| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Juutinen, Petri", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Sivil, Ville", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-08-06T05:16:22Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-08-06T05:16:22Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/96517", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa k\u00e4sitell\u00e4\u00e4n Diskreetti\u00e4 Fourier-muunnosta sek\u00e4 Nopeaa Fourier-muunnosta, joka on tehokkaampi algoritmi diskreettej\u00e4 Fourier-muunnoksia varten. Diskreetti\u00e4 Fourier-muunnosta varten k\u00e4sitell\u00e4\u00e4n lis\u00e4ksi\ntarvittavat taustatiedot Fourier-sarjoista.\nFourier-sarja on matemaattinen ty\u00f6kalu, jonka avulla jaksollinen funktio\nvoidaan ilmaista eritaajuisten sini- ja kosinifunktioiden summana. Fourier-sarja toimii l\u00e4ht\u00f6kohtana Fourier-muunnokselle, josta on olemassa jatkuva\nsek\u00e4 diskreetti versio. Jatkuvaa Fourier-muunnosta hy\u00f6dynnet\u00e4\u00e4n l\u00e4hinn\u00e4\nmatematiikan ja fysiikan teoreettisissa sovelluksissa. Reaalimaailman sovelluksissa k\u00e4ytet\u00e4\u00e4n k\u00e4yt\u00e4nn\u00f6ss\u00e4 aina diskreetti\u00e4 versiota, jota t\u00e4ss\u00e4 tutkielmassa k\u00e4sitell\u00e4\u00e4n.\nDiskreetti Fourier-muunnos eli DFT on Fourier-analyysiss\u00e4 k\u00e4ytetty ty\u00f6kalu, jonka avulla ajan suhteen diskreetti ja \u00e4\u00e4rellinen signaali saadaan esitetty\u00e4 taajuuden suhteen. T\u00e4m\u00e4n avulla voidaan selvitt\u00e4\u00e4, mit\u00e4 taajuuksia\nsignaali sis\u00e4lt\u00e4\u00e4 ja mik\u00e4 on kunkin taajuuden amplitudi.\nDiskreetti\u00e4 Fourier-muunnosta hy\u00f6dynnet\u00e4\u00e4n laajasti k\u00e4yt\u00e4nn\u00f6n sovelluksissa, mutta se on algoritmina kuitenkin hidas. T\u00e4m\u00e4n vuoksi reaalimaailman sovelluksissa hy\u00f6dynnet\u00e4\u00e4nkin l\u00e4hes aina nopeaa Fourier-muunnosta\neli FFT:t\u00e4, jonka avulla p\u00e4\u00e4st\u00e4\u00e4n samaan lopputulokseen k\u00e4ytt\u00e4en huomattavasti tehokkaampia algoritmeja. FFT:n vaatimien laskutoimitusten m\u00e4\u00e4r\u00e4\non vain murto-osa verrattuna DFT:hen, mik\u00e4 korostuu entisest\u00e4\u00e4n n\u00e4ytteiden m\u00e4\u00e4r\u00e4n kasvaessa suureksi. FFT:n tehokkuuden vuoksi sit\u00e4 k\u00e4ytet\u00e4\u00e4nkin\nlaajasti erilaisia signaalink\u00e4sittely\u00e4 vaativissa sovelluksissa, kuten \u00e4\u00e4nen- ja\nkuvank\u00e4sittelyss\u00e4 sek\u00e4 l\u00e4\u00e4ketieteellisess\u00e4 kuvantamisessa.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-08-06T05:16:22Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-08-06T05:16:22Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "39", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "diskreetti Fourier-muunnos", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "nopea Fourier-muunnos", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Diskreetti Fourier-muunnos DFT sek\u00e4 nopea Fourier-muunnos FFT", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202408065400", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikan opettajankoulutus", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teacher education programme in Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "Fourier'n sarjat", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
|