Fourier taui. Fourier nohopuku taui. Fourier motuhake taui

panoni Fourier - panoni, e feohi he tetahi mahi o te tāupe tūturu. whakamana ana tēnei mahi te wa katoa tatou e kite rerekē oro. Taringa hua aunoa "tātaitanga", e rave faaoti i to matou mahara e taea i muri i anake te whakamātautau o te wāhanga o te pāngarau teitei. rongo okana i roto i te huringa tangata Ka hangaia e, i roto i nei ngā te tangi (tikanga nekehanga vibrational o matūriki i roto i te reo rapa, e tohaina i roto i te puka poipoi i roto i te reo totoka, wai haurehu waihā ranei) i roto i te whānuitanga o ngā uara karapīpiti o te taumata rōrahi o pepe o tiketike rerekē. I muri i tenei, tahuri te roro te mōhiohio ki te tangi maheni katoa.

Mathematical Fourier taui

Te faafariuraa o ngaru oro tukanga atu wiri ranei (i paheke marama, me te moana tai, me ki huringa oranga solar ranei) e taea te whakamana me te tikanga o ngā tikanga pāngarau. Ko te kupu, te whakamahi i enei tikanga, e taea te whakawhānui i te whakauru tukanga vibrational whakaturia o wāhanga sinusoidal, i.e. hononga Karekare e haere i te iti ki te mōrahi me ka ano ki te iti, rite te ngaru o te moana nga mahi. panoni Fourier - panoni mahi e whakaahua ana i te wāhanga kaha tīwera ranei o ia sinusoid ōrite ki te auau ngā. Wāhanga ko te tīmatanga o te ānau, me te kaha tīwera - o tona tiketike.

Fourier taui (e whakaaturia tauira i roto i te whakaahua) ko te taputapu rawa kaha, whakamahia nei i roto i mara ngā o te pūtaiao. I roto i ētahi wā, kua whakamahia te reira rite te otinga whārite kaua matatini e whakaahua te tukanga hihiri e puta ana i raro i te mana o te marama, wera pūngao hiko ranei. I roto i te tahi atu te wā, ka taea te reira ki a koe te tautuhi i ngā wāhanga i ia te wā i roto i waveforms matatini, e tika ana ki tenei e taea e pono ki te whakamāori i ngā kitenga whakamātautau i roto i te matū, rongoā me te tātai arorangi.

mōhiohio hītori

Ko te tangata tuatahi ki te tono i tēnei tikanga, ko te mathematician French Zhan Batist Fure. Faafariuraa, muri ingoa i muri ia ia, i whakamahia tuatahi ki te whakaahua i te tikanga kawenga wera. Fourier whai wāhi i roto i te haapiiraa i te āhuatanga o te wera tona ora pakeke katoa. hanga e ia he takoha nui ki te ariā pāngarau o te faaotiraa o te pakiaka o whārite taurangi. Fourier ko te ahorangi o te tātaritanga i te Ecole Polytechnique, te Hekeretari o te Institute o Egyptology, ko te mahi emepaea, i meinga he pororaru i te wa o te hanga o te rori ki a Turin (i raro i tona kaiārahi i ringihia o neke atu i te 80 mano kiromita tapawha o repo malarial). Heoi, kihai i tenei ngā katoa mutu te kaipūtaiao whai wāhi i roto i te tātari pāngarau. I te 1802 ka ahu mai te reira i te whārite e whakaahua ana i te whakatö o te wera i roto i te totoka. I roto i te 1807, kitea pūtaiao he tikanga mō te whakaoti i tēnei whārite, i ka mohiotia rite "Fourier taui".

tātari kawe ia ngāwhā

whakamahia kairangahau he tikanga pāngarau ki te whakaahua i te tikanga kawenga wera. He tauira watea, ai kore fifi i roto i te tätaitanga ko te whakatö o te pūngao waiariki i te mowhiti rino, kotahi wahi rumakina i roto i te ahi. Hei kawe i ngā Fourier wahi wera whero o te whakakai me tanu ia i roto i te onepu pai. I muri iho, kawea te inenga pāmahana i roto i runga i te wahi i te ritenga atu o reira. I te tīmatanga, ko te tohatoha wera kōhikohiko: wahi o te mowhiti - makariri, me te tahi atu - wera, i waenganui o nga rohe e taea mau te rōnaki pāmahana koi. Heoi, i roto i te tohatoha puta noa i te mata whakarewa wera, riro te reira atu kākahu. Na, hohoro, e tenei tukanga te puka o te ngaru aho. kauwhata Tuatahi āta faarahi a hoki heke pai, tika nga ture o rerekētanga o te whenu mahi aho ranei. Ngaru māmālie ea me rite ki te hua o te pāmahana riro kākahu i runga i te mata katoa o te whakakai.

riro te kaituhi o tenei tikanga e ko tino kōhikohiko taea te decomposed ki te maha o ngaru sine pūmotu te tohatoha tuatahi. Ka whai ia o ratou tona wā (tūnga tuatahi) me tona pāmahana mōrahi. Ko te kupu ki ia huringa wāhanga pērā i te iti ki te mōrahi me te hoki whakaoti revolution huri noa i te wā mowhiti tau tōpū. Wae he wā i huaina te hawarite taketake, me te uara ki e rua, neke atu rānei ngā wā - te tuarua, me te pera i runga i. Hei tauira, he mahi pāngarau e whakaahua ana i te pāmahana mōrahi, te wāhanga tūnga ranei huaina te Fourier whakaahua ke o te mahi tuari. kawea Scientist te wāhanga kotahi e he uaua ki te whakaahuatanga pāngarau, hoki taputapu ngāwari-ki-te whakamahi - rarangi o aho me te whenu, i te nui o hoatu te tohatoha tuatahi.

Ko te ngako o te tātari

Hoatu tenei tātaritanga ki te faafariuraa o te tohatoha i runga i te ahanoa mārō wera, he he āhua annular, korerorero te mathematician e arahi te whakanui ake wā o ngā wāhanga sinusoidal ki tona damping tere. Kei te mārama kitea tenei i runga i te hawarite matua, me te tuarua. Te pāmahana whakamutunga tae rua nga uara mōrahi me te mōkito i roto i te haere kotahi, a i roto i te tuatahi - kotahi anake. Huri i te reira i roto i taua i te tawhiti haere e wera i roto i te rua i te hawarite ko te hawhe e o te matua. I tua atu, ka hoki hei poupou atu te tuatahi te rōnaki o te hawhe tuarua. Na, mai haere he rere waiariki atu kaha pouaru tawhiti iti, katahi tenei ka e damped hawarite wha nga wa tere atu i te matua, ka rite ki te mahi o te wā. I roto i te whai ake i te tukanga ka kia noa tere. Mathematician whakapono e taea tenei tikanga ki a tatou tātai i te tukanga o te tohatoha tuatahi o te pāmahana ki te wā.

to'utangata Call

Fourier taui i te hātepe kua meinga hei wero ki te turanga ariā o te pāngarau i te wa. I roto i te tīmatanga o te rautau tekau mā iwa, kihai i te nuinga o kaipūtaiao rongonui, tae atu Lagrange, Rāpāra, Poisson, Legendre ko Biot manako tona whakapae e te decomposed te pāmahana o te tohatoha tuatahi ki ngā wāhanga i roto i te puka o te poipoi taketake, me te auautanga teitei. Heoi, e kore i taea e te Academy o Pūtaiao tau'a ore i te hua whiwhi mathematician, ka whakawhiwhia a ia i te Taonga mo te ariā o te pūkawe o nga ture wera, me te whakahaere i tona rite ki ngā tinana. I roto i te huarahi Fourier, te whakahe matua ko te meka i māngai he mahi ka motu e te moni o te maha ngā mahi sinusoidal, e he tonu. I muri i te katoa, whakaahua ratou te pakaru tonu me kōpiko rārangi. kore pūtaiao Contemporary i tūpono he āhuatanga taua, ka te mahi ka motu whakaahuatia e te huinga o tonu, pērā i pūrua, rārangi, sine exhibitor ranei. I roto i te kaupapa i he tika i roto i tona tāpaetanga i te mathematician, kia iti te moni o te raupapa mure ore o pānga pākoki ki te tere tangohia. I au ra heahea te kerēme taua. Heoi, ahakoa te feaa o te tahi mau kairangahau (hei tauira Claude Navier, Sofi Zhermen) whānui te hōkai o te rangahau, a kawea ana ratou e i o te tātaritanga o te tohatoha wera. He pāngarau, takiwa, tonu ki mamae te pātai o mehemea iti te moni o te maha ngā mahi sinusoidal te ki te kanohi tangohia o pakaruhanga.

hītori-tau 200

Kua tipu tēnei ariā i runga i rua rau tau, i tenei ra kei te pae hopea te reira i hanga. Ki te awhina o nga mahi mokowā pae tino ranei e pakaru ki wāhanga sinusoidal e whai he auau, wāhanga, me te kaha tīwera. whiwhi ana tēnei faafariuraa e rerekē tikanga pāngarau rua. Ko te tuatahi o ratou whakamahia i roto i te take, ka te pūtake ko te mahi tonu, me te tuarua - i roto i te take i reira e māngai ai e te plurality o huringa motuhake takitahi. Ki te whiwhi te te faaiteraa i ngā uara, e tautuhi i wā motuhake, e taea te wehea te reira ki te maha motuhake iarere sinusoidal kīanga - i te raro, a ka tuaruatia, tata'i toru, a pera atu ki runga ake i te faufaa. huaina ana tēnei moni ko te raupapa Fourier. Ki te whakatakoto ana te faaiteraa tuatahi te uara o ia tau tūturu, e taea te whakakahore te reira iho ki sinusoidal iarere taea katoa maha. Kei te karangatia e te reira i te Fourier wāhi, ka titau te whakatau he huringa o te mahi wāhi. Ahakoa o te tikanga mo te whiwhi huringa, mo ia auau kia tohu e rua tau: tīwera me te auautanga. E faaite ēnei uara rite te kotahi tau matatini. Expression taurangi matatini ariā tahi ki Fourier panoni ki te mahi i ngā tātaitanga whakaaetia te hoahoa o ngā iahiko hiko, te tātaritanga o wiri aunoa, te ako o te whakatö poipoi tikanga me tetahi atu.

Fourier taui i teie mahana

I tčnei wā, te ako o tenei tukanga waiwai whewhe ki raro ki te kimi tikanga whai hua mo te whakawhiti i te mahi ki te tahuri i te reira hoki ki te ngakau. huaina ana tēnei otinga ko te Fourier tika, me te kōaro taui. Eaha te auraa? I roto i te tikanga ki te whakatau i te wāhi me te hanga i te Fourier tika taui, ka taea e koe te whakamahi i ngā tikanga pāngarau, engari ka taea e koe analytic. Ahakoa te meka e ka e whakamahia ratou i roto i te mahi i reira e te tahi mau fifi, kua oti kē i kitea, ka tomo i roto i tu'utu'uni pāngarau te nuinga o pāwhaitua. Ki te kīanga e taea te tatau te awhina o te tikanga tātai, te āhua o i hāngai te i runga i nga raraunga whakamātautau, he mahi nei e ngaro pāwhaitua i nga papa, a ka he uaua ki te whakaaro i roto i te puka tātari ratou.

I mua i te taeraa mai o tātaitanga engineering rorohiko kua rawa whakaware taua panoni, e rapu ratou mahi ā-ringa o te maha nui o ngā mahi tātai e whakawhirinaki i runga i te maha o ngā e whakaahua te mahi poipoi. Ki te whakahaere i te whakataunga i teie mahana, i reira he hōtaka motuhake, whakaaetia ki te whakatinana i hou tikanga tātari. Na, i roto i te 1965, i hanga Dzheyms Kuli ko Dzhon Tyuki pūmanawa e ka mohiotia rite "Fourier Nohopuku Panoni". whakaora te reira i te wa o te tātai mā te whakaiti i te maha o whakareatanga i roto i te tātari o te ānau. "Fourier Tere Panoni" E hāngai ana te tikanga i runga i wehewehe i te ānau ki te maha nui o ngā uara tauira ōrite. Nä, heke te maha o whakareatanga e te hawhe i te taua whakaiti i te maha o ngā.

Hoatu ana te Fourier taui

whakamahia ana tēnei tukanga i roto i ngā mara: I roto i te tau ariā, te ahupūngao, te tukatuka tohu, combinatorics, ariā tūponotanga, tuhiwhakamuna, tatauranga, Oceanography, optics, Acoustics, me ētahi atu geometries. hāngai taea Rich mo tona whakamahi e i runga i te maha o ngā āhuatanga whai hua, e te hunga kua huaina "āhuatanga o te huringa Fourier." Kia titiro tatou ki a ratou.

1. Ko te mahi faafariuraa ko te operator rārangi, me te he kotahitanga he māori hāngai. mohiotia ana tēnei taonga te rite te ture tauwehe Parseval, ranei i roto i te take whānui, te ture tauwehe Plansherelja Pontrjagin ranei dualism.

2. Ko reversible te faafariuraa. Ano, ko te hua ritenga he āhua nui rite rite i roto i te tika whakatutuki.

3. Ko te kīanga taketake sinusoidal ko ratou ake mahi rerekëtanga. Tenei te tikanga e taui taua kanohi whārite rārangi ki whakarea tamau i roto i te taurangi tikanga.

4. E ai ki te "convolution" tauwehe, hanga te tukanga he mahi matatini i roto i te whakarea pūmotu.

5. Discrete Fourier Panoni taea te hohoro hangaia i runga i te rorohiko whakamahi i te "nohopuku" tikanga.

Momo o te Fourier taui i

1. nuinga maha whakamahia te wā kei te ki te kōrero ki te hurihanga tonu, whakarato i tetahi faaiteraa quadratically integrable rite te moni o te faaiteraa taupūtanga matatini ki iarere t motuhake me amplitudes. He maha ngā momo rerekē, e ai kia rerekē whakarea tonu tenei momo. Ko te tikanga tonu ngā te tepu faafariuraa, e taea te kitea i roto i tu'utu'uni pāngarau. He take te whakatakiruatanga o ko te faafariuraa hautanga, ai e taea te tenei tukanga whakaarahia ki te mana tūturu hiahiatia.

2. Ko te tikanga tonu ko te whakatau o te tikanga mua o raupapa Fourier tautuhia hoki tetahi mahi wā ranei kīanga, e te tīariari i roto i te iti wāhi me tohu ratou rite te raupapa o sinusoids.

3. Discrete Fourier taui. whakamahia tēnei tikanga i roto i rorohiko mō te tätaitanga pūtaiao me te tukatuka tohu mamati. Hei kawe i tenei momo o te tātaitanga e hiahiatia ki te whai i te mahi o te whakatau i runga i te huinga motuhake o ngā takitahi, wā iti ranei rohe hei utu o pāwhaitua Fourier tonu. kanohi faafariuraa Tohu i roto i tenei take e rite te moni o sinusoids. Ko te whakamahi o "nohopuku" tikanga ka taea te whakamahi o rongoā mamati mō ngā take mahi katoa.

4. Ko te matapihi Fourier taui ko te tirohanga whānui o te tikanga matarohia. Rerekē rongoā paerewa ka whakamahia te tūāwhiorangi tohu e, tangohia nei i roto i te ki tonu i ngā o te oraraa o tenei tāupe ko o ngā moni i konei ko anake te tohatoha auau rohe i te tiaki i te tāupe taketake (wā).

5. Ko te Fourier rua-ahu taui. whakamahia tēnei tikanga te ki te mahi ki ngā huānga e rua-ahu o raraunga. I roto i te take i taua, whakamana te faafariuraa i roto i te kotahi aronga, a ka - i roto i te tahi atu.

mutunga

I teie mahana, Kei te pūmau te tikanga Fourier i te mara ngā o te pūtaiao. Hei tauira, i roto i te 1962 whakatuwheratia reira te āhua o te DNA helix rua te whakamahi i Fourier tātaritanga roto i te taha ki te X-ray ttara. arotahi tioata Tata i runga i muka DNA, hua i roto i te whakapakoko i whiwhi nei i ttara, tuhia i runga i te kiriata. hoatu tenei pikitia mōhiohio e pā ana ki te uara o te kaha tīwera mā te whakamahi i te Fourier whakaahua ke ki tenei hanganga karaihe. raraunga Wāhanga whiwhi e te whakatairite i te kāri DNA ttara ki kāri e kua whiwhi i roto i te tātari o ngā hanganga matū rite. Ka rite ki te hua, whakahokia ōmataora hanganga karaihe - te mahi taketake.

Fourier taui tākaro he wāhi nui i roto i te ako o te wāhi o waho, te ahupūngao o ngā rauemi Semiconductor me wē, Acoustics ngaruiti, Oceanography, hihiani, seismology me whakamātautau hauora.