higher-level analysis usually do notneed access to all the raw data of each individual event. Theyrather need information about reconstructed quantities derivedby the low-level analysis pipeline. A data format to store suchquantities reconstructed by an Offline-based analysis is the Ad-vanced Data Summary Tree (ADST). ADST files hold relevantdata for FD, SD and now also radio-reconstructed quantities.The structure of the radio data within the ADST files is de-picted in Fig. 4. In addition to accessing the content of ADSTfiles directly from end-user analysis programs, a graphicaluserinterface exists for browsing the contents of ADST files and vi-sualizing the included events. ThisEventBrowserhas also beencomplemented with radio-specific functionality, so that also the

4At the moment, we assume that the propagation direction of radio emissionfrom extensive air showers can be approximated well with theshower axis.

6

radio part of the event (such as traces, spectra, a map of the ar-ray and event geometry, ...) can be visualized in a user-friendlyand intuitive fashion.

3.9. Easy extension to hybrid analysis

One of the main motivations for including radio functional-ity in the Offline framework was to exploit the hybrid nature ofthe data acquired within the Pierre Auger Observatory. Han-dling all detector data within the same analysis software willmake it easily possible to develop analysis procedures combin-ing data from SD and radio, FD and radio or SD, FD and radioaltogether. This will be possible both for measured data andfor simulated events. Developing the “radio-hybrid” analysisstrategies is yet a challenge for the future. The technical pre-requisites for this development have, however, been success-fully provided with the inclusion of radio functionality intheOffline framework.

4. Example for an analysis pipeline

To illustrate the flexibility and level of sophisticationachieved with the radio functionality in Offline, we discusshere a module sequence processingsimulated data with areconstruction pipeline that incorporates all relevant detectoreffects. Each line in the XML file listed in Fig. 5 denotesa module being invoked to perform a specific analysis step.Radio modules starting withRdChannelmanipulate the eventdata on theChannel level, modules starting withRdStationmanipulate data on theStation level. The modules startingwith RdAntennaperform the transitions between the two levels(cf. section 3.7). Modules can easily be removed, replaced orrearranged to change the analysis procedure without havingtorecompile the source code. In the following, we will brieflydiscuss the individual steps of the module sequence and showhow the signal evolves on its way through the analysis pipeline.

4.1. Read-in and association

The module sequence starts with the read-in of simulatedevent data5 using theEventFileReaderOG module. Afterread-in, the simulated data represent an “abstract” simulationthat is not yet associated to any detector stations. This as-sociation is performed by theRdStationAssociatior mod-ule, which associates the simulated signal traces with the corre-sponding stations in the field, and at the same time pads themappropriately to ensure that the signal falls into the correct partof the time series trace. Afterwards, theStationdata structurecontains the physical electric field vector as predicted by thesimulation, without the inclusion of any detector effects. Thecorresponding traces and spectra are depicted in Fig. 6.

5The example event used here has an energy of 2.1 · 1018 eV, a zenith angleof 58.4◦, an azimuth angle of 291.0◦ corresponding to an arrival direction ofapproximately SSW, and has been simulated with a proton as primary particle.

1 <module > EventFileReaderOG </module >

2 <module > RdStationAssociator </module >3 <!-- cf. Fig. 6 raw simulated electric fields -->

4

5 <module > RdAntennaStationToChannelConverter </module >

6 <module > RdChannelNoiseGenerator </module >7 <!-- cf. Fig. 7 voltages at antenna foot - points -->8

9 <module > RdChannelResponseIncorporator </module >10 <!-- cf. Fig. 8 voltages at ADC -->

11

12 <module > RdChannelResampler </module >13 <module > RdChannelTimeSeriesClipper </module >

14 <module > RdChannelVoltageToADCConverter </module >15 <!-- signal is now equivalent to raw ADC values -->

16

17 <module > RdChannelADCToVoltageConverter </module >

18 <module > RdChannelPedestalRemover </module >19 <module > RdChannelResponseIncorporator </module >20 <module > RdChannelRFISuppressor </module >

21 <module > RdChannelUpsampler </module >22 <module > RdChannelBandpassFilter </module >

23 <!-- cf. Fig. 9 voltages after signal processing -->24

25 <loop numTimes ="unbounded">

26 <module > RdAntennaChannelToStationConverter </module >27 <module > RdStationSignalReconstructor </module >

28 <module > RdDirectionConvergenceChecker </module >29 <module > RdPlaneFit </module >

30 </loop>31

32 <module > RdStationWindowSetter </module >

33 <!-- cf. Fig. 10 field strengths in clipped trace -->34

35 <module > RdStationTimeSeriesWindower </module >36 <!-- cf. Fig. 11 Hann - windowed field strengths -->

37

38 <module > RecDataWriter </module >

Figure 5: Example module sequence for performing a full detector simulationand event reconstruction of a simulated radio event. The time series data andfrequency spectra extracted at certain steps during this analysis pipeline areillustrated with the figures referenced in the sequence. Analysis modules canbe re-ordered or exchanged without any recompilation of thesource code.

4.2. Simulation of the detector response

The next steps in the module sequence change the datasuch that they become equivalent to data measured experimen-tally. TheRdAntennaStationToChannelConverter calcu-lates the signal voltages that eachChannelof a givenStationwould have seen at the foot-points of the corresponding an-tennas by folding in the antenna response applicable to eachindividual channel. In the typical case of two antennaChan-nels per Station, this means that the three-dimensional elec-tric field vector is projected to a two-dimensional surface.TheRdChannelNoiseGenerator module then adds broad-bandradio noise to the event. The resulting, simulated data for theeast and north channels are shown in Fig. 7.

The following call of theRdChannelResponseIncorporator incorporates the (for-ward) detector response of the cables, filters and amplifierscomprising the correspondingChannel. After this module, thesignal represents the voltages that would be measured at thechannel ADCs, depicted in Fig. 8.

The following steps convert this voltage at the ADCs tothe signal that the channel ADC would indeed have mea-sured. TheRdChannelResampler module re-samples theChannel time series data to the time-base with which thedata are sampled in the experiment. (The prerequisite to

7

this module is that high-frequency components which couldlead to aliasing effects have been suppressed. This is en-sured here because theRdChannelResponseIncorporatorincludes filters that do just that in the experimental setup.) TheRdChannelTimeSeriesClipper then clips theChanneltracesto the number of samples which are taken in the experimentalsetup. Finally, theRdChannelVoltageToADCConverter con-verts the voltages of each sample to ADC counts that wouldhave been recorded by the channel ADCs, thereby taking intoaccount quantization and saturation effects.

At this point, all of the relevant detector effects have been in-corporated in the simulated traces. In other words, the datanowhave the same properties as measured data directly after read-in. Consequently, the remainder of the reconstruction pipelineis identical to one that would be applied directly to measureddata. Choosing the reconstruction procedure applied to thesim-ulated data identical to the one applied to measured data makessure that even subtle changes introduced by individual analysismodules can be investigated on the basis of simulations.

4.3. Signal cleaning

After converting the ADC counts back to voltageswith the RdChannelADCToVoltageConverter and re-moving a possible DC offset of the ADC with theRdChannelPedestalRemover, the characteristics of the ana-logue components of eachChannelare folded out from the datawith a second call of theRdChannelResponseIncorporator.

The following steps are intended to improve the reconstruc-tion quality by the use of advanced digital processing tech-niques. In a first step, theRdChannelRFISuppressor mod-ule suppresses narrow-band signals (e.g., TV carriers presentin measured data) using a median filter. It is followed by theRdChannelUpsampler module which correctly reconstructs(interpolates) the signal on a finer time-base. (This is possi-ble if the complete signal information is present in the digi-tized signal, i.e., if the Nyquist criterion for data sampling isfulfilled.) In a further step the signal bandwidth is limitedby adigital bandpass filter using theRdChannelBandpassFiltermodule. After these steps, the signal is ready for the reconstruc-tion of the three-dimensional electric field vector and looks likethe data presented in Fig. 9.

4.4. Vectorial reconstruction

The following loop performs an iterative reconstruction ofthe three-dimensional electric field vector and the signal arrivaldirection. The RdAntennaChannelToStationConverter

performs the reconstruction of the three-dimensional elec-tric field described in section 3.7. Afterwards, theRdStationSignalReconstructor identifies the times atwhich radio pulses have been detected and quantifies the param-eters of these pulses. Next, theRdPlaneFit reconstructs thearrival direction of the radio signal with a plane-wave assump-tion based on the previously established pulse arrival times.Finally, theRdDirectionConvergenceCheckermodule testswhether the iterative procedure has converged or not and breaksthe loop accordingly.

4.5. Post-processing

After breaking the iterative reconstruction loop, the vecto-rial, detector-independent electric field has been completely re-constructed. For practical purposes, the time series is thenrestricted to a window of 500 ns around the detected pulseswith the RdStationWindowSetter. This leads to leak-age effects in the frequency spectra, visible in Fig. 10. Tosuppress these leakage artifacts, a Hann window is appliedwith the RdStationTimeSeriesWindower. The final recon-structed signal is then seen in Fig. 11. As a last step, theRecDataWriter call writes out the reconstructed event data toan ADST file for further processing in higher-level analyses.

8

5. Conclusions and Outlook

We have implemented a complete set of radio analysis func-tionality in the Offline software framework of the Pierre AugerObservatory. The radio functionality has been included in acanonical and seamless way in addition to the existing SD andFD functionality. This approach will make the realization of“radio-hybrid” analysis strategies in the future straight-forward.

Already now, however, the radio functionality in Offline hasreached a high degree of sophistication with highlights such asa very fine-grained simulation of detector effects, advanced sig-nal processing algorithms, transparent and efficient handling ofFFTs, read-in of multiple file formats for measured and sim-ulated radio data, and in particular the reconstruction of thethree-dimensional electric field vector from two-dimensionalmeasurements. Planned improvements encompass the imple-mentation of a curved fit, inclusion of interferometric radioanalysis functionality, and the handling of a time-variable de-tector including a fine-grained treatment of the instrumental cal-ibration.

Parties interested in using the functionality are encouraged tocontact the corresponding author. The source code can be madeavailable on request.

Acknowledgements

We would like to thank our colleagues from the LOPES col-laboration for providing the source code of their analysis soft-ware openly to the public [15]. Many algorithms for radio anal-ysis and reconstruction have been inspired by or based on thoseused within LOPES. This research has been supported by grantnumber VH-NG-413 of the Helmholtz Association.

The successful installation and commissioning of the PierreAuger Observatory would not have been possible without thestrong commitment and effort from the technical and adminis-trative staff in Malargue.

We are very grateful to the following agencies and organi-zations for financial support: Comision Nacional de Energ´ıaAtomica, Fundacion Antorchas, Gobierno De La Provincia deMendoza, Municipalidad de Malargue, NDM Holdings andValle Las Lenas, in gratitude for their continuing cooperationover land access, Argentina; the Australian Research Coun-cil; Conselho Nacional de Desenvolvimento Cientıfico e Tec-nologico (CNPq), Financiadora de Estudos e Projetos (FINEP),Fundacao de Amparo a Pesquisa do Estado de Rio de Janeiro(FAPERJ), Fundacao de Amparo a Pesquisa do Estado de SaoPaulo (FAPESP), Ministerio de Ciencia e Tecnologia (MCT),Brazil; AVCR, AV0Z10100502 and AV0Z10100522, GAAVKJB300100801 and KJB100100904, MSMT-CR LA08016,LC527, 1M06002, and MSM0021620859, Czech Repub-lic; Centre de Calcul IN2P3/CNRS, Centre National dela Recherche Scientifique (CNRS), Conseil Regional Ile-de-France, Departement Physique Nucleaire et Corpuscu-laire (PNC-IN2P3/CNRS), Departement Sciences de l’Univers(SDU-INSU/CNRS), France; Bundesministerium fur Bildungund Forschung (BMBF), Deutsche Forschungsgemeinschaft

(DFG), Finanzministerium Baden-Wurttemberg, Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF), Minis-terium fur Wissenschaft und Forschung, Nordrhein-Westfalen,Ministerium fur Wissenschaft, Forschung und Kunst, Baden-Wurttemberg, Germany; Istituto Nazionale di Fisica Nucle-are (INFN), Istituto Nazionale di Astrofisica (INAF), Minis-tero dell’Istruzione, dell’Universita e della Ricerca (MIUR),Gran Sasso Center for Astroparticle Physics (CFA), Italy; Con-sejo Nacional de Ciencia y Tecnologıa (CONACYT), Mexico;Ministerie van Onderwijs, Cultuur en Wetenschap, NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Sticht-ing voor Fundamenteel Onderzoek der Materie (FOM), Nether-lands; Ministry of Science and Higher Education, Grant Nos.1 P03 D 014 30 and N N202 207238, Poland; Fundacao paraa Ciencia e a Tecnologia, Portugal; Ministry for Higher Edu-cation, Science, and Technology, Slovenian Research Agency,Slovenia; Comunidad de Madrid, Consejerıa de Educacion dela Comunidad de Castilla La Mancha, FEDER funds, Min-isterio de Ciencia e Innovacion and Consolider-Ingenio 2010(CPAN), Generalitat Valenciana, Junta de Andalucıa, Xuntade Galicia, Spain; Science and Technology Facilities Coun-cil, United Kingdom; Department of Energy, Contract Nos.DE-AC02-07CH11359, DE-FR02-04ER41300, National Sci-ence Foundation, Grant No. 0969400, The Grainger Founda-tion USA; ALFA-EC / HELEN, European Union 6th Frame-work Program, Grant No. MEIF-CT-2005-025057, EuropeanUnion 7th Framework Program, Grant No. PIEF-GA-2008-220240, and UNESCO.

References

[1] J. V. Jelley, J. H. Fruin, N. A. Porter, et al., Radio Pulses from ExtensiveCosmic-Ray Air Showers, Nature 205 (1965) 327.

[2] D. Ardouin, A. Belletoile, D. Charrier, et al., Radio-detection signatureof high-energy cosmic rays by the CODALEMA experiment, Nucl. Instr.Meth. A 555 (2005) 148–163.

[3] H. Falcke, W. D. Apel, A. F. Badea, et al., Detection and imaging ofatmospheric radio flashes from cosmic ray air showers, Nature 435 (2005)313–316.

[4] T. Huege, for the Pierre Auger Collaboration, Radio detection of cosmicrays in the Pierre Auger Observatory, Nucl. Instr. Meth. A 617 (2009)484–487.

[5] J. Abraham, M. Aglietta, I. C. Aguirre, et al., Properties and performanceof the prototype instrument for the Pierre Auger Observatory, Nucl. In-strum. Meth. A 523 (2004) 50–95.

[6] S. Argiro, S. L. C. Barroso, J. Gonzalez, et al., The offline softwareframework of the Pierre Auger Observatory, Nucl. Instr. Meth. A 580(2007) 1485–1496.

[7] S. Fliescher and the Pierre Auger Collaboration, Radio detector arraysimulation: A full simulation chain for an array of antenna detectors, in:Proceedings of the ARENA 2008 Conference, Rome, Italy, Nucl. Instr.Meth. A, 604 (2009) S225–S229.

[8] J. Coppens and the Pierre Auger Collaboration, Observation of radiosignals from air showers at the Pierre Auger Observatory, in: Proceedingsof the ARENA 2008 Conference, Rome, Italy, Nucl. Instr. Meth. A, 604(2009) S41–S43.

[9] B. Revenu and the Pierre Auger and CODALEMA Collaborations, Ra-diodetection of cosmic air showers with autonomous radio detectors in-stalled at the Pierre Auger Observatory , in: Proceedings ofthe ARENA2008 Conference, Rome, Italy, Nucl. Instr. Meth. A, 604 (2009) S37–S40.

[10] O. Scholten, K. Werner, F. Rusydi, A macroscopic description of coher-ent geo-magnetic radiation from cosmic-ray air showers, AstroparticlePhysics 29 (2008) 94–103.

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[11] T. Huege, R. Ulrich, R. Engel, Monte Carlo simulations of geosyn-chrotron radio emission from CORSIKA-simulated air showers, As-tropart. Physics 27 (2007) 392–405.

[12] M. Ludwig, T. Huege, REAS3: Monte Carlo simulations of radio emis-sion from cosmic ray air showers using an ”end-point” formalism, As-tropart. Phys. 34 (2011) 438–446.

[13] M. A. DuVernois, B. Cai, D. Kleckner, Geosynchrotron radio pulse emis-sion from extensive air showers: Simulations with AIRES, in: Proc. ofthe 29th ICRC, Pune, India, pp. 311–+.

[14] http://www.fftw.org.[15] http://usg.lofar.org/svn/code/trunk/.

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Figure 1: Within Offline, the detector and event data structures are clearly separated. Both data structures have been complemented with theanalogous classes forradio detection (marked in blue). In both theRDetectorand theREvent, classes forStationsandChannelsare present. Those in the detector data structures provideaccess to the detector description, the ones in the event data structures store data applying to specific radio events.

Figure 2: At both theStationandChannellevels of theREvent, data structures exist to store time-series and frequency-domain data. These are encapsulated inFFTDataContainerswhich transparently and efficiently handle all necessary FFTs without explicit interaction from the end-user.

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Figure 7: Time traces (left) and frequency spectra (right) of the simulated event for the east and north channels. Using the simulated antenna characteristics(including the amplification by the LNA), the three-dimensional electric field vector has been projected to the two measurement channels. After the projection,white noise has been added by theRdChannelNoiseGenerator. The signal depicted here is what would be measured at the antenna foot-points over the wholefrequency bandwidth. Please note that the frequency spectra correspond to the complete trace and not the zoomed-in timewindow shown here.

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Figure 8: Time traces (left) and frequency spectra (right) of the simulated event for the east and north channels after folding in the channel response (amplifiers,filters, cable). Note that the cable delays have shifted the time pulses to later times. Also, the spectral bandwidth has been limited to the design bandwidth ofthe experimental channels, leading to a broadening of the pulses. The signal depicted here is what would be measured at the channel ADCs. Please note that thefrequency spectra correspond to the complete trace and not the zoomed-in time window shown here.

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Figure 9: Time traces (left) and frequency spectra (right) of the simulated event after all processing steps on theChannellevel. The smoothing in the frequencyspectra is due to theRdChannelRFISuppressor. These data again correspond to the signal measured at the foot-points of the antennas, but this time limited to the40-70 MHz band. They are the starting point for the reconstruction of the three-dimensional electric field vector. Please note that the frequency spectra correspondto the complete trace and not the zoomed-in time window shownhere.

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Figure 10: Time traces (left) and frequency spectra (right)for the reconstructed three-dimensional electric field vector of the simulated event after application of theRdChannelWindowSetter. The leakage visible in the frequency spectra is due to the cutting of the time traces to a 500 ns window around the detectedpulses. Thefrequency spectra correspond to the time traces shown here.

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Figure 11: Time traces (left) and frequency spectra (right)of the simulated event for the final, Hann-windowed three-dimensional electric field vector. The significantvertical component of the raw simulation has been reconstructed by the analysis chain. The final reconstructed arrival direction isθ = 60.7◦ andφ = 295.1◦. Theinput direction for the simulated event wasθ = 58.4◦ andφ = 291.0◦. The frequency spectra correspond to the time traces shown here.

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