Fourier gbanwee. Fast Fourier gbanwee. Pụrụ iche Fourier gbanwee

Fourier mgbanwe - mgbanwe, ha na-akpa a na-ọrụ nke a n'ezie agbanwe. Nke a na ime ihe a rụrụ oge ọ bụla anyị na-aghọta dị iche iche ụda. Ntị na-arụpụta akpaka "ngụkọta oge", nke mezuo anyị nsụhọ nwere ike nanị mgbe nnyocha nke ngalaba nke elu mgbakọ na mwepụ. ikpe ngwa na a mmadụ mgbanwe chepụtara, nke na ụda (ot ọma jijiji na ngagharị nke ahụ na ihe na-agbanwe na-ajụ, nke mgba na-efegharị efegharị ụdị ke siri ike, mmiri mmiri ma ọ bụ gaseous ajụ) na-nyere na a nso nke consecutive ụkpụrụ nke olu larịị nke aj u ná mgbanwe nke elu. Mgbe nke a, ụbụrụ amama ozi niile maara ụda.

Mathematical Fourier gbanwee

Akakabarede nke ụda ebili mmiri ma ọ bụ ndị ọzọ vibration Filiks (ìhè emission na oké osimiri tide na stellar ma ọ bụ anyanwụ cycles) nwere ike rụrụ na site mgbakọ na mwepụ ụzọ. N'ihi ya, iji ndị a usoro, na ọrụ nwere ike gbasaa site na-ewebata ọma jijiji na Filiks ka nke sinusoidal mmiri, i.e. wavy akụkụ nke na-aga site na a kacha nta ka a kacha wee ọzọ a kacha nta, dị ka ebili mmiri nke oké osimiri. Fourier mgbanwe - mgbanwe ọrụ nke na-akọwa na-adọ ma ọ bụ njupụta nke ọ bụla sinusoid kwekọrọ a akpan akpan ugboro. Adọ bụ a amalite nke usoro, na njupụta - nke ya elu.

Fourier gbanwee (atụ na-egosi na foto) bụ nnọọ ngwá ọrụ dị ike, nke a na-eji dị iche iche ubi nke sayensị. Mgbe ụfọdụ, ọ na-eji dị ka a ngwọta kama mgbagwoju arụmarụ nke na-akọwa ike Filiks aa n'okpuru nduzi nke ìhè, okpomọkụ ma ọ bụ eletriki ike. N'ọnọdụ ndị ọzọ, ọ na-enye ohere ị na-akọwa mgbe mmiri na mgbagwoju waveforms, n'ihi na nke a nwere ike ịbụ eziokwu ịkọwa dị iche iche ibuo kwuru na onwu, nkà mmụta ọgwụ na mbara igwe.

ya mere eme

Onye mbụ itinye usoro a bụ French mgbakọ na mwepụ Zhan Batist Fure. Akakabarede, ekemende aha ya, mbụ ji kọwaa okpomọkụ conduction usoro. Fourier ya dum okenye aku amụ Njirimara nke okpomọkụ. O mere ka nnukwu ihe onyinye mgbakọ na mwepụ ozizi mkpebi siri ike nke na mgbọrọgwụ nke algebraic arụmarụ. Fourier bụ a prọfesọ nke analysis na Ecole Polytechnique, Odeakwụkwọ nke Institute of Egyptology, bụ eze ukwu ọrụ, nke mere ka a bido na oge nke na-ewu nke ụzọ Turin (n'okpuru idu ndú ya drained nke ihe karịrị 80 puku square Kilomita ogwu iba swamps). Otú ọ dị, ihe a nile activism emeghị ka ha kwụsị ọkà mmụta sayensị na-mgbakọ na mwepụ analysis. Na 1802 e nwetara ihe akụkụ na-akọwa Mgbasa nke okpomọkụ na solids. Na 1807, ọkà mmụta sayensị chọpụtara a usoro maka idozi a akụkụ, nke a bịara mara dị ka "Fourier gbanwee".

thermal conductivity analysis

Researchers na-eji a mgbakọ na mwepụ usoro na-akọwa na okpomọkụ conduction usoro. A adaba atụ, ebe ọ dịghị ihe isi ike na mgbakọ bụ Mgbasa nke kwes ume site ígwè mgbaaka, otu akụkụ mikpuru a ọkụ. Iji mepụta nwere Fourier red ọkụ akụkụ nke mgbanaka ma lie ya na ezi ájá. Mgbe nke ahụ gasịrị, na ọnọdụ okpomọkụ hà rụrụ na ndị na-abụghị akụkụ ya. Ná mmalite, okpomọkụ na-ekesa bụ oge ufodu: akụkụ nke mgbanaka - oyi, na ndị ọzọ - na-ekpo ọkụ, n'etiti zones nwere ike na-edebe ihe a nkọ okpomọkụ grajentị. Otú ọ dị, n'oge okpomọkụ nkesa gafee metal elu, ọ na-aghọ ihe edo. Ya mere, n'oge na-adịghị, nke a na-ewe n'ụdị a enweghị ife. First eserese nwayọọ nwayọọ enwekwu na mbelata were were, n'ụzọ ziri ezi na iwu nke mgbanwe nke cosine ma ọ bụ enweghị ọrụ. Wave nwayọọ nwayọọ equalized na dị ka a n'ihi okpomọkụ na-aghọ edo ke ofụri elu nke mgbanaka.

Na-ede nke usoro a na-eche na mbụ nkesa bụ nnọọ oge ufodu nwere ike ghoro a nọmba nke mbụ enweghị mmiri na ebili mmiri. Onye ọ bụla n'ime ha ga-enwe ya na-adọ (mbụ ọnọdụ) na ya kacha okpomọkụ. N'ihi ya ọ bụla dị otú ahụ akụrụngwa mgbanwe site na a kacha nta ka a kacha na azụ mezue mgbanwe gburugburu mgbanaka integer ugboro. Akụrụngwa na-enwe a oge nke a na-akpọ isi harmonic, na uru abụọ ma ọ bụ karịa oge - nke abụọ na na. Dị ka ihe atụ, a mgbakọ na mwepụ ọrụ na-akọwa na kacha okpomọkụ, na-adọ ma ọ bụ ọnọdụ a na-akpọ Fourier gbanwee nke nkesa ọrụ. Scientist me otu akụrụngwa nke siri ike mgbakọ na mwepụ nkọwa, maka mfe na-eji ngwá ọrụ ndị - ahịrị enweghị na cosine, na ego nke na-enye mbụ nkesa.

Ihe kachasi mkpa n'ime analysis

Ime nke a na analysis na akakabarede nke okpomọkụ nkesa na ihe siri ike ihe, na-enwe ihe annular udi, a mgbakọ na mwepụ na-eche na-amụba oge nke sinusoidal mmiri iduga ya ngwa ngwa damping. Nke a na-anya na isi na nke abụọ harmonics. The ikpeazụ okpomọkụ esịmde ugboro abụọ karịa na kacha nta ụkpụrụ ke otu ngafe, na mbụ - nanị otu ugboro. Ọ na-enyo na anya njem okpomọkụ nke abụọ harmonic bụ ọkara na nke isi. Ke adianade do, grajentị nke nkera nke abụọ ga-steeper karịa nke mbụ. Ya mere, ebe a ọzọ ufiop thermal agbanwe oge na-aga nwaanyị di ya nwụrụ ntakiri anya, mgbe ahụ, a ga-damped harmonic ugboro anọ ngwa ngwa karịa isi, dị ka a ọrụ nke oge. Na ndị na-esonụ usoro ga-ọbụna ngwa ngwa. Mgbakọ na mwepụ kweere na usoro a na-enye ohere anyị gbakọọ usoro nke mbụ nkesa nke okpomọkụ na oge.

Call dịkọrọ ndụ

Fourier gbanwee algọridim aghọwo a ịma aka ndị n'ọnụ ntọala nke mgbakọ na mwepụ na n'oge ahụ. Ná mmalite nke iri na itoolu na narị afọ, ọtụtụ ndị a ma ama ndị ọkà mmụta sayensị, gụnyere Lagrange, Laplace, Poisson, Legendre na Biot anabataghị ya mkwuputa na okpomọkụ nke mbụ nkesa na-ghoro mmiri n'ụdị isi-efegharị efegharị na elu ugboro. Otú ọ dị, Academy nke Sciences ike eleghara pụta nwetara mgbakọ na mwepụ, na ọdịda ya na Nrite maka ozizi nke okpomọkụ conduction nke iwu, nakwa dị ka na-eduzi ya tụnyere ahụ nwere. Na Fourier obibia, isi ihe mgbochi bụ na a discontinuous ọrụ na-anọchi anya a nchikota nke ọtụtụ sinusoidal ọrụ, nke na-aga n'ihu. Mgbe niile, ha na-akọwa na bursting ogologo na curved edoghi. Contemporary ọkà mmụta sayensị ama mgbe zutere ndị dị otú ahụ a ọnọdụ, mgbe discontinuous ọrụ kọwara a Nchikota na-aga n'ihu, dị ka quadratic, linear, enweghị ma ọ bụ exhibitor. Ke edinam na a mgbakọ na mwepụ ziri ezi ya na-azọrọ, nchikota nke enweghi ngwụcha usoro nke trigonometric ọrụ kwesịrị ịbụ nanị kpọmkwem ọsọ. Mgbe ndị dị otú ahụ a na-ekwu yiri uche na-adịghị. Otú ọ dị, n'agbanyeghị na obi abụọ nke ndị nnyocha ụfọdụ (eg Claude Navier, Sofi Zhermen) mụtakwuo akporo nke nnyocha ma kpọpụta ha nke analysis nke okpomọkụ nkesa. A mgbakọ na mwepụ, ugbu a, wee na-ata ahụhụ ajụjụ bụ ma a nchikota nke ọtụtụ sinusoidal ọrụ na-ebelata ka ihe onyinyo nke bursting.

200 afọ akụkọ ihe mere

Nke a Ozizi ghọrọ usoro karịrị narị afọ abụọ, taa, a akpatre kpụrụ. Site n'enyemaka nke gbasara ohere ma ọ bụ Na ɛhe na ọrụ na-waba sinusoidal mmiri nwere a ugboro, na-adọ na njupụta. Nke a akakabarede na-enwetara site na abụọ dị iche iche mgbakọ na mwepụ ụzọ. The mbụ n'ime ha na-eji na o mere mgbe ndị isi iyi bụ a na-aga n'ihu ọrụ, na nke abụọ - ke ikpe ebe ọ na-anọchi anya a plurality nke pụrụ iche na onye mgbanwe. Ọ bụrụ na okwu a na-enwetara site na ụkpụrụ, nke na-kọwaa na pụrụ iche etiti oge, ọ pụrụ ekewa n'ime ọtụtụ sinusoidal pụrụ iche frequencies okwu - si kasị ala na mgbe ahụ okpukpu abụọ, okpukpu atọ, na otú pụta n'elu isi. A ego a na-akpọ ndị Fourier usoro. Ọ bụrụ na ndị mbụ okwu esetịpụrụ uru nke ọ bụla ezigbo nọmba, ọ ga-agbajikwa ala n'ime multiple sinusoidal niile kwere omume frequencies. Ọ na-akpọ a Fourier integral, na mkpebi na-egosi a mgbanwe nke integral ọrụ. N'agbanyeghị nke usoro maka inweta mgbanwe, ka onye ọ bụla ugboro ga-egosi abụọ nọmba: njupụta na ugboro. Ndị a ụkpụrụ na-owụt dị ka otu mgbagwoju nọmba. Expression mgbagwoju variables ozizi ọnụ na Fourier mgbanwe ịrụ mgbawa kwere imewe nke dị iche iche na electric na sekit na sekit, na analysis nke n'ibu vibrations, ọmụmụ nke ife Mgbasa usoro na ibe ya.

Fourier gbanwee taa

N'oge ndị a, ọmụmụ nke usoro isi Juda ala ịchọta ụzọ dị irè maka mgbanwe site ọrụ iji tọghata ya azụ na-uche. Nke a ihe ngwọta na-akpọ kpọmkwem na inverse Fourier gbanwee. Gịnị ka ọ pụtara? Iji chọpụta integral na-eme ka a kpọmkwem Fourier gbanwee, i nwere ike iji mgbakọ na mwepụ ụzọ, ma i nwere ike analytic. N'agbanyeghị eziokwu na mgbe ha na-eji na-eme, e nwere ụfọdụ ihe isi ike, ọtụtụ integrals ama na e hụrụ ma banye na mgbakọ na mwepụ obere akwụkwọ. Site n'enyemaka nke space ụzọ pụrụ ịgbakọta okwu, na udi nke dabeere na ibuo data, a ọrụ onye integrals na tebụl na-efu efu, na ha bụ ndị siri ike iche n'echiche na ihe gbasara nyocha ụdị.

Tupu biakwa obibia nke na kọmputa engineering mgbawa ndị dị otú ahụ mgbanwe ndidi agwụ nnọọ ike, ha na-achọ ntuziaka ogbugbu nke a ọnụ ọgụgụ buru ibu nke som arụmọrụ na-adabere na ọnụ ọgụgụ nke ihe ndị na-akọwa na-efegharị efegharị ọrụ. Iji ikwado mmezi taa, e nwere ndị pụrụ iche na mmemme, na-ekwe ka mejuputa ọhụrụ gbasara nyocha ụzọ. Ya mere, na 1965, Dzheyms Kuli na Dzhon Tyuki kere software bịara mara dị ka "Fast Fourier ịgbanwe". Ọ na-azọpụta oge nke ngụkọta oge site na mbenata ọnụ ọgụgụ nke multiplications na analysis nke usoro. "Fast Fourier ịgbanwe" The usoro a dabeere na nkerisi usoro n'ime a ọnụ ọgụgụ buru ibu nke edo sample ụkpụrụ. N'ihi ya, ọnụ ọgụgụ nke multiplications na-belata ọkara n'otu mbenata ọnụ ọgụgụ nke ihe.

N'itinye Fourier gbanwee

Usoro a na-eji dị iche iche ubi: Na nọmba Ozizi, physics, mgbaàmà nhazi, combinatorics, puru Ozizi, Cryptography, ọnụ ọgụgụ, Oceanography, Gbasara Anya, acoustics, na ndị ọzọ geometries. Rich ohere na ya iji na-dabere na a ọnụ ọgụgụ nke bara uru atụmatụ, nke na-akpọ "Njirimara nke Fourier mgbanwe." Ka anyị tụlee ha.

1. The akakabarede ọrụ bụ a linear ọrụ na a kwekọrọ ekwekọ normalisation bụ unitary. Nke a ihe onwunwe a maara dị ka Parseval Theorem, ma ọ bụ na ọ dị n'ozuzu, ndị Theorem Plansherelja ma ọ bụ Pontrjagin dualism.

2. The akakabarede bụ reversible. Ọzọkwa, ndị na-abụghị N'ihi bụ n'ụzọ yiri udi dị ka kpọmkwem na-agwa okwu.

3. The sinusoidal isi okwu bụ ha onwe ha differentiated ọrụ. Nke a pụtara na ndị dị otú ahụ yiri agbanwe linear arụmarụ na mgbe nile ọnụọgụ na a ot algebraic.

4. Dị ka "convolution" Theorem, usoro na-eme ka a mgbagwoju ime ihe na elementrị multiplication.

5. pụrụ iche Fourier ịgbanwe nwere ike ngwa ngwa e mere na a na kọmputa na-eji "ngwa ngwa" usoro.

Ọdịiche nke Fourier gbanwee

1. Ọtụtụ mgbe na okwu a ji na-ezo aka a na-aga n'ihu mgbanwe, na-enye ọ bụla quadratically integrable okwu dị ka nchikota nke mgbagwoju exponential okwu na kpọmkwem angular frequencies na amplitudes. Nke a ụdị nwere ọtụtụ dị iche iche iche-iche, nke nwere ike ịbụ dị iche iche mgbe nile na ọnụọgụ. The na-aga n'ihu usoro na-agụnye a akakabarede table, nke nwere ike dị na mgbakọ na mwepụ obere akwụkwọ. A generalized ikpe bụ fractional akakabarede, adịru usoro a nwere ike akpọlite ndị chọrọ n'ezie ike.

2. The na-aga n'ihu usoro bụ a generalization nke mbụ Usoro nke Fourier usoro kọwaa nke ọ bụla oge na ọrụ ma ọ bụ okwu, nke adị a mmachi ebe na-anọchi anya ha dị ka a usoro nke sinusoids.

3. pụrụ iche Fourier gbanwee. Nke a na usoro na-eji na Mgbakọ maka nkà mmụta sayensị na mgbakọ na digital mgbaàmà nhazi. Iji mepụta ụdị ngụkọta oge a chọrọ ka a ọrụ nke ịchọpụta na a pụrụ iche set nke onye ihe, oge ma ọ bụ mmachi region kama na-aga n'ihu Fourier integrals. Signal akakabarede na nke a na-anọchi anya dị ka a nchikota nke sinusoids. The iji "ngwa ngwa" usoro enye ohere iji ihe digital ngwọta maka niile bara uru na nzube.

4. The window Fourier gbanwee bụ a generalized echiche nke classic usoro. N'adịghị ka ọkọlọtọ ngwọta mgbe mgbaàmà ụdịdị dị iche iche na-eji, nke a na-weere na na nso nke ịdị adị nke a na agbanwe bụ nke otu mmasị ebe a bụ nanị obodo ugboro nkesa ma na-na mbụ agbanwe (oge).

5. The abụọ akụkụ Fourier gbanwee. Nke a na usoro a na-eji na-arụ ọrụ na abụọ akụkụ arrays nke data. N'ọnọdụ dị otú ahụ, na ntughari a rụrụ n'ime otu direction, na mgbe ahụ na - na ndị ọzọ.

ọgwụgwụ

Taa, Fourier usoro a gbanyesiri mkpọrọgwụ ike na ihe dị iche iche ubi nke sayensị. Ka ihe atụ, na 1962 ọ meghere udi nke DNA abụọ helix iji Fourier analysis na njikọ na X-ray diffraction. Adịbeghị anya kristal lekwasịrị anya DNA emep uta eri, n'ihi na ihe oyiyi nke na-enwetara site diffraction, dere na film. Nke a na foto nyere ihe ọmụma banyere uru nke njupụta site na iji Fourier gbanwee a crystal Ọdịdị. Adọ data nwetara site atụnyere DNA diffraction kaadị na kaadị na-nwetara na analysis of yiri chemical owuwu. N'ihi ya, ndị ọkà weghachiri crystal Ọdịdị - mbụ ọrụ.

Fourier gbanwee egwu a nnukwu ọrụ ke ọmụmụ nke mbara, na physics nke okporo ọkụ ihe na plasma, ngwa ndakwa nri acoustics, Oceanography, Rada, seismology na ọgwụ na ule na-eweta.