Fourier Series vs Fourier Hloov pauv
Fourier series decomposes ib ntus ua haujlwm rau hauv cov lej ntawm sines thiab cosines nrog ntau zaus thiab amplitudes. Fourier series yog ib ceg ntawm Fourier tsom xam thiab nws tau qhia los ntawm Joseph Fourier. Fourier Transform yog kev ua lej ua lej uas tawg lub teeb liab rau hauv nws cov khoom siv ntau zaus. Thawj lub teeb liab uas hloov lub sij hawm yog hu ua lub sij hawm domain sawv cev ntawm lub teeb liab. Lub Fourier transform yog hu ua zaus domain sawv cev ntawm lub teeb liab vim nws nyob ntawm qhov zaus. Ob qhov ntau zaus sawv cev ntawm lub teeb liab thiab cov txheej txheem siv los hloov lub teeb liab mus rau qhov zaus sau npe yog hu ua Fourier transform.
Fourier Series yog dab tsi?
Raws li tau hais ua ntej, Fourier series yog qhov nthuav dav ntawm lub sijhawm ua haujlwm siv cov lej tsis kawg ntawm sine thiab cosines. Fourier series tau pib tsim thaum daws qhov sib npaug ntawm cov cua sov tab sis tom qab ntawd nws tau pom tias tib cov txheej txheem tuaj yeem siv los daws cov teeb meem lej loj tshwj xeeb rau cov teeb meem uas cuam tshuam nrog cov kab sib txawv sib txawv nrog cov coefficients tas li. Tam sim no, Fourier series muaj cov ntawv thov hauv ntau thaj chaw xws li hluav taws xob engineering, kev vibration tsom xam, acoustics, optics, teeb liab ua, ua duab, quantum mechanics thiab econometrics. Fourier series siv cov kev sib raug zoo ntawm sine thiab cosine. Kev suav thiab kev kawm ntawm Fourier series yog lub npe hu ua kev soj ntsuam kev sib haum xeeb thiab muaj txiaj ntsig zoo thaum ua haujlwm nrog kev ua haujlwm tsis tu ncua, txij li nws tso cai rau kev ua txhaum txoj haujlwm hauv cov ntsiab lus yooj yim uas tuaj yeem siv los daws qhov teeb meem qub.
Fourier transform yog dab tsi?
Fourier transform txhais tau tias muaj kev sib raug zoo ntawm lub teeb liab hauv lub sijhawm sau npe thiab nws cov sawv cev hauv qhov zaus. Lub Fourier hloov decomposes ib qho kev ua haujlwm rau hauv oscillatory functions. Txij li qhov no yog ib qho kev hloov pauv, cov teeb liab qub tuaj yeem tau txais los ntawm kev paub txog kev hloov pauv, yog li tsis muaj cov ntaub ntawv tsim lossis ploj hauv cov txheej txheem. Kev kawm ntawm Fourier series yeej muab kev txhawb siab rau Fourier hloov. Vim hais tias ntawm cov khoom ntawm sine thiab cosine nws muaj peev xwm rov qab tau cov nyiaj ntawm txhua yoj pab rau cov sum siv ib qho tseem ceeb. Fourier transform muaj qee yam khoom siv xws li linearity, translation, modulation, scaling, conjugation, duality thiab convolution. Fourier transform yog siv nyob rau hauv kev daws qhov sib txawv sib npaug txij li Fourier transform yog ze ze rau Laplace transformation. Fourier transform kuj tseem siv hauv nuclear magnetic resonance (NMR) thiab lwm yam spectroscopy.
Qhov txawv ntawm Fourier Series thiab Fourier Transform
Fourier series yog qhov nthuav dav ntawm lub sijhawm teeb liab raws li kev sib xyaw ua ke ntawm sines thiab cosines thaum Fourier hloov pauv yog cov txheej txheem lossis kev ua haujlwm siv los hloov cov teeb liab ntawm lub sijhawm sau rau hauv ntau zaus. Fourier series yog txhais rau cov cim qhia raws sijhawm thiab Fourier hloov pauv tuaj yeem siv rau aperiodic (tshwm sim tsis muaj sijhawm) cov cim. Raws li tau hais los saum no, txoj kev kawm ntawm Fourier series yeej muab kev txhawb siab rau Fourier transform.
