{"id":247,"date":"2025-10-31T00:25:51","date_gmt":"2025-10-31T00:25:51","guid":{"rendered":"https:\/\/vibromera.eu\/glossary\/spectral-leakage\/"},"modified":"2026-05-23T22:15:32","modified_gmt":"2026-05-23T22:15:32","slug":"spectral-leakage","status":"publish","type":"glossary","link":"https:\/\/vibromera.eu\/hr\/glossary\/spectral-leakage\/","title":{"rendered":"\u0160to je spektralno propu\u0161tanje u FFT analizi?"},"content":{"rendered":"

Razumijevanje spektralnog curenja<\/h1>\n\t\t
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\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Balanset-1A\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\ture\u0111aji<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tPortable balancer & Vibration analyzer Balanset-1A<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>1,975.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t
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\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Detalj\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tdijelovi<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tsenzor vibracija<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>90.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Opti\u010dki\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tdijelovi<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tOpti\u010dki senzor (laserski tahometar)<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>124.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Vibromera\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\ture\u0111aji<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tBalanset-4<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>6,803.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>
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\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Magnetska\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tdijelovi<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tMagnetski stalak Insize nosivosti 60 kgf<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>46.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t
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\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Reflektiraju\u0107a\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tdijelovi<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tReflektiraju\u0107a traka<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>10.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\"Sadr\u017eaj\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t
<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\ture\u0111aji<\/a><\/span>\n\t\t\t\t\t\t\t\t

\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tDinami\u010dki balanser \u201cBalanset-1A\u201d OEM<\/a>\n\n\t\t\t\t\t\t\t\t<\/h4>\n\n\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t
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\u20ac<\/span>1,735.00<\/span> + PDV (ako je primjenjivo)<\/h4><\/div>\n\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t<\/i><\/a>\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/a>Dodaj u ko\u0161aricu<\/a>\t\n\t\t\t<\/span>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/section>\n\t\t\n

Spektralno propu\u0161tanje<\/strong> je oblik gre\u0161ke mjerenja koji se javlja tijekom Brza Fourierova transformacija (FFT)<\/a> analize signala. Radi se o “razmazivanju”, ili \u0161irenju, energije iz jedne diskretne frekvencijske vr\u0161ne vrijednosti u vrhu spektra<\/a> susjedne frekvencijske kanale. Ovo razmazivanje iskrivljuje i amplitudu i prividnu frekvenciju prave vibracijske komponente, a mo\u017ee sakriti manje signale ili dovesti do neispravne dijagnoze. Razumijevanje je bitno za pouzdanost bilo kojeg FFT rezultata.<\/p>\n

1. Definicija: \u0160to je spektralno curenje?<\/h2>\n

U idealnom svijetu, \u010dist sinusoidan na jednoj frekvenciji pojavio bi se u spektru kao jedna, beskona\u010dno tanka linija. Spektralno curenje je \u0161to se u stvarnom svijetu umjesto toga ereigna: energija koja bi trebala biti u jednom FFT<\/a> kanalu “curi” bo\u010dno u susjedne kanale, stvaraju\u0107i vr\u0161nu vrijednost sa \u0161irokim marginama umjesto o\u0161troga vrha. Rezultat je spektar koji izgleda nejasnije i bu\u010dnije nego \u0161to sama fizika opravdava, \u0161to je posebno va\u017eno kad poku\u0161avate odvojiti mali signal gre\u0161ke od velike obli\u017enje vr\u0161ne vrijednosti.<\/p>\n

2. Osnovni uzrok: Diskontinuitet<\/h2>\n

Spektralno curenje proizlazi iz kr\u0161enja temeljne pretpostavke FFT algoritma. Algoritam pretpostavlja da je kona\u010dni blok vremenski valni oblik<\/a> podataka koji analizira jedan savr\u0161eno ponavljaju\u0107i ciklus periodi\u010dnog signala. Da bi to vrijedilo, vrijednost signala na samom kraju bloka mora biti identi\u010dna toj vrijednosti na samom po\u010detku, tako da se blok mogao bez prekida petljati od kraja do po\u010detka.<\/p>\n

U praksi, pri mjerenju stvarnog vibracijskog signala gotovo je nemogu\u0107e snimiti blok koji sadr\u017ei to\u010dan cijeli broj ciklusa za svaki<\/em> prisutnu frekvencijsku komponentu. Rezultat je diskontinuitet<\/strong>: kraj snimljenog signala ne poklapa se s po\u010detkom. FFT algoritam ovu naglu skokovitu promjenu interpretira kao prijelaznu pojavu na visokoj frekvenciji \u2014 sli\u010dno kao udar \u2014 i ta umjetna prijelazna pojava nosi energiju koja nikada nije bila u originalnom signalu. To je upravo ta la\u017ena energija koja se razmazi preko \u0161irokoga niza frekvencija u rezultiraju\u0107em spektru.<\/p>\n

\u0160to je kra\u0107i blok podataka i \u0161to su dva prava vrha bli\u017ee jedno drugome, to je curenje \u0161tetnije \u2014 zbog toga se curenje, frekvencijska rezolucija i duljina bloka uvijek raspravlja zajedno.<\/p><\/blockquote>\n

3. Utjecaji spektralnog curenja<\/h2>\n

Razmazivanje energije proizvodi dva glavna negativna u\u010dinka:<\/p>\n

    \n
  1. Smanjena to\u010dnost amplitude:<\/strong> energija koja je trebala biti koncentrirana u jednom kanalu sada je razmotana preko mnogih. Glavna vr\u0161na vrijednost stoga \u010dita donji<\/em> nego \u0161to je njena prava amplituda, dok su susjedni kanali “bo\u010dne la\u017edivosti” umjetno povisani. O\u010ditana amplituda<\/a> vrijednost direktno sa cure\u0107eg vrha mo\u017ee biti zavaravaju\u0107a za procjenu te\u017eine.<\/li>\n
  2. Smanjena frekvencijska rezolucija:<\/strong> curenje mo\u017ee biti toliko te\u0161ko da potpuno sakri manije obli\u017enje vrhove. Slab signal iz kvar le\u017eaja<\/a>, na primjer, mo\u017ee biti u potpunosti izgubljen u \u0161irokoj margini curenja iz velikoga 1\u00d7 neravnote\u017ea<\/a> .<\/li>\n<\/ol>\n

    Oba u\u010dinka direktno rade protiv ciljeva analiti\u010dara: to\u010dne amplitude za trendove i ozbiljnost te \u010dista rezolucija za rano otkrivanje neispravnosti.<\/p>\n

    4. Rje\u0161enje: Windowing<\/h2>\n

    Spektralno curenje kontrolira se sa prozori<\/a><\/strong> funkcijama. Prozor je matemati\u010dka funkcija ponderiranja pomno\u017eena s podacima vremenskog oblika vala prije<\/em> proslje\u0111uje se FFT-u.<\/p>\n

    Naj\u010de\u0161\u0107e rje\u0161enje za generalne radove s rotiraju\u0107im strojevima je Hanningov prozor<\/a><\/strong>. Ima glatki, zvonoliki profil koji postupno gu\u0161enje signala do nule na po\u010detku i kraju bloka. Ovo prigu\u0161ivanje prisiljava dva kraja da se podudaraju, efektivno uklanjaju\u0107i umjetnu diskontinuiranost koja je uzrokovala curenje na po\u010detku. Predstavljanjem FFT-u glatko periodi\u010dkog signala, windowing dramati\u010dno smanjuje curenje \u2014 daju\u0107i o\u0161tre vrhove, ni\u017eu razinu buke i osjetljiviju analizu.<\/p>\n

    Windowing je kompromis, a ne lijek. Isto prigu\u0161ivanje koje potiskuje curenje tako\u0111er neznatno pro\u0161iruje glavni vrh i smanjuje njegovu izmjerenu amplitudu, zato instrumenti primjenjuju faktor korekcije amplitude. Razli\u010diti prozori ova svojstva ostvaruju na razli\u010dite na\u010dine: prozor s ravnim vrhom (flat-top) preferira se kada je to\u010dna amplituda jednog tona va\u017ena (primjerice tijekom kalibriranje<\/a>), uniformni (pravokutni) prozor odgovara hvatanju prijelaznih pojava u Ispitivanje udarcima<\/a>, dok Hanning ostaje svakodnevna zadana postavka.<\/p>\n

    5. Za\u0161to je to va\u017eno u praksi<\/h2>\n

    Za in\u017eenjera na terenu lekcija je jednostavna: \u010dist spektar je preduvjet za ispravnu dijagnozu. Curenje koje skriva mali ton le\u017eaja ili podcjenjuje amplitudu vrha mo\u017ee istragu poslati u krivu smjer. Pri mjerenju amplitude 1\u00d7 i faza<\/a> za posao uravnote\u017eavanja \u2014 rutinsku zada\u0107u koju prenosivi instrument kao \u0161to je Balanset-1A<\/a> obavlja u vlastitim le\u017eajima stroja \u2014 odgovaraju\u0107i windowing \u010duva taj sinkrioni vrh o\u0161trim i njegovu amplitudu pouzdanom, tako da je izra\u010dunata korekcija temeljena na pravoj vibraciji umjesto na zamu\u0107enoj gre\u0161ke.<\/p>\n

    \n

    \u2190 Natrag na glavni indeks<\/a><\/p>","protected":false},"excerpt":{"rendered":"

    Saznajte vi\u0161e o spektralnom curenju, pogre\u0161ci u FFT analizi uzrokovanoj diskontinuitetima u vremenskom signalu i kako se funkcije prozora poput Hanninga koriste za njegovo sprje\u010davanje.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[114,109],"tags":[],"class_list":["post-247","glossary","type-glossary","status-publish","hentry","category-analysis","category-glossary"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/glossary\/247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/glossary"}],"about":[{"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/types\/glossary"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/glossary\/247\/revisions"}],"predecessor-version":[{"id":101206,"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/glossary\/247\/revisions\/101206"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/media?parent=247"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/categories?post=247"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/hr\/wp-json\/wp\/v2\/tags?post=247"}],"curies":[{"name":"radni list","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}