LEADER 04154nam  22007935  450 
001 9910255019703321
005 20200705203740.0
010   $a3-319-45581-8
024 7 $a10.1007/978-3-319-45581-5
035   $a(CKB)3710000000926201
035   $a(DE-He213)978-3-319-45581-5
035   $a(MiAaPQ)EBC6315908
035   $a(MiAaPQ)EBC5589250
035   $a(Au-PeEL)EBL5589250
035   $a(OCoLC)962018316
035   $a(PPN)196324130
035   $a(EXLCZ)993710000000926201
100   $a20161026d2016      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aMusic Through Fourier Space $eDiscrete Fourier Transform in Music Theory /$fby Emmanuel Amiot
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XV, 206 p. 129 illus., 45 illus. in color.) 
225 1 $aComputational Music Science,$x1868-0305
311   $a3-319-45580-X 
327   $aDiscrete Fourier Transform of Distributions -- Homometry and the Phase Retrieval Problem -- Nil Fourier Coefficients and Tilings -- Saliency -- Continuous Spaces, Continuous Fourier Transform -- Phases of Fourier Coefficients.
330   $aThis book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.
410  0$aComputational Music Science,$x1868-0305
606   $aApplication software
606   $aMusic
606   $aMathematics
606   $aComputer science?Mathematics
606   $aUser interfaces (Computer systems)
606   $aSignal processing
606   $aImage processing
606   $aSpeech processing systems
606   $aComputer Appl. in Arts and Humanities$3https://scigraph.springernature.com/ontologies/product-market-codes/I23036
606   $aMusic$3https://scigraph.springernature.com/ontologies/product-market-codes/417000
606   $aMathematics in Music$3https://scigraph.springernature.com/ontologies/product-market-codes/M33000
606   $aMathematics of Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I17001
606   $aUser Interfaces and Human Computer Interaction$3https://scigraph.springernature.com/ontologies/product-market-codes/I18067
606   $aSignal, Image and Speech Processing$3https://scigraph.springernature.com/ontologies/product-market-codes/T24051
615  0$aApplication software.
615  0$aMusic.
615  0$aMathematics.
615  0$aComputer science?Mathematics.
615  0$aUser interfaces (Computer systems).
615  0$aSignal processing.
615  0$aImage processing.
615  0$aSpeech processing systems.
615 14$aComputer Appl. in Arts and Humanities.
615 24$aMusic.
615 24$aMathematics in Music.
615 24$aMathematics of Computing.
615 24$aUser Interfaces and Human Computer Interaction.
615 24$aSignal, Image and Speech Processing.
676   $a781.0151
700   $aAmiot$b Emmanuel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0976799
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910255019703321
996   $aMusic Through Fourier Space$92225285
997   $aUNINA