Raupapa Fourier: te hītori, me te mana o te huarahi pāngarau mō te whanaketanga o te pūtaiao

raupapa Fourier - tenei tirohanga takirihia whiriwhiria mahi ki te wā i roto i te rarangi. I roto i te ngā whānui, huaina tenei otinga ko te huānga roha i runga i te pūtake poutū. Ko te roha o ngā mahi i roto i te raupapa Fourier he rawa he taputapu kaha mō te whakaoti ngā raruraru e tika ana ki te āhuatanga o te huringa i roto i te tuitui, pārōnaki, me te he nekehanga i roto i te faaiteraa tohenga me convolution.

Ko te tangata e kore he mōhio ki pāngarau teitei, me te ki te mahi o te Fourier pūtaiao Wīwī nei, te nuinga pea e kore e matau ki ta te "rarangi" me aha mahi ratou. Otiia kua tino mau tomo tenei tauiraa to tatou oraraa. Kei te whakamahia te reira i kore pāngarau anake, engari ano hoki i physicists, Utaina, tākuta, arorangi, mau aivanaa no, oceanographers me etahi atu. Me tango ano hoki tatou i te titiro ki nga mahi o te pūtaiao nui French nei i hanga te kitea, i mua o tona wa.

Ko te tangata me te Fourier taui

raupapa Fourier Ko tetahi o nga tikanga (me ki tātari me ētahi atu) o te Fourier taui. e tenei tukanga wahi wā katoa rongo te tangata tetahi tangi. To tatou taringa tahuri aunoa i te ngaru oro. E faaaano kaupapa Oscillatory o matūriki timatanga i roto i te reo rapa i roto i te raupapa (te tūāwhiorangi) uara rōrahi ngā mō pepe o tiketike rerekē. Next, e tahuri te roro tenei raraunga ki oro waia hoki tatou. Ko tenei katoa i roto i te tua ki to tatou hiahia mahara iho ranei, engari i roto i te tikanga ki te matau i te tukanga e tangohia e rave rahi tau ki te ako pāngarau teitei.

Ētahi atu kōrero mō te Fourier taui

Te Fourier taui taea te kawea i roto i tātari, ngā tau, me te tahi atu tikanga. raupapa Fourier he tukanga whika mō te decomposing tetahi tukanga oscillatory - i te tai moana me te ngaru o te marama ki te huringa solar (me ētahi atu taonga arorangi) mahi. Mā te whakamahi i enei tikanga pāngarau, he reira taea ki te wetewete i te mahi, e tohu ana i tetahi tukanga oscillatory i roto i te maha o ngā wāhanga sinusoidal e haere i te iti ki te mōrahi me te hurihia. taui i te Fourier ko te mahi whakaahua i te wāhanga me te kaha tīwera o sinusoids ōrite ana ki te auau ngā. Ka taea te whakamahi i tēnei tukanga mō te whakaoti i te whārite rawa matatini e whakaahua te tukanga hihiri e puta ana i raro i te mahi o te wera, te marama pūngao hiko ranei. Ano, whakamahia te raupapa Fourier ki te wehewehe i DC wāhanga i roto i waveforms matatini, te taea te reira ki te whakamāori tika te kitenga whakamātautau i roto i te rongoa, matū me te tātai arorangi.

mōhiohio hītori

Ko te papa taketake o tenei ariā ko te mathematician French Zhan Batist Zhozef Fure. Tona ingoa i muri me tenei tauiraa kua huaina. I te tīmatanga, whakamahia te kaimātai pūtaiao he tikanga ki te ako me te whakamārama i te tikanga o ngāwhā kawe ia - whakatö i roto i totoka wera. fokotu'u Fourier e taea te decomposed te tohatoha kōhikohiko tuatahi o te ngaru waiariki ki sinusoid ohie, ka whai i tona iti pāmahana me te mōrahi, me te tona wā ia o nei. Ko te kupu wae ia taua ki te kia whanganga i iti ki mōrahi me te hurihia. Ko te mahi pāngarau e whakaahua ana i te tihi o runga me raro o te ānau, me te te wāhanga o ia hawarite, ka karanga te Fourier whakaahua ke o te pāmahana tohatoha o whakapuaki. Ko te kaituhi o te ariā o heke mahi tohatoha whānui e he uaua ki te whakamārama pāngarau, i roto i te ngāwari rawa ki te hapai i te maha o ngā mahi wā o te aho, me te whenu, i te nui o hoatu te tohatoha tuatahi.

Ko te parau tumu o te faafariuraa, me nga whakaaro o to'utangatá

To'ume'a o te pūtaiao - te numera ārahi o te tīmatanga o te rau tau tekau mā iwa - kihai i manako ki tenei ariā. ko te whakaaetanga o te Fourier i haea te mahi ka motu whakaahua i te rārangi tika ānau ranei ko te whakahe matua, e taea te māngai reira rite te moni o kīanga sinusoidal e he tonu. Ka rite ki te tauira, whakaaro he "taahiraa" Heaviside: tona uara ko te kore ki te maui o te āputa me tetahi i runga i te matau. E whakaahua ana tēnei mahi te fakafalala o nāianei hiko i runga i te tāupe wa mo te mekameka katinga. ariā Contemporary i taua wa, kore rawa i tūpono he āhuatanga taua, ina e te faaiteraa ka motu ka whakaahuatia e te huinga o tonu, mahi noa, pērā i taupūtanga, sine, rārangi pūrua ranei.

He aha raru te pāngarau French i roto i te ariā o Fourier?

I muri i te katoa, ki te tika ki te tautohe i te mathematician, ka, Whakarāpopoto he raupapa Fourier pākoki mure ore, he taea reira ki te whiwhi i te kanohi tika o te taahiraa o te whakapuaki, ara, ki te te mea he huinga o rite kaupae. I roto i te tīmatanga o te rautau tekau mā iwa, te whakaaro heahea tenei tauākī. Otiia ahakoa nga feaa katoa, kua whakawhānui maha mathematicians te hōkai o te ako o tenei āhuatanga, neke i te reira tua atu i te ako kawenga waiariki. Heoi, haere tonu te nuinga o pūtaiao ki mamae te pātai: "? E ahei te moni o te raupapa poipoi aho converges ki te uara tangohia o te mahi ka motu"

Pūtahitanga o te raupapa Fourier: tauira

te putanga mai i te take o te pūtahitanga wā katoa e hiahia ana koe te aofangatuku o te raupapa mure ore o tau. whakaaro he tauira matarohia mo te māramatanga o tenei āhuatanga. Taea tonu e koe tae te taiepa, ki te he te hawhe te mua ia taahiraa? Akuanei pea e koe e rua mita i te whāinga, te taahiraa matamua piri ki a tawhio noa te hawhe ara, te muri - te tohu o te toru-hauwhā, me muri i te tuarima, ka hinga koe tata 97 ōrau o te ara. Heoi, noa'tu eaha te maha kaupae kua mahi koe e kore, i te ūnga tikanga tae koutou i roto i te tikanga pāngarau tino. Mā te tātaitanga tau, ka taea e tatou e whakamatautau e i roto i te mutunga kia ofi ki he tawhiti i homai takirihia iti. Ko te ōrite ki te tohu whakaatu e te uara tapeke o tetahi hawhe, kotahi tuawha, a na i runga i. E ahu E. ki kotahitanga tenei.

Ko te take o te pūtahitanga: rua nga mai, ranei mauhaa a te Ariki Kelvin

Toutou whakatika te pātai i roto i te mutunga o te rautau tekau mā iwa, ka kua tamata te raupapa Fourier ki te whakamahi ki te matapae i te kaha o nga timu me rere. I taua wa, i whakaaro Ariki Kelvin pūrere ko te rorohiko tairitenga i whakaaetia kaumoana kaipuke, me te kaihokohoko moana aroturuki ko te āhuatanga māori. Tenei tikanga tautuhi huinga o wāhanga, me amplitudes o te teitei tepu o nga tai, me nga taime wa hāngai, āta whanganga i roto i te whanga, puta noa i te tau. Ia tawhā Ko te sinusoidal tiketike faaiteraa wae tai, a ko tetahi o nga wae auau. Ko te hua ine e whai wāhi ki te pūrere rorohiko Ariki Kelvin, synthesizing ānau e tohu teitei o te wai, ano he mahi o te tau e whai ake nei. Tino hohoro, unu enei hononga i runga mo nga whanga katoa o te ao.

A ki te mea ka pakaru te tukanga mahi ka motu?

I taua wa, e au ra te reira kitea e taea te pūrere te matapae i te ngaru tai, ki maha āhuatanga o te pūkete tātai i te maha nui o wāhanga me amplitudes, a pera whakarato i tētahi matapae tika atu. Otiia, ka tahuri te reira i roto i taua kore e kitea i tenei tauira i roto i te wā i reira te faaiteraa tai kia e ka synthesized, i roto i te peke koi, e ko, he ka motu. I roto i te kaupapa e ki te taputapu tomo raraunga i te ripanga o ngā wā, Tātaitia reira torutoru whakarea Fourier. Ora i te mahi taketake e tika ana ki te wāhanga sinusoidal (i roto i runga i te tau whakarea i kitea). taea ana te ruri te rerekētanga i waenganui i te taketake me te whakapuaki toe langa i tetahi wāhi. A, no te taea te kite i nga tātaitanga tukurua me whakataurite e kore e heke te uara o te hapa nui. Heoi, kei te paetata ratou i roto i te rohe e hāngai ana ki te wāhi o te whaturama, me tetahi atu wāhi ahu ki te kore. I roto i te 1899, whakapumautia tenei hua i takahi Hohua Willard Gibbs o University Yale.

Pūtahitanga o te raupapa Fourier me te whanaketanga o pāngarau rite te katoa

e kore e tātari Fourier tono ki kīanga kei roto i te maha mure ore o pakū i te tetahi wā. I roto i te raupapa Fourier whānui, ki te māngai te mahi taketake e te hua o te inenga tinana tūturu, ūngutungutu tonu. Kua arahina ngā pātai o pūtahitanga o tenei tukanga mō ngā akomanga motuhake o ngā mahi ki peka hou o te pāngarau, pērā i te ariā o ngā mahi te whakatakiruatanga o. Kei te whai pānga te reira ki te ingoa pērā i Schwartz, J .. Mikusiński me Temipale J.. I raro i tenei ariā, he pūtake ariā mārama, me te pau mo taua faaiteraa kua whakapumautia rite te raorao mahi Dirac (whakaahua ana te reira i te rohe o te wāhi kotahi, hāngai i roto i te tata ore o te pūwāhi) me "taahiraa" Heaviside. Na roto i tenei mahi ka hāngai mō te whakaoti whārite me ngā raruraru, e whai wāhi ariā pūmanawa raupapa Fourier: ira tiaki, wāhi papatipu, dipoles autō, me te kawenga takiwa i runga i te kurupae.

tikanga Fourier

raupapa Fourier, i runga i te mau parau tumu o te pokanoa, timata ki te whāwehe o ngā puka matatini ki ohie. Hei tauira, he huringa i roto i te rere wera e tika ana ki tona wahi i roto i te aukati ngā o te wera te tuuraa rauemi o āhua kōhikohiko ranei te huri mata whenua - he ru, he huringa i roto i te ohuraa o te tinana fakasilesitialé - te mana o te aorangi. Tikanga, enei whārite whakaahua māmā pūnaha puāwaitanga ohie faatiti'aifarohia hoki ia roangaru takitahi. whakaaturia Fourier kua e taea te whakarapopototia rongoā ohie ake rite hoki atu mahi matatini. I roto i te reo o pāngarau, raupapa Fourier - he tikanga mo te tukunga o te moni faaiteraa o hawarite - whenu me ngaru sine. Na reira, tenei tātaritanga kua mohiotia ano i raro i te ingoa "tātari hawarite".

raupapa Fourier - he tikanga pai ki te "tau rorohiko"

I mua ki te hanga o te hangarau rorohiko tikanga Fourier ko te patu pai i roto i te täoro o pūtaiao mahi ki te āhua poipoi o to tatou ao. raupapa Fourier i roto i te puka matatini taea ki a koe whakaoti kore anake raruraru ohie e te hunga Nireaha ki te whakatika tono o ture a Newton o rehe, engari ano hoki nga whārite taketake. ka te nuinga o nga āhuatanga o te pūtaiao Newtonian o te rautau tekau mā iwa taea anake e tika ana ki te tikanga Fourier.

raupapa Fourier tenei ra

Ki te whanaketanga o Fourier taui i whakatika rorohiko ki te taumata hou. Kei te pūmau tenei tikanga i roto i tata mara katoa o te pūtaiao me te hangarau. Ka rite ki te tauira, he audio mamati me te ataata. Kua Ko tōna whakatinanatanga kua meinga taea whakawhetai anake ki te ariā whakawhanakehia e te mathematician French o te tīmatanga o te rau tau tekau mā iwa. Ko te kupu, kua whakaaetia te raupapa Fourier i roto i te puka matatini ki te hanga i te pakaruhanga i roto i te ako o te wāhi i waho. I tua atu, kua pāngia reira te ako o te ahupūngao o ngā rauemi Semiconductor me wē, Acoustics ngaruiti, Oceanography, hihiani, seismology.

raupapa pākoki Fourier

I roto i te pāngarau, he raupapa Fourier ko te ara o te māngai mahi matatini noho rite te moni o ohie. I roto i te wā whānui, kia kia e taea te maha o ngā kīanga. Ko te rahi te tokomaha kiia i roto i te tatauranga, i whiwhi ai te tika atu te hua whakamutunga te. Ko te whakamahi te nuinga noa o te whenu pākoki ohie mahi sine ranei. I roto i tenei take, ka karanga te raupapa Fourier te pākoki, me te whakatau o taua mau parau - whāwehe hawarite. Tenei tikanga e whai wāhi nui i roto i te pāngarau. Tuatahi o te katoa, te raupapa pākoki whakarato he tikanga mo te whakapakoko, me te te ako o ngā mahi, ko reira te wae matua o te ariā. I tua atu, ka taea te reira ia tatou ki te whakaoti i te maha o ngā raruraru i roto i te ahupūngao pāngarau. I te pae hopea, kua whai wāhi tenei ariā ki te whanaketanga o te tātari pāngarau, hoatu ana e ia ara ki te maha o peka tino nui o te pūtaiao pāngarau (ariā o pāwhaitua, te ariā o ngā mahi wā). I tua atu, i te tīmatanga mō te whanaketanga o te whai ake ariā: huinga, mahi o te tāupe tūturu, tātari mahi, a hoki whakatakotoria te turanga mo te tātari hawarite.