Pryamokutna Funkciya odinichnij impuls pryamokutnij impuls abo pryamokutne vikno kuskovo stala funkciya sho viznachayetsya yak Pryamokutna Funkciya r e c t t t 0 t gt 1 2 1 2 t 1 2 1 t lt 1 2 displaystyle mathrm rect t sqcap t begin cases 0 amp t gt frac 1 2 3pt frac 1 2 amp t frac 1 2 3pt 1 amp t lt frac 1 2 end cases Inodi znachennya funkciyi v tochkah r e c t 1 2 displaystyle mathrm rect pm tfrac 1 2 mozhe viznachatisya yak 0 abo 1 Inshe viznachennya Funkciyi cherez Funkciyu Gevisajda 8 t displaystyle theta t r e c t t t 8 t t 2 8 t t 2 displaystyle mathrm rect left frac t tau right theta left t frac tau 2 right theta left t frac tau 2 right abo po inshomu r e c t t 8 t 1 2 8 t 1 2 displaystyle mathrm rect t theta left t frac 1 2 right theta left t frac 1 2 right Zmist 1 Vlastivosti 2 Vikoristannya v teoriyi jmovirnostej 3 Posilannya 4 Div takozhVlastivosti RedaguvatiIntegral pryamokutnoyi Funkciyi r e c t t d t 1 displaystyle int limits infty infty mathrm rect t dt 1 nbsp Pohidna pryamokutnoyi funkciyi rivna 0 okrim tochok 1 2 displaystyle pm tfrac 1 2 nbsp de yiyi ne isnuye v klasichnomu rozuminni Yaksho rozglyadati uzagalneni funkciyi po pohidna pryamokutnoyi funkciyi zapishetsya cherez delta funkciyu Diraka rect t d t 1 2 d t 1 2 displaystyle operatorname rect t delta left t frac 1 2 right delta left t frac 1 2 right nbsp Peretvorennya Fur ye pryamokutnoyi Funkciyi r e c t t e i 2 p f t d t sin p f p f s i n c p f displaystyle int infty infty mathrm rect t cdot e i2 pi ft dt frac sin pi f pi f mathrm sinc pi f nbsp dlya zvichajnoyi chastoti f i1 2 p r e c t t e i w t d t 1 2 p s i n w 2 w 2 1 2 p s i n c w 2 displaystyle frac 1 sqrt 2 pi int infty infty mathrm rect t cdot e i omega t dt frac 1 sqrt 2 pi cdot frac mathrm sin left omega 2 right omega 2 frac 1 sqrt 2 pi mathrm sinc left omega 2 right nbsp dlya kutovoyi chastoti w de u formulah ye nenormalizovana versiya funkciyi sinc dijsnoF r e c t f r e c t e i 2 p f t d t 1 2 1 2 e i 2 p f t d t 1 2 i p f e i 2 p f t 1 2 1 2 1 2 i p f e i p f e i p f 1 p f sin p f s i n c p f displaystyle begin aligned mathcal F mathrm rect f amp int infty infty mathrm rect rm e rm i 2 pi ft mathrm d t amp int 1 2 1 2 rm e rm i 2 pi ft mathrm d t amp frac 1 2 rm i pi f left rm e rm i 2 pi ft right 1 2 1 2 amp frac 1 2 rm i pi f left rm e rm i pi f rm e rm i pi f right amp frac 1 pi f sin left pi f right amp mathrm sinc left pi f right end aligned nbsp dd dd Navpaki dlya normovanoyi funkciyi sinc peretvorennya Fur ye rivne pryamokutnij funkciyi s i n c t e 2 p i f t d t r e c t f displaystyle int limits infty infty mathrm sinc t e 2 pi ift dt mathrm rect f nbsp Pryamokutna funkciya rivna granici racionalnih funkciyi r e c t t lim n n Z 1 2 t 2 n 1 displaystyle mathrm rect t lim n rightarrow infty n in mathbb Z frac 1 2t 2n 1 nbsp Trikutna funkciya mozhe buti viznachena yak zgortka dvoh pryamokutnih Funkcij t r i t r e c t t r e c t t displaystyle mathrm tri t mathrm rect t mathrm rect t nbsp Vikoristannya v teoriyi jmovirnostej RedaguvatiDokladnishe Neperervnij rivnomirnij rozpodilYaksho rozglyadati pryamokutnu funkciyu yak funkciyu gustini jmovirnosti to vona zadaye okremij vipadok neperervnogo rivnomirnogo rozpodilu z a b 1 2 1 2 displaystyle a b frac 1 2 frac 1 2 nbsp Harakteristichna funkciya dlya neyi rivna f k sin k 2 k 2 displaystyle varphi k frac sin k 2 k 2 nbsp a tvirna funkciya momentiv M k s i n h k 2 k 2 displaystyle M k frac mathrm sinh k 2 k 2 nbsp de s i n h t displaystyle mathrm sinh t nbsp giperbolichnij sinus Posilannya RedaguvatiWeisstein Eric W Rectangle Function angl na sajti Wolfram MathWorld Div takozh RedaguvatiPeretvorennya Fur ye Trikutna funkciya Funkciya sinc Funkciya Gevisajda Otrimano z https uk wikipedia org w index php title Pryamokutna funkciya amp oldid 19315533
