Fourier uchungechunge: umlando nethonya mshini zezibalo sokuthuthukiswa isayensi

Fourier uchungechunge - lokhu umbono ezinqumela abakhethiwe imisebenzi nesikhathi ilandelana. Nakubukwa jikelele, lesi sisombululo libizwa element ukunwetshwa njalo orthogonal. Ukwanda imisebenzi Fourier uchungechunge impela ithuluzi elinamandla ukuxazulula izinkinga ezihlukahlukene ngenxa izakhiwo yokushintsha ukuhlanganiswa, kuphakanyiswa, kanye shift ethi agumenti futhi convolution.

Umuntu ongeyena ujwayelene wezibalo ephakeme, kanye imisebenzi French usosayensi Fourier, cishe ngeke baqonde ukuthi "ezinhlwini" futhi enzani. Nokho lolu shintsho is ngempela ngokuqinile langena ezimpilweni zethu. Isetshenziselwa hhayi wezibalo kuphela, kodwa futhi sesayensi yemvelo, osokhemisi, odokotela, izazi zezinkanyezi, izazi zokuzamazama komhlaba, oceanographers nabanye. Asihambe nathi sihlolisise ngemisebenzi usosayensi omkhulu French ozitholile, ngaphambi kwesikhathi sakhe.

Le ndoda kanye Fourier uguqule

Fourier uchungechunge ingenye yezindlela (kanye nokuhlaziywa nabanye) we-Fourier uguqule. Le nqubo ithatha indawo ngaso sonke isikhathi umuntu owezwayo yimuphi umsindo. indlebe yethu iguqula ngokuzenzakalela igagasi umsindo. ukunyakaza Oscillatory izinhlayiya aphansi e i osebenzelana nokunwebeka kuthiwa wandisa ochungechungeni (spectrum) ivolumu ngokulandelana amanani wanoma amathoni eziphakeme ezahlukene. Ngokulandelayo, ubuchopho iguqula le datha ku umsindo ajwayelekile kithi. Konke lokhu kungenxa ngaphezu isifiso sethu noma ukwazi ngokwayo, kodwa ukuze nokuqonda izinqubo kuthathe iminyaka eminingana ukuba zifunde izibalo ephakeme.

Funda kabanzi mayelana ne-Fourier uguqule

I-Fourier uguqule kungaba kwenziwe kohlaziyo, tinombolo ezinye izindlela. Fourier uchungechunge kukhona inqubo inani for ukubola iyiphi izinqubo oscillatory - kusukela namagagasi olwandle amagagasi yokukhanya emjikelezweni welanga (nezinye izinto yezinkanyezi) umsebenzi. Ukusebenzisa lezi amasu zezibalo, kungenzeka ukuqaqa umsebenzi, emelela iyiphi izinqubo oscillatory eziningi izingxenye sinusoidal abahamba ubuncane esiphezulu, noHezekeli. I-Fourier uguqule umsebenzi echaza esigabeni kanye amplitude sinusoids elihambisana imvamisa othize. Le nqubo ingasetshenziswa ngokuxazulula zibalo eziyinkimbinkimbi kakhulu ezichaza izinqubo ashukumisayo ezenzeka ngaphansi isenzo ukushisa, ukukhanya noma amandla kagesi. Futhi, Fourier uchungechunge esetshenziswa ukuhlukanisa DC izingxenye waveforms eziyinkimbinkimbi, okwenza kube lula ngendlela efanele ahumushe kokuma zokuhlola kwezokwelapha, i-chemistry nesayensi yokuhlolwa kwezinkanyezi.

Imininingwane zomlando

Uyise ekusungulweni lo mbono kuyinto sezibalo French Zhan Batist Zhozef Fure. Igama lakhe kamuva futhi lolu shintsho eliye labizwa phezu kwazo. Ekuqaleni, ososayensi babesebenzisa isu ukufunda nokuchaza izindlela conductivity ezishisayo - ukushisa esiphelweni e ukudla okuqinile. Fourier wasikisela ukuthi ukusatshalaliswa kokuqala okungajwayelekile we wave ezishisayo kungenziwa ukubola zibe sinusoid elula, ngamunye okuzodingeka lokushisa yayo minimum futhi esiphezulu, kanye isigaba salo. Ngakho ingxenye ngayinye enjalo ukuba esilinganisiwe esivela ubuncane nalokho esiphezulu kungokufanayo. Umsebenzi zezibalo echaza iziqongo engenhla nengezansi ijika, kanye esigabeni ngasinye harmonic, ebizwa ngokuthi i-Fourier uguqule wokusabalalisa lokushisa yokukhuluma. Umbhali inkolelo-mbono yokuziphendukela encishisiwe jikelele umsebenzi wokusabalalisa okunzima incazelo zezibalo, in a lula kakhulu ukusingatha eziningi imisebenzi ngezikhathi sine futhi cosine, ngenani akunika ukusatshalaliswa kokuqala.

Umgomo we ukuguqulwa kanye ukubukwa ababephila ngesikhathi

Abaphila Besikhathi usosayensi - the zezibalo ehola kwekhulu nesishiyagalolunye - lalingasamukeli lesi theory. I ukuphikisana main kwaba ukwamukelwa Fourier ukuthi umsebenzi discontinuous echaza umugqa oqondile noma ijika idabukile, kungashiwo imelelwa isizumbulu izinkulumo sinusoidal ukuthi kukhona okuqhubekayo. Njengoba isibonelo, cabanga "isinyathelo" Heaviside: ukubaluleka kwalo zero kwesokunxele igebe futhi omunye ngakwesokunene. Lomsebenzi uchaza ukwencika kagesi kwi variable isikhathi sokuvala chain. ithiyori Contemporary ngaleso sikhathi, wayengakaze ihlangabezane Esimweni esinjalo, uma inkulumo discontinuous yayiyobizwa esachazwa inhlanganisela okuqhubekayo, imisebenzi evamile, ezifana lomchazi, sine, komugqa noma quadratic.

Yini ukhathazwa le zezibalo French imfundiso yokuziphendukela Fourier?

Phela, uma sezibalo tye uxabana ke, efingqa engaqinisekile Trigonometric Fourier chungechunge, kungenzeka ukuthola i ukumelwa olunembile isinyathelo yokukhuluma, ngisho noma unalo iqoqo izinyathelo ezifanayo. Ekuqaleni kwekhulu nesishiyagalolunye, kwakhishwa lesi simemezelo kwakubonakala aluhlaza cwe. Kodwa naphezu kwazo zonke ukungabaza, zezibalo eziningi ziye zandisa kwenkululeko cwaningo zalesi simo, ukuthuthela khona ngaphesheya ezishisayo izifundo conduction. Nokho, ososayensi abaningi aqhubeka nokuhlukumezeka lo mbuzo: "? Can isamba sine wave uchungechunge converges nenani esiqondile umsebenzi discontinuous"

Kuhlanganiswa Fourier uchungechunge: isibonelo

Udaba tekuhlangani liphuma njalo udinga summation i uchungechunge esingapheliyo izinombolo. cabangela isibonelo zakudala ngokuba ukuqonda lesi simanga. Ingabe wake ukufinyelela odongeni, uma isinyathelo ngasinye kuba nengxenye owedlule? Ake sithi wena amamitha amabili kusukela umgomo, isinyathelo sokuqala eduze emhlabeni nengxenye endleleni, olandelayo - uphawu we-ngamakwata amathathu, futhi ngemva yesihlanu, ngeke unqobe cishe 97 amaphesenti indlela. Nokho, kungakhathaliseki ukuthi ziningi kangakanani izinyathelo wenze futhi, ilitshe okuhloswe ufinyelela endaweni zezibalo ngomqondo esiqinile. Ukusebenzisa izibalo zezinombolo, singaba ukuthi ekugcineni cishe siyizigidi ibanga ezinqumela encane enikeziwe. Lokhu okulingana ubufakazi ebonisa ukuthi inani eliphelele nengxenye eyodwa, wesine, nokunye. E. Ingabe bavame indlela eya ebunyeni.

Udaba tekuhlangani: ukuza wesibili, noma ithuluzi uLord Kelvin

Ngokuphindaphindiwe kwaphakama umbuzo ngasekupheleni kwekhulu nesishiyagalolunye, lapho Fourier uchungechunge uzamile ukusebenzisa ukubikezela ukushuba ebbs bese ugelezela. Ngaleso sikhathi, uLord Kelvin yasungulwa idivayisi kuyinto ikhompyutha-analog okwamvumela amatilosi wasemanzini lokuqeqesha amatilosi angabahwebi qapha kuyinto engokwemvelo. Le ndlela yokwenza kuchazwe iqoqo izigaba futhi amplitudes yokuphakama ithebula namagagasi futhi lunikeza isikhathi nezikhathi, kulinganiswa ngokucophelela ethekwini unyaka wonke. ipharamitha ngamunye sinusoidal ingxenye Inkulumo tide eziphakeme futhi kwaba kwenye yezingxenye njalo. Imiphumela nesilinganiso kukhona okokufaka kudivayisi Computing uLord Kelvin, Kuhlanganisa ijika ezazibikezela ukuphakama kwamanzi njengoba umsebenzi ngonyaka olandelayo. Maduze, lezi Curves abadonsekela i wonke amachweba emhlabeni.

Futhi uma inqubo ziyophulwa umsebenzi discontinuous?

Ngaleso sikhathi-ke kwabonakala kusobala ukuthi idivayisi ukubikezela igagasi olwandle, oluxube eziningi akhawunti ungakwazi ukubala inani elikhulu izigaba futhi amplitudes, ngakho ahlinzeke isibikezelo esinembile. Noma kunjalo, kwathi lo mkhuba is hhayi waphawula ezimweni lapho inkulumo olwandle ukuthi uzobe kwemiqondo, equkethwe gxuma abukhali, okungukuthi, kukhona discontinuous. Esimweni lapho iinsetjenziswa faka idatha kusuka itafula isikhathi amaphuzu, ke sinquma ambalwa Fourier okuza. Kutholwa umsebenzi yokuqala ngenxa ingxenye sinusoidal (ngokuhambisana okuza okutholakele). I iphutha phakathi kwemibhalo yokuqala futhi le nkulumo kabusha lingalinganiswa nganoma yingasiphi. Lapho izibalo uphinda futhi ukuqhathanisa kuyabonakala ukuthi ukubaluleka iphutha elikhulu kunawo wonke hhayi ziyancipha. Nokho, ngokuvamile ukuba isebenze esifundeni elihambisana iphuzu ukudabuka, futhi yimuphi omunye iphuzu bavame zero. Ngo-1899, lo mphumela kwaqinisekiswa kwakuthiwa uJoshuwa Willard Gibbs ka-Yale University.

Kuhlanganiswa Fourier uchungechunge kanye nokuthuthukiswa wezibalo sisonke

Fourier ukuhlaziywa asisebenzi izinkulumo equkethe isibalo esingapheliyo Ukuvutha ngesikhathi isikhawu ezithile. Ngokuvamile Fourier chungechunge, uma umsebenzi original imelelwa umphumela izilinganiso ngokomzimba uqobo, njalo izingxenye. Imibuzo tekuhlangani yale nqubo amaklasi ezithile imisebenzi sezishiye amagatsha amasha wezibalo, ezifana imfundiso yokuziphendukela imisebenzi generalized. Lihlobene nokubhekana ubuso amagama ezifana Schwartz, J .. Mikusiński noJ Temple. Ngaphansi mbono, ecacile eqondile isisekelo ezicatshangelwayo inkulumo enjengokuthi usumisiwe njengoba Dirac delta umsebenzi (ichaza esifundeni endaweni eyodwa, bagxila i endaweni kuncane iphuzu) kanye "isitebhisi" Heaviside. Ngalesi umsebenzi Fourier uchungechunge baba esebenzayo ukuxazulula zibalo nezinkinga, ezibangela imiqondo enembile: iphuzu kwenkokhiso, iphuzu mass, dipoles kazibuthe, futhi umthwalo kanzulu ugongolo.

Fourier indlela

Fourier chungechunge, ngokuhambisana nezimiso ukugxambukela, uqale nge noqhekeko amafomu eziyinkimbinkimbi ku lula. Ngokwesibonelo, ushintsho ukushisa ukugeleza ngenxa ndima yayo ngokusebenzisa izithiyo ahlukahlukene yokushisa nangokuvikela impahla ijamo okungajwayelekile noma ukushintsha phansi indawo - ukuzamazama komhlaba, ushintsho emzileni komhlaba nendikimba esemkhathini - ithonya amaplanethi. Ngokuvamile, lezi zibalo echaza elula classical uhlelo aphansi ixazululwe ngayinye wavelength ngabanye. Fourier selukhombisile ukuthi izixazululo ezilula kungenziwa kufingqwe for more imisebenzi eziyinkimbinkimbi. Ngo ilimi le-IiMbalo, Fourier uchungechunge - indlela ukuze afake yokukhuluma isamba harmonic - cosine futhi amagagasi sine. Ngakho-ke, lokhu ukuhlaziywa yaziwa ngaphansi kwegama "ukuhlaziywa harmonic".

Fourier uchungechunge - indlela enhle eya "ikhompyutha yobudala"

Ngaphambi ukudalwa ubuchwepheshe bama-computer Fourier indlela yisona sikhali engcono ku arsenal of ososayensi ukusebenza ubunjalo wave zezwe lethu. Fourier uchungechunge ngefomu eziyinkimbinkimbi ikuvumela ukuba uxazulule izinkinga elula ukuthi kukhona amenable ukuqondisa ukusebenza kwemithetho Newton sika Mechanics, kodwa futhi zibalo eliyisisekelo hhayi kuphela. Iningi nalokho okutholwe yisayensi Newton yekhulu nesishiyagalolunye lenziwa latholakala kuphela ngenxa indlela Fourier.

Fourier uchungechunge namuhla

With ukuthuthukiswa Fourier uguqule amakhompyutha ivukile ezingeni elisha. Le nqubo ibizwa lizimelele cishe yonke imikhakha ngesayensi nobuchwepheshe. Njengoba isibonelo, i-audio digital nevidiyo. nokuqaliswa kwalo okuye kwafezwa sibonga kuphela tiyori akhiwa sezibalo French kwekhulu nesishiyagalolunye. Ngakho, i-Fourier uchungechunge ngefomu eziyinkimbinkimbi ukuvumele ukwenza intuthuko ekuhloleni emkhathini. Ngaphezu kwalokho, kuye kwathinta ekutadisheni yemvelo ka Semiconductor izinto ne-plasma, microwave umsindo, Oceanography, radar, seismology.

Trigonometry Fourier uchungechunge

Esifundweni sezibalo, uchungechunge Fourier iyindlela emelela ngokungenasizathu imisebenzi eziyinkimbinkimbi njengoba isamba lula. Ezimweni jikelele, inani izinkulumo kungenzeka elingapheli. Kukhula inani abalwa kulesi sibalo, inembe more umphumela wokugcina eyatholakala. Ukusetshenziswa ezivame kakhulu cosine elula Trigonometric noma umsebenzi sine. Kulokhu, lo Fourier uchungechunge libizwa Trigonometric, futhi isinqumo amagama anjalo - noqhekeko harmonic. Le ndlela linendima ebalulekile mathematics. Okokuqala, uchungechunge Trigonometric ihlinzeka izindlela yesithombe, kanye kufundza imisebenti, kuba iyunithi oyinhloko le mfundiso. Ngaphezu kwalokho, kusivumela ukuthi ukuxazulula izinkinga eziningi eziphathelene ne-physics zezibalo. Ekugcineni, lo mbono uye nomthelela ekuthuthukiseni sokuhlaziya zezibalo, ke emenza amagatsha amaningana ebaluleke kakhulu isayensi zezibalo (imfundiso yokuziphendukela integrals, imfundiso yokuziphendukela imisebenzi gqwa). Ngaphezu kwalokho, lapho ucala khona kubhala sokuthuthukiswa okulandelayo eyeza nezazi zezinkanyezi ezikhuluma: lishona, imisebenzi kwenombolo Okuyınqo, ukuhlaziywa ukusebenza, futhi wabeka isisekelo sokuba ukuhlaziywa harmonic.