Lub tswv yim ntawm "lub teeb liab" tuaj yeem txhais tau ntau txoj hauv kev. Qhov no yog tus lej lossis kos npe xa mus rau qhov chaw, tus neeg nqa khoom ntawm cov ntaub ntawv, txheej txheem lub cev. Qhov xwm txheej ntawm kev ceeb toom thiab lawv txoj kev sib raug zoo rau lub suab nrov cuam tshuam nws tus qauv tsim. Lub teeb liab spectrum tuaj yeem muab faib ua ntau txoj hauv kev, tab sis ib qho ntawm qhov tseem ceeb tshaj plaws yog lawv qhov kev hloov pauv lub sijhawm (tsis tu ncua thiab sib txawv). Qhov thib ob hom kev faib loj yog frequencies. Yog hais tias peb xav txog cov hom ntawm cov teeb liab nyob rau hauv lub sij hawm sau nyob rau hauv ntau nthuav dav, ntawm lawv peb muaj peev xwm paub qhov txawv: zoo li qub, quasi-static, periodic, repetitive, transient, random thiab chaotic. Txhua qhov ntawm cov cim no muaj cov khoom tshwj xeeb uas tuaj yeem cuam tshuam rau kev txiav txim siab tsim qauv.
Signal types
Static, los ntawm txhais, tsis hloov pauv rau lub sijhawm ntev heev. Quasi-static yog txiav txim siab los ntawm qib DC, yog li nws yuav tsum tau ua haujlwm nyob rau hauv qis-drift amplifier circuits. Hom teeb liab no tsis tshwm sim ntawm xov tooj cua zaus vim tias qee qhov ntawm cov circuits no tuaj yeem tsim cov theem tsis tu ncua. Piv txwv li, nruamamplitude nthwv dej tsis tu ncua.
Lo lus "quasi-static" txhais tau tias "yuav luag tsis hloov" thiab yog li hais txog lub teeb liab uas hloov pauv qeeb qeeb hauv lub sijhawm ntev. Nws muaj cov yam ntxwv uas zoo li kev ceeb toom zoo li qub (nruab mus tas li) dua li kev ceeb toom dynamic.
Lub Sijhawm Sijhawm Sijhawm
Cov no yog cov uas rov ua raws nraim li niaj zaus. Piv txwv ntawm lub sij hawm waveforms muaj xws li sine, square, sawtooth, daim duab peb sab nthwv dej, thiab lwm yam. Qhov xwm ntawm lub sij hawm waveform qhia tias nws zoo tib yam nyob rau tib lub ntsiab lus raws lub sij hawm. Nyob rau hauv lwm yam lus, yog hais tias lub ncua sij hawm nce raws nraim ib lub sij hawm (T), ces qhov voltage, polarity, thiab kev taw qhia ntawm waveform hloov yuav rov ua dua. Rau qhov voltage waveform, qhov no yuav qhia tau hais tias: V (t)=V (t + T).
Rov ua dua cov cim
Lawv yog quasi-periodic nyob rau hauv qhov xwm txheej, yog li lawv dais qee qhov zoo ib yam li lub caij nyoog waveform. Qhov sib txawv tseem ceeb ntawm lawv yog pom los ntawm kev sib piv cov teeb liab ntawm f (t) thiab f (t + T), qhov twg T yog lub sijhawm ceeb toom. Tsis zoo li cov lus ceeb toom ib ntus, hauv cov suab rov qab cov dots yuav tsis zoo ib yam, txawm tias lawv yuav zoo sib xws, zoo li tag nrho cov waveform. Cov lus ceeb toom hauv nqe lus nug yuav muaj qhov qhia tau ib ntus lossis mus tas li, uas txawv.
Cov cim qhia hloov pauv thiab cov cim qhia tawm
Ob hom yog cov xwm txheej ib zaug lossisperiodic, nyob rau hauv uas lub sij hawm luv luv heev piv rau lub sij hawm ntawm lub waveform. Qhov no txhais tau tias t1 <<< t2. Yog tias cov teeb liab no tau hloov pauv, lawv yuav txhob txwm tsim tawm hauv RF circuits li pulses lossis lub suab nrov nrov. Yog li, los ntawm cov ntaub ntawv saum toj no, peb tuaj yeem txiav txim siab tias theem spectrum ntawm lub teeb liab muab kev hloov pauv hauv lub sijhawm, uas tuaj yeem ua tsis tu ncua lossis ntu ntu.
Fourier series
Txhua qhov kev ncua sij hawm tsis tu ncua tuaj yeem sawv cev los ntawm lub hauv paus zaus sine yoj thiab txheej cosine harmonics uas ntxiv linearly. Cov oscillations muaj cov Fourier series ntawm swell puab. Lub sine nthwv dej theem pib tau piav qhia los ntawm tus qauv: v=Vm sin(_t), qhov twg:
- v – instantaneous amplitude.
- Vm yog qhov siab tshaj plaws amplitude.
- "_" - angular zaus.
- t – time in vib nas this.
Lub Sijhawm yog lub sijhawm ntawm qhov rov ua dua ntawm cov xwm txheej zoo ib yam lossis T=2 _ / _=1 / F, qhov twg F yog qhov zaus hauv cycles.
Cov Fourier series uas ua rau lub waveform tuaj yeem pom tau yog tias tus nqi muab yog decomposed rau hauv nws cov frequencies xws li los ntawm ib tug zaus xaiv lim bank los yog los ntawm ib tug digital teeb liab ua algorithm hu ua ceev transform. Txoj kev tsim los ntawm kos kuj siv tau. Lub Fourier series rau txhua qhov waveform tuaj yeem qhia los ntawm cov qauv: f(t)=a o/2+_ -1 [a cos(n_t) + b sin(n_t). Qhov twg:
- an and bn –Cheebtsam deviations.
- n is an integer (n=1 is fundamental).
Amplitude thiab theem spectrum ntawm lub teeb liab
Deviating coefficients (ib thiab bn) qhia los ntawm kev sau ntawv: f(t)cos(n_t) dt. Here an=2/T, bn =2/T, f(t)sin(n_t) dt. Txij li thaum tsuas muaj qee zaus tam sim no, lub hauv paus zoo harmonics, txhais los ntawm ib tug integer n, lub spectrum ntawm ib tug periodic teeb liab yog hu ua discrete.
Lub sij hawm ao / 2 hauv Fourier series qhia yog qhov nruab nrab ntawm f(t) dhau ib lub voj voog ua tiav (ib lub voj voog) ntawm lub waveform. Hauv kev xyaum, qhov no yog DC tivthaiv. Thaum lub waveform nyob rau hauv kev txiav txim siab yog ib nrab-yoj symmetric, piv txwv li, qhov siab tshaj plaws amplitude spectrum ntawm lub teeb liab yog siab tshaj xoom, nws yog sib npaug rau lub ncov sib txawv hauv qab tus nqi teev ntawm txhua qhov taw tes hauv t lossis (+ Vm=_–Vm_), ces tsis muaj DC tivthaiv, yog li ao=0.
YWaveform symmetry
Nws tuaj yeem txiav txim siab qee qhov kev tshaj tawm txog qhov spectrum ntawm Fourier cov cim los ntawm kev tshuaj xyuas nws cov qauv, ntsuas thiab qhov sib txawv. Los ntawm cov kab zauv saum toj no, peb tuaj yeem txiav txim siab tias kev sib haum xeeb nthuav tawm mus rau infinity ntawm tag nrho cov waveforms. Nws yog tseeb hais tias muaj tsawg dua infinite bandwidths nyob rau hauv lub tswv yim systems. Yog li ntawd, qee qhov ntawm cov kev sib haum xeeb no yuav raug tshem tawm los ntawm kev ua haujlwm ntawm cov hluav taws xob hluav taws xob. Tsis tas li ntawd, qee zaum pom tias cov neeg siab dua yuav tsis tseem ceeb heev, yog li lawv tuaj yeem tsis quav ntsej. Raws li n nce, lub amplitude coefficients thiab bn yuav txo. Qee lub sij hawm, cov khoom me me heev uas lawv qhov kev koom tes rau lub waveform yog qhov tsis zoo raulub hom phiaj tswv yim, los yog ua tsis tau. Tus nqi ntawm n ntawm qhov no tshwm sim nyob ntawm ib feem ntawm lub sijhawm nce ntawm cov lus nug. Lub sijhawm nce yog txhais raws li lub sijhawm xav tau rau nthwv dej kom nce ntawm 10% mus rau 90% ntawm nws qhov kawg amplitude.
Lub square nthwv dej yog qhov tshwj xeeb vim nws muaj lub sijhawm nce nrawm heev. Raws li txoj cai, nws muaj cov lej tsis kawg ntawm kev sib haum xeeb, tab sis tsis yog txhua qhov ua tau yog txhais tau. Piv txwv li, nyob rau hauv cov ntaub ntawv ntawm ib tug square nthwv dej, tsuas pom qhov khib 3, 5, 7. Lwm cov kws tshawb fawb hais tias lawv xav tau 1000.
Cov ntsiab lus rau Fourier series
Lwm yam uas txiav txim siab txog qhov profile ntawm qhov kev txiav txim siab ntawm ib qho kev waveform yog lub luag haujlwm los txheeb xyuas qhov khib lossis txawm. Qhov thib ob yog qhov uas f (t)=f (–t), thiab thawj – f (t)=f (–t). Hauv ib qho kev ua haujlwm, tsuas muaj cosine harmonics. Yog li ntawd, sine amplitude coefficients bn yog sib npaug rau xoom. Ib yam li ntawd, tsuas yog sinusoidal harmonics nyob rau hauv ib qho kev ua haujlwm khib. Yog li ntawd, cov cosine amplitude coefficients yog xoom.
Ob qho tib si symmetry thiab opposites tuaj yeem tshwm sim lawv tus kheej hauv ob peb txoj hauv kev ua yoj. Tag nrho cov xwm txheej no tuaj yeem cuam tshuam qhov xwm txheej ntawm Fourier series ntawm hom o. Los yog, nyob rau hauv cov nqe lus ntawm kab zauv, lub sij hawm ao tsis yog xoom. DC tivthaiv yog ib rooj plaub ntawm lub teeb liab spectrum asymmetry. Qhov offset no tuaj yeem cuam tshuam loj rau kev ntsuas hluav taws xob uas txuas nrog rau qhov tsis sib xws.
Kev ruaj ntseg hauv kev sib txawv
Zero-axis symmetry tshwm sim thaum lub hauv paus taw tes ntawm nthwv dej yog raws thiab qhov amplitude yog siab tshaj qhov xoom puag. Cov kab sib npaug rau qhov sib txawv hauv qab kab hauv qab, lossis (_ + Vm_=_ –Vm_). Thaum qhov o yog xoom-axis symmetrical, nws feem ntau tsis muaj qhov sib haum xeeb, tsuas yog khib xwb. Qhov teeb meem no tshwm sim, piv txwv li, nyob rau hauv square waves. Txawm li cas los xij, xoom-axis symmetry tsis tshwm sim tsuas yog nyob rau hauv sinusoidal thiab rectangular swells, raws li qhia los ntawm tus nqi sawtooth nyob rau hauv nqe lus nug.
Muaj kev zam rau txoj cai dav dav. Nyob rau hauv daim ntawv symmetrical, lub xoom axis yuav tshwm sim. Yog hais tias txawm harmonics nyob rau hauv theem nrog lub hauv paus sine yoj. Cov xwm txheej no yuav tsis tsim ib qho DC tivthaiv thiab yuav tsis tawg qhov sib luag ntawm xoom axis. Ib nrab-yoj invariance kuj txhais tau tias tsis muaj kev sib haum xeeb. Nrog rau hom invariance no, lub waveform yog saum toj kawg nkaus lub hauv paus xoom thiab yog daim iav duab ntawm qhov o.
Qhov tseem ceeb ntawm lwm cov ntawv xov xwm
Lub quarter symmetry muaj tshwm sim thaum sab laug thiab sab xis ntawm lub waveform sab yog daim iav duab ntawm ib leeg ntawm tib sab ntawm xoom axis. Saum tus xoom axis, lub waveform zoo li lub xwmfab nthwv dej, thiab qhov tseeb ntawm ob sab yog tib yam. Nyob rau hauv cov ntaub ntawv no, muaj ib tug tag nrho txheej ntawm txawm harmonics, thiab txhua yam khib uas yog tam sim no nyob rau hauv-theem nrog lub hauv paus sinusoidal.yoj.
Ntau qhov kev xav tau ntawm cov cim qhia ua tau raws li lub sijhawm ntsuas. Hais txog lej, lawv nyob rau hauv qhov tseeb periodic. Kev ceeb toom ib ntus tsis zoo sawv cev los ntawm Fourier series, tab sis tuaj yeem sawv cev los ntawm sine nthwv dej hauv cov teeb liab spectrum. Qhov txawv yog tias qhov kev ceeb toom tsis tu ncua tsis tu ncua es tsis muaj kev sib cais. Cov qauv qhia dav dav yog qhia raws li: sin x / x. Nws kuj tseem siv rau kev ceeb toom rov ua dua thiab rau daim ntawv hloov pauv.
Sampled signals
Ib lub khoos phis tawj digital tsis muaj peev xwm tau txais cov suab analog tawm suab, tab sis yuav tsum muaj tus lej lej ntawm cov teeb liab no. Ib qho analog-to-digital converter hloov cov input voltage (los yog tam sim no) mus rau hauv ib tug sawv cev binary lo lus. Yog hais tias lub cuab yeej khiav clockwise los yog tuaj yeem pib asynchronously, ces nws yuav siv sij hawm tas li ntawm cov qauv teeb liab, nyob ntawm lub sijhawm. Thaum sib xyaw ua ke, lawv sawv cev rau qhov qub analog teeb liab hauv daim ntawv binary.
Lub waveform nyob rau hauv cov ntaub ntawv no yog ib tug tas mus li muaj nuj nqi ntawm lub sij hawm voltage, V (t). Lub teeb liab yog kuaj los ntawm lwm lub teeb liab p(t) nrog zaus Fs thiab lub sijhawm ua piv txwv T=1 / Fs thiab tom qab ntawd rov tsim dua. Thaum qhov no yuav yog tus sawv cev ncaj ncees ntawm lub waveform, nws yuav rov tsim kho dua nrog qhov tseeb dua yog tias tus qauv tus nqi (Fs) nce ntxiv.
Nws tshwm sim tias sine yoj V (t) yog ua piv txwv los ntawm kev ntsuas pulse sampling p (t), uas muaj qhov sib npaug ntawm qhov sib npaug.spaced nqaim qhov tseem ceeb sib cais nyob rau hauv lub sij hawm T. Ces lub teeb liab spectrum zaus Fs yog 1 / T. Qhov tshwm sim yog lwm impulse teb, qhov twg cov amplitudes yog ib tug qauv version ntawm tus thawj sinusoidal ceeb toom.
Cov piv txwv zaus Fs raws li Nyquist theorem yuav tsum yog ob zaug qhov siab tshaj plaws zaus (Fm) hauv Fourier spectrum ntawm cov teeb liab analog V (t). Yuav kom rov qab tau qhov qub teeb liab tom qab kuaj, cov qauv waveform yuav tsum tau dhau los ntawm cov lim dej qis uas txwv cov bandwidth rau Fs. Hauv kev siv RF systems, ntau tus engineers pom tias qhov tsawg kawg nkaus Nyquist ceev tsis txaus rau cov qauv zoo li qub, yog li yuav tsum tau hais kom ceev ceev. Tsis tas li ntawd, qee qhov kev siv ntau dhau yog siv los txo qis suab nrov.
Signal spectrum analyzer
Cov txheej txheem piv txwv zoo ib yam li daim ntawv ntawm amplitude modulation nyob rau hauv uas V (t) yog lub teeb ceeb toom nrog ib tug spectrum ntawm DC rau Fm thiab p(t) yog tus cab kuj zaus. Cov txiaj ntsig tau txais zoo ib yam li ob chav sideband nrog tus nqa khoom kom muaj nuj nqis AM. Lub spectra ntawm lub modulation signals tshwm nyob ib ncig ntawm lub zaus Fo. Tus nqi tiag tiag yog qhov nyuaj me ntsis. Zoo li lub xov tooj cua AM uas tsis tau lim dej, nws tshwm tsis tau tsuas yog nyob ib ncig ntawm lub hauv paus zaus (Fs) ntawm tus cab kuj, tab sis kuj nyob rau hauv harmonics spaced Fs nce thiab nqis.
Piv txwv tias qhov piv txwv zaus sib raug rau qhov sib npaug Fs ≧ 2Fm, cov lus teb qub yog rov tsim dua los ntawm cov qauv qauv,hla nws los ntawm qhov qis oscillation lim nrog qhov sib txawv ntawm kev txiav Fc. Nyob rau hauv rooj plaub no, tsuas yog cov analog suab spectrum kis tau.
Nyob rau hauv rooj plaub ntawm qhov tsis sib xws Fs <2Fm, muaj teeb meem tshwm sim. Qhov no txhais tau hais tias qhov spectrum ntawm lub teeb liab zaus zoo ib yam li yav dhau los. Tab sis cov seem nyob ib ncig ntawm txhua qhov sib xyaw ua ke kom "-Fm" rau ib lub kaw lus tsawg dua "+ Fm" rau thaj tsam qis dua ntawm oscillation. Qhov kev sib tshooj no ua rau pom cov teeb liab uas nws qhov dav spectral rov qab los ntawm kev lim dej qis. Nws yuav tsis tsim cov thawj zaus ntawm sine yoj Fo, tab sis qis dua, sib npaug rau (Fs - Fo), thiab cov ntaub ntawv nqa nyob rau hauv lub waveform ploj los yog distorted.
