sounds, spectra, audio illusions, and data representationsmilotti/didattica/segnali/sound-2.pdf ·...
TRANSCRIPT
Sounds,spectra,audioillusions,anddatarepresentations
EdoardoMilotti,Dipartimento diFisica,Università diTriesteIntroductiontoSignalProcessingTechniques
A.Y.2016-17
time(samplenumber)
amplitude(volt,ampere,normalizedamplitudeunits…)
Backtotheinitialrecording,leftchannel
0 1000 2000 3000 4000 5000
-0.004
-0.002
0.000
0.002
0.004
amplitude(volt,ampere,normalizedamplitudeunits…)
time(samplenumber)
0 1000 2000 3000 4000 5000
-0.004
-0.002
0.000
0.002
0.004
amplitude(volt,ampere,normalizedamplitudeunits…)
time(samplenumber)
• Originalaudiofile
• Reconstructionwiththelargestamplitudefrequencycomponentonly
• Reconstructionwith7frequencycomponents
• Reconstructionwith7frequencycomponents +phaseinformation
IncludeonlyFouriercomponentswithamplitudesABOVEagiventhreshold
18Fouriercomponents
squaredamplitude
frequency(frequencyindex)
IncludeonlyFouriercomponentswithamplitudesABOVEagiventhreshold
39Fouriercomponents
squaredamplitude
frequency(frequencyindex)
Glissando
Inmusic,aglissando[ɡlisˈsando](plural:glissandi,abbreviatedgliss.)isaglidefromonepitchtoanother.ItisanItalianizedmusicaltermderivedfromtheFrenchglisser,toglide.
(fromWikipedia)
J.S.Bach- Musicalisches Opfer - 6.CanonA2
G.Ligeti – GlissandiandArtikulation
APairofParadoxes utilizestwosensoryillusionsinone— thevisualillusioncalledthePenroseSteps(popularizedbyMCEscher)oftheendlesslyclimbingstaircase,andthelesser-knownaudiocorrelation— theendlesslyascendingtone,calledaShepardtone.RogerShepardandEdwardZajac madethisfilmin1967.Zajac,aBellscientist,isalsocreditedwiththeveryfirstcomputer-animatedfilm.ThePenroseStepswereavisualtrickdiscoveredin1958byafamilyteam,LionelPenroseandhissonRoger.TheartistMCEscherusedthetechniquetocreatehisartworkKimmen enDalen (AscendingandDescending)in1960.Hefolloweditupwithasimilarworkonthesamethemein1961,Waterval (Waterfall).TheShepardToneisasoundconsistingofgroupsofsinewavesseparatedbyoctaves,fadingfromonetotheotherandbackagain.It'sanauditoryillusion—andcanbemadeinanascendingordescendingversion.It'sbeendescribedasa"sonicbarber'spole."Thisillusionisthe1964inventionofpsychologistRogerShepard,acognitivespecialistwhoworkedatBellLabsuntil1966,whenhewenttoStanfordasapsychologyprofessor.FootagecourtesyofAT&TArchivesandHistoryCenter,Warren,NJhttp://techchannel.att.com/play-video.cfm/2011/10/10/AT&T-Archives-A-Pair-of-Paradoxes
Maurits Cornelis Escher(17June1898– 27March1972)Self-portrait
CircleLimitIII (1959),isoneofaseriesoffourwoodcutsbyEscherdepictingideasfromhyperbolicgeometry.
ThePenrosestairsorPenrosesteps,alsodubbedtheimpossiblestaircase,isanimpossibleobjectcreatedbyLionelPenroseandhissonRogerPenrose.AvariationonthePenrosetriangle,itisatwo-dimensionaldepictionofastaircaseinwhichthestairsmakefour90-degreeturnsastheyascendordescendyetformacontinuousloop,sothatapersoncouldclimbthemforeverandnevergetanyhigher.Thisisclearlyimpossibleinthreedimensions.
The"continuousstaircase"wasfirstpresentedinanarticlethatthePenroses wrotein1959,basedontheso-called"triangleofPenrose"publishedbyRogerPenroseintheBritishJournalofPsychologyin1958.M.C.EscherthendiscoveredthePenrosestairsinthefollowingyearandmadehisnowfamouslithographyKlimmen endalen(AscendingandDescending)inMarch1960.PenroseandEscherwereinformedofeachother'sworkthatsameyear.EscherdevelopedthethemefurtherinhisprintWaterval (Waterfall),whichappearedin1961.
IntheiroriginalarticlethePenroses notedthat"eachpartofthestructureisacceptableasrepresentingaflightofstepsbuttheconnexions aresuchthatthepicture,asawhole,isinconsistent:thestepscontinuallydescendinaclockwisedirection.”
AtanEscherconferenceinRomein1985,RogerPenrosesaidthathehadbeengreatlyinspiredbyEscher'sworkwhenheandhisfatherdiscoveredboththetri-barstructure(i.e.,thePenrosetriangle)andthecontinuoussteps,althoughEscher,inthe1950s,hadnotyetdrawnanyimpossiblefiguresandwasnotawareoftheirexistence.RogerPenrosehadbeenintroducedtoEscher'sworkattheInternationalCongressofMathematiciansinAmsterdamin1954.Hewas"absolutelyspellbound"byEscher'swork,andonhisjourneybacktoEnglandhedecidedtoproducesomething"impossible"onhisown.Afterexperimentingwithvariousdesignsofbarsoverlyingeachotherhefinallyarrivedattheimpossibletriangle.Rogershowedhisdrawingstohisfather,whoimmediatelyproducedseveralvariants,includingtheimpossibleflightofstairs.Theywantedtopublishtheirfindingsbutdidn'tknowinwhatfieldthesubjectbelonged.BecauseLionelPenroseknewtheeditorofBritishJournalofPsychologyandconvincedhimtopublishtheirshortmanuscript,thefindingwasfinallypresentedasapsychologicalsubject.Afterthepublicationin1958thePenroses sentacopyofthearticletoEscherasatokenoftheiresteem.
WhilethePenroses creditedEscherintheirarticle,EscherhimselfnotedinalettertohissoninJanuary1960thathewas:
workingonthedesignofanewpicture,whichfeaturedaflightofstairswhichonlyeverascendedordescended,dependingonhowyousawit.[Thestairs]formaclosed,circularconstruction,ratherlikeasnakebitingitsowntail.Andyettheycanbedrawnincorrectperspective:eachstephigher(orlower)thanthepreviousone.[...]Idiscoveredtheprincipleinanarticlewhichwassenttome,andinwhichImyselfwasnamedasthemakerofvarious'impossibleobjects'.ButIwasnotfamiliarwiththecontinuousstepsofwhichtheauthorhadincludedaclear,ifperfunctory,sketch,althoughIwasemployingsomeofhisotherexamples.
EscherwascaptivatedbytheendlessstairsandsubsequentlywrotealettertothePenroses inApril1960:
Afewmonthsago,afriendofminesentmeaphotocopyofyourarticle...Yourfigures3and4,the'continuousflightofsteps',wereentirelynewtome,andIwassotakenbytheideathattheyrecentlyinspiredmetoproduceanewpicture,whichIwouldliketosendtoyouasatokenofmyesteem.Shouldyouhavepublishedotherarticlesonimpossibleobjectsorrelatedtopics,orshouldyouknowofanysucharticles,Iwouldbemostgratefulifyoucouldsendmefurtherdetails.
(fromtheWikipediaarticlehttps://en.wikipedia.org/wiki/Penrose_stairs)
ThePenroses
• JamesDoylePenrose,(9May1862– 2January1932)wasanIrishpainter.
• LionelSharples Penrose,(11June1898– 12May1972)sonofJames,wasaBritishpsychiatrist,medicalgeneticist,mathematicianandchesstheorist.
• SirRolandAlgernonPenrose,(14October1900– 23April1984)sonofJames,wasanEnglishartist,historianandpoet.HewasamajorpromoterandcollectorofmodernartandanassociateofthesurrealistsintheUnitedKingdom.[1]DuringtheSecondWorldWarheputhisartisticskillstopracticaluseasateacherofcamouflage.
• OliverPenrose,(born1929)isaBritishtheoreticalphysicist.HeisthesonofthescientistLionelPenrose,brotherofthemathematicalphysicistRogerPenrose,andbrotherofchessmasterJonathanPenrose.Hisareasofinterestincludestatisticalmechanics,phasetransitionsinmetalsandphysicalchemistryofsurfactants.Heisparticularlyknownfortheconceptofoff-diagonallong-range order,whichiscentraltoourpresent-dayunderstandingofsuperfluids andsuperconductors.Othermoreabstracttopicsinwhichhehasworkedincludeunderstandingthephysicalbasisforthedirectionoftimeandinterpretationsofquantummechanics.
• SirRogerPenrose,(born8August1931)isanEnglishmathematicalphysicist,mathematicianandphilosopherofscience.HeisthesonofthescientistLionelPenrose,brotherofthetheoreticalphysicistOliverPenrose,andbrotherofchessmasterJonathanPenrose.Heisknownforhisworkinmathematicalphysics,inparticularforhiscontributionstogeneralrelativityandcosmology.Hehasreceivedseveralprizesandawards,includingthe1988WolfPrizeforphysics,whichhesharedwithStephenHawkingfortheircontributiontoourunderstandingoftheuniverse.
• JonathanPenrose,(born7October1933,inColchester)isanEnglishchessGrandmasterandInternationalCorrespondenceChessGrandmaster(1983)whowontheBritishChessChampionshiptentimesbetween1958and1969.HeisthesonofLionelPenrose,aworldfamousprofessorofgenetics,thegrandsonofthephysiologistJohnBeresfordLeathes,andbrotherofRogerPenroseandOliverPenrose.Heisapsychologistanduniversitylecturerbyprofession.
• ShirleyVictoriaHodgson,(néePenrose,born22February1945)isaBritishgeneticist.SheisProfessorofCancerGeneticsatStGeorge's,UniversityofLondon.