Mengapa Kita Membutuhkan FFT dan Contoh Aplikasinya ???

PLhn{ Ogncqy % GG WJD" Inceng{ihT

DGNJH]H @ISH DGDAWSWO@HN FFS555

]hch wdwdnyh" i{yhqhs hbhdi ciw`wq chbhd `hzh{hn zh`sw. H}h`ho sich` ai{h cizh`ibi chbhd `hzh{hn fqg`wgn{i5 sgnsw ai{h" nhdwn isw dgdawswo`hn }gqbh`whn hshw }gnjebhohn. @gqh} `hbi }gnjebhohn sgq{gaws ciicgnsi``hn cgnjhn dgsecg hbio qhjhd. Dgnjh}h i{yhqhs hbhdi hshw yhnj sgqg`hd ci`his`hn cgnjhn zh`sw5 @hqgnh i{yhqhs yhnj sgqw`wq dgnjhbhdi cifgqgn{ih{i ahi` hd}biswcg dhw}wn }oh{g chbhd }gqlhbhnhn zh`sw. In{sqwdgns }gnjw`wqhn chn `ed}engn gbg`sqeni{ yhnj cijwnh`hn lwjh sgqagnsw` chbhd `hzh{hn zh`sw" di{hbnyh {gawho `h}h{iseq yhnj dgnjhbhdi kohqjinj chn ci{kohqjinj  lwjh sgqjhnswnj }hch zh`sw. ]gnlgbh{hn sgq{gaws dgqw}h`hn awho }gdi`iqhn {hlh" {goinjjh ai{h ci`ensqhci`{i. [gagbwd dgdahoh{ sgnshnj FFS hshw Fh{s Fewqigq Sqhn{feqd" {hyh h`hn dgdwbhinyh cgnjhn dgdahoh{ sgnshnj ]gqiecg chn Fqg`wgn{i. Ohb ini }gnsinj wnsw` dgnlgbh{`hn {gkhqh qinki sgnshnj fwnj{i chqi FFS chbhd }gnjebhohn i{yhqhs. 8. ]gqiecg [gkhqh wdwd }gqiecg cicgfini{i`hn {gahjhi zh`sw yhnj ciawswo`hn wnsw` {gawho i{yhqhs hshw jgbedahnj dgnkh}hi {hsw jgbedahnj }gnwo. Sgnsw cgfini{i ini {hnjhs dwcho wnsw` cidgnjgqsi. Aho`hn cgnjhn dgbiohs agnsw` i{yhqhsnyh {hlh" {gkhqh jhdabhnj `ish ch}hs dgngnsw`hn nibhi }gqiecg{ish{nyh. Yhnj }gqbw cikgqdhsi hchbho ahozh }gnjgqsihn ini agqbh`w wnsw` i{yhqhs dene`qedhsi{ /{hyh nch` shw h}h`ho i{sibho ini ah`w hshw sich`). I{yhqhs dene`qedhsi{ yhnj cidh`{wc hchbho jgbedahnjnyh agq{ifhs swnjjhb" cidhnh cih }h{si dgdibi`i {gawho }gqiecg. Cgnjhn cgdi`ihn i{yhqhs isw ci`gnhb cgnjhn i{sibho }gqieci{. [gkhqh jhdabhnj `ish ai{h dgnjgnhbi nibhi$nibhi yhnj sgq`hncwnj ci chbhd i{yhqhs sgqdh{w` nibhi }gqiecg nyh. ]gqohsi`hn jhdahq ci ahzho wnsw` dgd}gqlgbh{ }gnjgqsihn ci hsh{.

Jhdahq 8. I{yhqhs [inw{

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PLhn{ Ogncqy % GG WJD" Inceng{ihT

1. Fqg`wgn{i Hch }gqiecg" dh`h hch fqg`wgn{i. [gkhqh wdwd fqg`wgn{i cihqsi`hn {gahjhi lwdbho jgbedahnj yhnj sgqlhci chbhd 8 cgsi`. Fqg`wgn{i cicgfini{i`hn {gkhqh {gcgqohnh {gahjhi `gahbi`hn chqi zh`sw. [goinjjh zh`sw yhnj {hswhnnyh hchbho cgsi` / {gkenc ) h`hn dgnlhci Ogqs| /8%{gkenc ) wnsw` fqg`wgn{i. @iqh$`iqh h}h yhnj ai{h cishnj`h} chqi cgfini{i isw {hlh5 Yh" sgnsw fqg`wgn{i ohnyh h`hn dgdibi`i sg}hs {hsw nibhi {}g`sqwd. Yhnj ci`gnhb cgnjhn {}g`sqwd fqg`wgn{i. ]gnjgqsihn fqg`wgn{i ini lwjh agqbh`w wnsw` jgbedahnj d ene`qedhsi{.

Bhbw sidawb }gqdh{hbhohn" aibh i{yhqhs yhnj hch sgqnyhsh dgdibi`i `gagqhjhdhn }gqiecg{ish{ chn fqg`wgn{i. Wnsw` bgaio dwcho" di{hb`hn hnch dgdibi`i ; awho i{yhqhs cgnjhn fqg`wgn{i yhnj agqagch bhbw cilwdbho`hn {goinjjh dgdagnsw` i{yhqhs ahqw. ]gqohsi`hn jhdahq ci ahzho ini.

Jhdahq 1. I{yhqhs Jhawnjhn chqi ; i{yhqhs cgnjhn fqg`wgn{i yhnj agqagch

H}h`ho ai{h cisgnsw`hn fqg`wgn{i `ed}engn }gnyw{wn chqi i{yhqhs ci hsh{ {gkhqh jhdabhnj5 Isw dgqw}h`hn {gawho ohb yhnj {wbis. Agbwd bhji li`h i{yhqhs nyh dgqw}h`hn i{yhqhs yhnj agnhq$agnhq hkh`. Di{hb`hn i{yhqhs chqi oh{ib }gnjw`wqhn cgais vebwdg hiq {wnjhi agqi`ws ini.

Jhdahq ;. I{yhqhs Hkh` [wdagq < oh{ib }gngbisihn agq{hdh qg`hn wnsw` dg qhdhb`hn h`sifish{ cgais chqi {gawho {wnjhi.

Wnsw` isw" ciawswo`hn {gawho hbjeqisdh yhnj ai{h dgdahnsw wnsw` dgdi{ho`hn i{yhqhs sgq{gaws dgnlhci agagqh}h `ed}engn fqg`wgn{i. Swlwhnnyh hjhq chsh dgnsho sgq{gaws ai{h ci`gbed}e``hn

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PLhn{ Ogncqy % GG WJD" Inceng{ihT

agqch{hq`hn }gqiecg{ish{nyh. Hbjeqisdh sgq{gaws hchbho FFS. FFS }hch ch{hqnyh dgqw}h`hn hbio qhjhd Fewqigq sh}i wnsw` `ed}engn ci{`qis aw`hn `ensinyw. FFS dgqw}h`hn CFS / ci{kqgsg fewqigq sqhn{feqd) yhnj dgdibi`i lwdbho `ed}wsh{i bgaio {gci`is ciahncinj `ed}wsh{i CFS aih{h. CFS h`hn dgnjoh{ib`hn  lwdbho `ed}wsh{i {gag{hq N1 {gchnj`hn FFS h`hn dgnjoh{ib`hn lwdbho `ed}wsh{i {gag{hq /N)bej 1/N). ]gqoiswnjhn FFS dgnjjwnh`hn awssgqfby  Qhcix$1 dgnjoh{ib`hn lwdbho `ed}wsh{i bgaio {gci`is yh`ni /N%1)bej1/N). Lwdbho sisi` chbhd `gsi`h dgnjjwnh`hn FFS lwjh dgdgnwoi {yhqhs 1 N. Wnsw` hbh{hn sgq{gaws FFS dgnlhci }ibiohn `gsi`h ciohch}`hn cgnjhn hbio qhjhd fewqigq. Nhdwn hch yhnj ohqw{ ci}gnwoi {gagbwd dgdwsw{`hn wnsw` dgnjjwnh`hn FFS {gahjhi {ebw{i. I{yhqhs yhnj h`hn ciebho ohqw{ agq{ifhs {sh{iengq" h}gqieci{ /sich` }gqieci{). I{yhqhs }gqieci{ `ensinw ch}hs cihnhbi{h dgnjjwnh`hn cgqgs Fewqigq. Sgbho cilgbh{`hn ahozh FFS cijwnh`hn wnsw` dgdi{ho`hn i{yhqhs dgnlhci `ed}engn }gnyw{wn fqg`wgn{inyh yhnj sich` ai{h ci}i{ho`hn {gkhqh jhdabhnj ohnyh cgnjhn dgbiohs i{yhqhs sgq{gaws chbhd `hzh{hn zh`sw. ]gqohsi`hn jhdahq agqi`ws ini wnsw` dgnlgbh{`hn {g}gqsi h}h oh{ib chqi FFS sgqohch} {gawho i{yhqhs yhnj dgdibi`i agqhjhd `ed}engn fqg`wgn{i.

Oh{ib ffs<

Shd}h` cgnjhn dgnjjwnh`hn FFS i{yhqhs yhnj dgqw}h`hn oh{ib }gnlwdbhohn chqi ; awho i{yhqhs cgnjhn fqg`wgn{i yhnj dh{inj$dh{inj agqagch" ch}hs ci}i{ho`hn cgnjhn ahi`. [goinjjh `gsijh `ed}engn fqg`wgn{i ai{h cicgsg`{i. [gchnj`hn chsh bhin yhnj sich` dgnlhci ahjihn chqi `gsijh

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PLhn{ Ogncqy % GG WJD" Inceng{ihT

`ed}engn fqg`wgn{i shci" h`hn cishd}ib`hn {gahjhi {}g`sqwd fqg`wgn{i yhnj nibhi dhjniswcg nyh {hnjhs `gkib hshw dgncg`hsi neb. Aibh dh{inj$dh{inj chsh }gnyw{wn `ed}engn fqg`wgn{i sgq{gaws ci`gnh`hn IFFS /invgq{g fh{s fewqigq sqhn{feqd) dh`h h`hn cioh{ib`hn i{yhqhs agqagnsw` {inw{ dwqni. FFS lwjh ai{h cijwnh`hn wnsw` `ed}qg{i chsh. Di{hbnyh {hlh chsh {whqh hbhs dw{ik lhzh jhdgbhn agqi`ws ini<

Aibh i{yhqhs sgq{gaws ci`gnhi FFS h`hn cioh{ib`hn `ed}engn fqg`wgn{i<

Ahjhidhnh khqhnyh FFS ai{h cijwnh`hn wnsw` `ed}qg{i5 ]gqohsi`hn {}g`sqwd fqg`wgn{i chqi i{yhqhs sgq{gaws /oh{ib FFS). Shd}h` ahozh sgqch}hs fqg`wgn{i fwnchdgnshb /{g`ishq ;=8 O|) yhnj dgdibi`i hd}biswcg sgqag{hq. Bhbw cgnjhn dgdagqi`hn nibhi hdahnj / soqg{oebc ) }hch hd}biswcg oh{ib FFS" dh`h

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PLhn{ Ogncqy % GG WJD" Inceng{ihT

}ibiobho fqg`wgn{i dhnh {hlh yhnj bhyh` wnsw` cilhci`hn `ed}engn }gnyw{wn i{yhqhs ahqw. Sgnsw {hlh cedinh{i fqg`wgn{i sgq{gaws ai{h cizh`ib`hn ebgo nibhi hd}biswcg nyh. Ini dgnwnlw``hn ahozh {gdh`in ahnyh` chsh yhnj dgnlhci `ed}engn }gnyw{wn chqi fqg `wgn{i sgq{gaws. Cgnjhn dgbh`w`hn soqg{oebcinj sgnsw h`hn cioh{ib`hn i{yhqhs cgnjhn `ed}engn fqg`wgn{i yhnj bgaio {gci`is chn chsh nyh lwjh dgnlhci {gci`is. Cgnjhn cgdi`ihn li`h `ed}engn$`ed}engn sgq{gaws ci{hsw`hn wnsw` dgdagnsw` i{yhqhs ahqw" dh`h h`hn cioh{ib`hn {gawho fibg hwcie yhnj ahqw cgnjhn w`wqhn yhnj bgaio `gkib. Sgnsw {hlh ciohqh}`hn chsh ahqw sgq{gaws ai{h dgzh`ibi infeqdh{i chsh h{bi. Wnsw` isw }gdibiohn nibhi hd}biswcg ohqw{ cibh`w`hn {gkhqh kgqdhs. ]gnibisihn ini cibh`w`hn agq{hdh qg`hn wnsw` qg`en{sqw`{i awnyi h{bi chqi jhdgbhn {gahjhi {shnchqi{h{i hshw dhbho sich` ai{h `hqgnh {gsih} hbhs h`hn dgdagqi`hn awnyi yhnj `oh{. [goinjjh i{yhqhs chn infeqdh{i ci chbhdnyh dgnlhci wni`. Hqsinyh sich` ai{h ciagqi`hn {shnchqi{h{i eng feq hbb . Id}bgdgnsh{i chqi FFS bhinnyh hnshqh bhin chbhd aichnj dgci{" {shsi{si`" }gnjebhohn kisqh" {whqh" sgbg`edwni`h{i chn bhin$bhin. [gawho hbjeqisdh yhnj agqnhdh DFKK lwjh dgnjjwnh`hn FFS hshw sqhn{feqdh{i fewqigq {gahjhi {yhqhs hzhb wnsw` dgd}qe{g{ i{yhqhs {whqh hshw {}ggko. Ohb ini cibh`w`hn `gsi`h dgdahnsw sgdhn chbhd dgbgnj`h}i hbjeqisdh  }qekg{{inj i{yhqhs {whqh wnsw` dgnjgnhbi }gdaikhqh agqch{hq`hn {whqh {gahjhi dh{w`hn. [gahjhi hbio qhjhd yhnj ai{h agqfwnj{i chbhd {shsi{si` lwjh cijhdahq`hn chbhd }gngbisihn sgnshnj dgqhdhb }gqibh`w {gawho {wnjhi ci chgqho lhzh sgnjho cidhnh {hyh lwjh swqws dgdahnsw. Cgais chqi hbiqhn {wnjhi yhnj sgqw`wq chbhd 88 shown cilhci`hn {gahjhi chsh yhnj h`hn ciebho. Cgnjhn dgnjjwnh`hn FFS" ci{gqshi h{wd{i hzhb ahozh ci chbhd }e}wbh{i chsh h`hn sgqch}hs }gqiecg{ish{ dh`h fqg`wgn{i `gdwnkwbhn {whsw chsh ch}hs cihdhsi. [}g`sqwd cgnjhn hd}biswcg yhnj sinjji bhyh` wnsw` cikwqijhi {gahjhi `wd}wbhn chsh yhnj dgdibi`i }gqiecg{ish{ yhnj sinjji }wbh. Cgnjhn dgdibio agagqh}h `ed}engn fqg`wgn{i" agqoh{ib ciswnlw``hn ahozh hch }gqwbhnjhn hbiqhn {wnjhi }hch }gqiecg sgqsgnsw dwbhi chqi lhnj`h zh`sw sgq}gncg`" dgngnjho chn sgq}hnlhnj. ]gqbw ci`gshowi ahozh infeqdh{i yhnj aih{hnyh cihdaib chqi FFS hchbho {ifhs }gqiecg{ish{nyh dgbhbwi `ed}engn fqg`wgn{i yhnj cioh{ib`hn. Wnsw` isw ciawswo`hn hbjeqisdh bhin wnsw` dgqhdhb`hn cgais yhnj dwnkwb }hch zh`sw$zh`sw sg q{gaws. Chbhd aichnj sgbg`edwni`h{i" FFS ai{h dgqw}h`hn ahjihn chqi }qe{g{nyh. Di{hbnyh {hlh `gsi`h dgdahnsw qg`hn chbhd hnhbi{h `hnhb 1 hnsgnh wnsw` zidhx. Hch lwjh chbhd {idwbh{i `hnhb Vhobgn|wgbh /dhhf li`h hch `g{hbhohn chbhd }gnygawshn). FFS ai{h lwjh cijwnh`hn wnsw` dgngnsw`hn fqg`wgn{i dhnh {hlh yhnj h`hn ci  fibsgq  hshw sh}i{ dgnjjwnh`hn bez}h{{" oijo}h{{"ahnc}h{{ chn ahnc{se} fibsgq  ahnc{se}  fibsgq . Cgnjhn dgdhnfhhs`hn }qin{i} ahozh oh{ib FFS aibh injin cish}i{ dh`h ohqw{ ci`hbi`hn cgnjhn FFS chqi fibsgq isw {gnciqi. Fibsgq ini sgnsw {hlh fibsgq cijishb. [hyh }gqnho dgdahnsw qg`hn chbhd dgdawhs fibsgq cijishb yhnj ci}gqwnsw``hn wnsw` F]JH cgnjhn {idwbh{i hzhb dgnjjwnh`hn DHSBHA agqch{hq`hn `en{g} FFS ini. Aibh sich` dgnjjwnh`hn FFS hshw hbioqhjhd fewqigq" sgnsw i{yhqhs in}ws ohqw{ ci`envebw{i cgnjhn fibsgq. Chbhd ohb ini FFS cijwnh`hn ohnyh wnsw` dgbiohs `ed}engn }gnyw{wn fqg`wgn{inyh {hlh. Sg`ni`$sg`ni` zincezinj hshw }gnlgncgbhhn lwjh ai{h cibiahs`hn chbhd }gdawhshn fibsgq cijishb ini. Chbhd aichnj }gnjebhohn kisqh cijishb" }gqhn FFS lwjh }gnsinj. Wnsw` dgnjgshowi fqg`wgn{i `gdwnkwbhn insgn{ish{ }i`{gb chbhd {gawho kisqh ci}gqbw`hn FFS. Di{hbnyh chbhd dgnjgnhbi ealg` dgnjjwnh`hn sgd}bhsg dhskoinj {gahjhi `bh{ifi`h{inyh {gchnj`hn FFS cijwnh`hn wnsw` g`{sqh`{i kiqinyh. Cgnjhn cgdi`ihn }qe{g{ nyh h`hn bgaio kg}hs `hqgnh dgdawswo`hn `ed}wsh{i yhnj {gci`is. Ohb ini bgaio ahi` chqi}hch dwqni dgnjjwnh`hn ahjihn chqi sgd}bhsg dhskoinj {g}gqsi   lhqh` Gwkbicghn wnsw` dgnkhqi `gcg`hshn hnshqh sgd}bhsg cgnjhn dh{w`hn. Ohb ini }gqnho cibh`w`hn lwjh wnsw` ealg` cgnjhn agqhjhd

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PLhn{ Ogncqy % GG WJD" Inceng{ihT

agnsw`. [goinjjh FFS shd}h` agjisw agqjwnh chn dgnygnhnj`hn `gsi`h `ish {wcho dgnjgqsi dh`nh chn dhnfhhsnyh. ]gnjjwnhhn FFS ai{h {hlh cijwnh`hn wnsw` `ed}qg{i kisqh" sh}i sg`ni` ini {hnjhs {gcgqohnh {goinjjh dwnj`in infeqdh{i yhnj sgqawhnj h`hn ahnyh`. Nhdwn" `glgbihn chqi {geqhnj qg{ghqkogq h`hn dgngnsw`hn oh{ib h`oiq chqi }gnjjwnhhn sg`ni` ini. Ai{h {hlh oh{ibnyh dgdhnj dgdwh{`hn ohnyh cgnjhn dgnjjwnh`hn sg`ni` yhnj {hnjhs {gcgqohnh. Wnsw` DHSBHA {gnciqi {gahjhi hbhs ahnsw" hnch ai{h dgnjjwnh`hn fwnj{i seebaex  ci ahzho ini< N 4 8=130 'lwdbho sisi` Y 4 ffs/y"N)0 ' FFS e}gqhsien Yy 4 ha{/Y/8
hshw cgnjhn agnsw` bhin< fa4bgnjso/y)0 Y 4 ffs/y"fa)0 ff 4 PfUi{yhqhs,/$fbeeq/fa%1)
]hch ch{hqnyh `gcwh ahjihn }qejqhd sgq{gaws h`hn dgnjoh{ib`hn nibhi yhnj {hdh" ohnyh {hlh {hhs cishd}ib`hn h`hn dgdibi`i agnsw` yhnj agqagch. Hnch ai{h dgnkeah `gcwhnyh. [glhwo ini" {hyh {wcho dgnjjwnh`hn `gcwh nyh wnsw` }gngbisihn yhnj agqagch.

~~ SGQIDH @H[IO ~~

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