oll 4 US os 3: pg Ulsou os 3: Ay Sysms Whl ly US sysms us sgl fous u mhl swpg of h su o ff gls, ly ll mo US sysms y sysms wh foussg s o ps bm sg s o hough m lys sso wh h lm of h y. Tsm mo: Foussg Bm Sg Typl y sysm show h sm mo: wh s h oo of h h lm s h of h y. Fo foussg z, z s h ly o: ' ', z, z z Aully, hs s gv ly o fous o-s h Fsl zo, w qu h h g lms f bfo h lm bus hy hv fh o popg. I pol oos, fo foussg, : ' ',, s os A fol ph o, s sl o wh h puls s sm. O lvs h su, o log b hg.
oll 4 US os 3: pg Rv mo: Dly-Sum Bmfomg - Sgls fom h su ly summ o pou sgl lolz o h fol po,.g., : v v ' - Sgl fom oh gls suppss by suv f of h wvfos wh summ ogh ll h h puls s m up of moul wvs fquy, f. - Ulk h sm s, h v b omb my ff wys. I ohwos, w sply fous fo y po m ph pl,. Also w fous o y gl by possg h. Typlly, ym foussg s us o fous fo h ph pl h hgs fo vy ph /. Smplg Sp A h po m, h y s ully smplg h sous pssu wv s fuo of sp. Alsg s polly poblm. A quk vw of smplg:
oll 4 US os 3: pg 3 Alsg b pv f lss h π hs u bw ghbog smpls. Fo ou s of wvs mpgg upo h o y, smplg boms bgg ssus f h sou of h wvs s omg fom lg gl, : Th smplg qum fo hs s b w s h mmum ff popgo ly bw po, wo ghbog su lms o l o phs ul of g h π:,,,, π,, ssumg h lm spg s.g., h:
oll 4 US os 3: pg 4 os os s os s os s,,,, Th wos s s fo pl wvs, h s : π π s s,,,, hus: s f w w o umbguously sgush bw vl os pos of flvy ov full π of gl, h: I hs s, h umb of su lms,, shoul b: Apu uml 4 Th uml Apu fo y s h sz of h su ms of h umb of wvlghs.g..a. /. Comms: W v jus lk bou h y smplg pssu wv popgg ows h su. I s mpo o lz h smplg lso ous ug sm s wll o o umbguously sm wv pul o ov π gls, w lso o ssfy h bov su spg. Blow u susso of h po sp fuo, w wll s h ffs of suff smplg by h y.
oll 4 US os 3: pg 5 Agul Smplg of h Obj Fo hs lyss, w wll os h f-fl o fol pl soluo: k os p, I{ s } u s K S s As sb bov, w mus sm ou bm pul gl hus, hs s s sz s wll: s S s smpl loos Ths s vs smplg gum w smplg h FT of s hus h smpls of Su mus b poso ls s los s hlf h mmum of s. Thus, f s gos fom [-, ], h: s s uml Apu Ths s h soluo fo h v oly o sm oly s. Rll h h ul bm fuo s: B, h T [ K ],, h [ p, ] R s S,, hs s h fuo h s us o smpl h obj h gul o. S w mus ow smpl h squ of h FT of h sp lm pu fuo, w mus kow h mmum of h s IFT, whh s s* s. If f s gos fom [-, ],
oll 4 US os 3: pg 6 h s* s s bou by fuo h s of [-, ]. Fo mpl, f s /, h s* s gl/, whh gos fom - o. Thus: s 4.A. - How my bms o smpl π? ms ms s / 4 8 4.A. - Is smplg ufom? o, smplg s ufom s. - Shoul w jus smpl mo fly h w o? o. I ks m you sm h puls w gl ul h ls o s v. I s o w fomo. - Wh hpps f w o smpl fly ough? W mgh mss obj fu.
oll 4 US os 3: pg 7 Po Sp Fuo fo Ds Tsus Fo o : s w h FT s: omb S u w s wu D * w [ omb u * D s Du ] Dw s wu s D u Subsug u s /, h f fl o fol pl fo o-s bm, w g: s s p, K os s w s - h fs s fuo povs ol wghg s fuo of. Ths oul u h gul fl of vw by sg ov wh g of gls w ffvly sm o/v fom. L s look hs ffs fo yqus smpl y /. Fs w look h ff of h ms wghg h gul fl of vw: s os s w W kow h w <, so w < /. Th wos s ows s fo w /. H plos of hs fuos h pou of hs fuos h lows l o h plos:
oll 4 US os 3: pg 8 Thus h wghg, whl ps, s o sgfly ff h h ogl os wghg. Ths wghg fuos p of h uml pu. Smulos Fo h yqus smpl y /, w g: s p, K os s w s.a. s Th gum of h s s zo oly fo h m lob s bm hs ous. Fo, w g: s p, K os s w s Th gum of h s s zo fo. Typ M Lob π/ Gg - π/ Gg Fo, w g:.a. s s p, K os s w s.a. s Th gum of h s s zo fo.
oll 4 US os 3: pg 9 Typ M Lob π/6 Gg - π/6 Gg π/ Gg - π/ Gg Comms: Obsv h h m lob os hg h s. Th gg lobs lss sulg fom subsmplg of h spl wvs by h s su. I h sum of s fuos, h m s h m bm Th ms gg lobs ol sposs gul loos oh h h s gl hs s. M gg lobs h followg smulo of s sms:
oll 4 US os 3: pg Gg Lobs wh Bm Sg W v h bov pssos fo h s wh h bm s s o oh loo, : s omb D whh hs s s sfom: hus: p, ks Dw S u s wu s s D u * s w K os s w s Flly, fo yqus smpl y /: s s s p.a. s s, K os s w s Th sz of h gg lobs, howv, s mlly ff by h uml pu. Fs, l s m f h m lob of y of h gg lobs pp h fl of vw. Fo π <, < π, h o ss fo whh s - s. Thus, h gum of h s v b zo h m lob of y of h gg lobs wll o pp h fl of vw. S lobs, howv, pp. Th vlu of h gum of h s s wgh by h uml pu hus, w push fh ou. I gl, hs slobs pou ol ppl h bkgou. H wo ss of ys fo whh yqus smplg hs o b hv.
oll 4 US os 3: pg Comms: - Obsv h h gg lobs wos fo off-s bms. - Fo yqus smpl ys, h ffs of gg lobs s mml. - Th gg lobs ff boh h sm v ps.
oll 4 US os 3: pg Possg fo Dly-Sum Bmfomg - Th US puls s f o hfo, w mus hoos pul sg ph of fous s up h lys h m of smsso. Ths s sly o - fo foussg, : s ' ',, os - Th v sgl m ospos o ph /. A h po w w fol ph,. Usully, h v gl s h sm s h sm gl,. W ff s of ly fo h ph m smpl. - O ommo wy of mplmg h lys s wh pp ly l. Eh su hs ly l suh s: Fs, w look foussg oly: hus h p umb s s by: ' m m Th pul p h hs b sl s hg wh: m m. k k
oll 4 US os 3: pg 3 - How smll os o b? Th phs o ou by h osss of h ly l s: φ πf - Typlly, phs o lss h gs s ssy fo goo quly bm fomg: π 36 πf 36 f - Fo mpl, f f 5 MHz, h 6 s smplg 8 MHz. Ths s hgh smplg vs woul b psv. Syhoy uy log log ly l fo my hls s fful. - How my ps woul b ssy? L s look fousg bm sg lys fo smpl ofguo wh m, m: m m m 6.7 µ s 67 s.5m/ µ s m Ths ospos o bou 3 ps. - Fo bm sg, h mmum ly -o- of y s: m 7 µ s.5m/ µ s Ths ospos o bou 5 3 ps. Pl Bm Fomg Sysm Whl h bov oul b bul wh oy s hology, h s loqu soluo o hs hw hllg h l o subsl os svgs. Ths soluo volvs h ompl moulo o m fquy, whh s h smpl follow by sofw phs oo m.
oll 4 US os 3: pg 4 Rll h ul v wvfom s l vlu fuo: { } os v R wh som slg fos opp. Fs, l s look moulo p of hs v. Th wo hls h I o -phs hl Q o quu hl: { } [ ] { } os os os LPF os os LPF l l l I wh << l h ff bw h sm fquy h lol osllo h v. Fo h Q hl: { } [ ] { } s s s LPF s os LPF l l l ow, w f h bsb sgl fo lm, b : Q I b ± m m To smplfy h followg lyss, w wll l l o, o: b ± Th ± s gv o h h h posv of gv fquy ompo b us o osu h bsb sgl.
oll 4 US os 3: pg 5 - ow, w o smpl b, bu hs hs phs vos h ou muh mo slowly. Th smplg mus ou oly fs ough o pu: Amplu hgs Chgg phs lys fo ffg fol phs o. - Smplg f s -4f s qu fo goo bm fomg. Thus w g -fol uo h smplg umb of ps h ly l. Wh osug h fl bsb sgl, w shf h moul sgl ou by s smpl vlus - [ ] '. W lso pply phs m ' l, bu hs vlu b sz. Th fl bsb sgl s: [ ] [ ] [ ] ' ' ' ' ' ' l l b b ± m m m Obsv h h l m s ommo o ll ms b pull ou of h summo. I v lu h ms h bus you my o lwys kow how you moulo s o.g. h US poj. ow, kpg oly h gv m, w mk ppomo h s vs ll ov hus: ' ' b Rll h: [ ] m s sz o ', os s ' os s hus: / / b
oll 4 US os 3: pg 6 - Obsv h ol phs m l '. Ths m s ssy o bg lg h phss bfo summg. Th l p s ussy bus os o p o b pull ous h summo w usully look b. - Th phs oo m s lul oly h m of h smpls whh m hus, - /. Ths phs m s usully mplm h glly smpl hus b pfom wh vy hgh uy. - Th fl v sgl s h popool o b h flvy po ph, /. - Commoly, s ps s R/,b o log R/,b. - L s look g os h o phs u o h osss of smpls s φ b m bly smll v. - Th oh sou of o s sl fom poo smplg of, bu wh smpl of f s -4f h puls lgh T3/f, w su h 6- smpls m ov h puls shp. Th lys lg h pulss po o summo. S Covso Th fl poss US sysm s s ovso o ps h s mg l oo sp o h us. Ths volvs ovso fom ou bm, whh ss om h s qully sp s, o physl sp, whh s om h s qully sp z:
oll 4 US os 3: pg 7 Ths poss s of v by s of sply mmoy, whh ss s om, z quss pols fom h qu s, sp. I hs s, h oupu oos vs h polo poss oh wos, s oupu-v. Th ppohs o polo h pu v, bu w wll o sb hos h.
oll 4 US os 3: pg 8 O smpl ommo ppoh o polo s bl polo: H, w f h 4 s ghbos pfom l polo wo os. Fs, l s k ou oupu oos gv s quvl h pu sp: z s Th of fou s ghbos m fom: h : l ; s s s l ;s s floo ; s s floo s P,s ; P,s ; P,s ; P,s 3 4 ss of svl sgms : ; b ; s s ; s s flly: bp bp P3 P4 P, z s Th, of ous, my oh b mhos fo polo D sp. Tmpol Rsoluo Th mpol soluo of US sysm s m by h m qu o mg so. Typlly oly o puls s vsg h boy y gv m. Thus h mmum m bw pulss s gv by:
oll 4 US os 3: pg 9 T Fo mpl, f m m, h T 67 µs. m Fo M bms so, h m fo o fm wll b T fm TM. Fo m m M 8 h T fm 33 ms. Thus h fm wll b bou 3 Hz. Ovll Sysm Ahu