sounds, spectra, audio illusions, and data representationsmilotti/didattica/segnali/sound-2.pdf ·...

Sounds,spectra,audioillusions,anddatarepresentations

EdoardoMilotti,Dipartimento diFisica,Università diTriesteIntroductiontoSignalProcessingTechniques

A.Y.2016-17

Pianonotes

Pure440Hzsound

time(samplenumber)

amplitude(volt,ampere,normalizedamplitudeunits…)

Backtotheinitialrecording,leftchannel

0 1000 2000 3000 4000 5000

-0.004

-0.002

0.000

0.002

0.004


time(samplenumber)

squaredamplitude

frequency(frequencyindex)

ShortTimeFourierTransform(STFT)

FourierTransform

FourierTransform

Asingleblockofdata

Segmenteddata

squaredamplitude


time

amplitudeofmostimportantFouriercomponent

frequency

time

Spectrogram

• Originalaudiofile

• Reconstructionwiththelargestamplitudefrequencycomponentonly

• Reconstructionwith7frequencycomponents

• Reconstructionwith7frequencycomponents +phaseinformation

time(samplenumber)


squaredamplitude


IncludeonlyFouriercomponentswithamplitudesABOVEagiventhreshold

18Fouriercomponents

squaredamplitude


IncludeonlyFouriercomponentswithamplitudesABOVEagiventhreshold

39Fouriercomponents

squaredamplitude


squaredamplitude


Glissando

Inmusic,aglissando[ɡlisˈsando](plural:glissandi,abbreviatedgliss.)isaglidefromonepitchtoanother.ItisanItalianizedmusicaltermderivedfromtheFrenchglisser,toglide.

(fromWikipedia)

J.S.Bach- Musicalisches Opfer - 6.CanonA2

G.Ligeti – GlissandiandArtikulation

frequencytime

TheShepard-Risset Glissandohttps://www.youtube.com/watch?v=MShclPy4Kvc

frequency

time

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

AscendingandDescending byM.C.Escher.

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)

ALEGObricksrendition…

http://www.andrewlipson.com/escher/ascending.html

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.

DianaDeutsch’sScaleIllusionhttps://www.youtube.com/watch?v=XS7IAcsRcgA

sounds, spectra, audio illusions, and data representationsmilotti/didattica/segnali/sound-2.pdf ·...

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