Signals and systems notes, Lecture notes of Signals and Systems

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UNIT-4 B Signol: TE ts 0 physicol quoctity cokich vores (5) depends Don time (or) Spore (or) Onolher inde pencent Vosiable 1 (@) Voxtables- cohtch ceperds on one Ore dimenstonal signal: A sigre! independent — Vooiable: a fgi- (1) AC Poor signol Ui) Speech sige! fees) | [aden 29) Room -tempesoture (wv) electro cordio Diagram fee) dimensionol ot: A signol Cohich, cle pends on ae indecendent Voni oles: ‘Sgn eq: 0) Ti i) Bono grey Mult dimenstonel sign : gnckp endent voxtobles: lie Geooge (1) Pree A-S Gis) X ~ Roy t Fgnob eohich epends on severck Video Signal = three dimensional Eq ECG repot e3: Jeteamintstic signals, The Signals, cobich ave ghie do rapredit by moth msthe matica! Pam is. Colled,, detomints te signols- eg: 3 | = Stnust Readom eegoe! The signals cohich ane inot able ftp represecit =n a Bapiecebcl fren -those. signols ore) Called O39 Random Contnuous Time signal: The Signals cohich Gre. deftne, fr evey —instont of dime ano known os continuous Hy Signels: — Continuo time Signal is also apse ar Peabo % —> Tt denotes corr “th: €9° Temperoture , Signok, AC power ‘iputh signel, Eg Sig Discrete Time Signal: “The signols cghich aro defned a Aserete fi cme are known as diecrete. time. Signal. | > Continusus in Araplitude ond’ ‘Giscrete ta tre. > Te chnoted by aly) Budurs pdt reroetd Falat) = «lt leeaty 9 Te SOmplig pevad N= Time indey (2olegen, Renge ~~» 0 b eo)" Som pling Preces: “The Grecrele representation . of ‘cordin tiene Signet iis. Colled Sarnpling proces . * “a(nt) —s Sompling signol Lor) a Bompling — Seqblene. of ALD as th gee nl! wo), LEN xo) o alr), 9 HOD, > Sompling Sequente toch is chscre Heed fn ie } ts Known as Ogttal Sp ! Digttel Signal: “The Signet ch and Quontitieed mm ompu bade | Pastant: The wnsStosb ot cohich stgeal appa Prstonb- Gom pling fs Kroon as Sampling Sampling of xf) ot Sampling jpexiod Merl x(at) 2 WW |ycan x(n) ) alnt) = 2 sn at - 2 sn Korn) x(n) = 28m O2DRN xc) = 2S8in oO. ano) =O , 20) 2 osnQ onl) = osing 2 = Plas 202) = osm O(a) = 25m Ou 2 PADD C3) 5 2 Sin O23) - DSM OGM = 902 xl) = ogm onnls)= 25m 08m 2 LS xs) = asmoarnls) = o. X(e) = ssmornls- -as XE) = 2 sin oo nla) = ~1/902 aU) = $i Orne) = -1-402r x(%) 2 asm ornla) > -11as xtte) 2. osm 0209) 20 | of 5 wns on aa a ; 7 > ; a t | VAS fe902-| 1-902] |. Lay 0 BP?) seeich the Signel alt= et fir on the signal coh oO Sam pling period Te 012 Set 1 Skelch the discrete time signel y a(y-et OLtK2 deo =) xo) =e7O=! teo2y = xlovs) = eS Ky Ats tos =) xtos) -e-OS . 0-66 ens. OAD = 0364 “2S 2 0-286 toons =) wos) = te. 3 al) ee! tilay > alrawie tevs 2 als) cel — 0/228 taras => xlr95)= el 2 018 ten ate) se? 20/1385 talewol ofA < 2 Semple oad then he 5 0s | os way} yt (os Ke has i 1) os | Or€6 | O-4AD] 0.269 10286 | 9.993 Vk) O13 ORs Aa aa of 025) os) BAS ; a DIU ! a Sample “(t) cotth T=02 Sec at) = 28) acing Sha ean 9 alo) a wot) et M ero rn) ~ O27 wid) ee ee oct) = er) sob > dt . «| | A c Functorel Representetion 1 fe ned x{n) ; 2 fa n= - > fm nil es fy 9-2 ves fa 3 is) fx oll clr voles oF yr stn Tabulon — Ise: va . ana @> in | | 0 ae 0) ie | a 3 n) | Ta 2 2 oe afr) = x(x) =¢ (4) =3 ue haa Basic operations performed on signs ( ) Time, ShP ing Operation j operation operation al. (9) Time yevtrsok (s) Time Scaling (4) Amelctide sealing Opecotion (s) Stgnek mater operotion (e) Sigrol addition eperation | i De eet : got) nace AN \ 7 e ty mts advence. (lett shift} Th me Reverso! ope rolt on. This qperotion — Yeverses te given Signo! fa Line. Conbkauovs “Tine. Stgnel! ime. Yew@sol Operation on Conkinuous Ste, nol x ly “The. mehemoticoh ree resenbobion oft exp resston 1s yt) = a4) op is veversoh Sgrol of given Conti Asus Sigrod Can ob tamed by following she Given Signol ebout += i 1) | | ' o{<—+-__} fb | ws ae ; 2 3 st aa) e 0 EA) ! 1 acti, “RS cho ot co) le ice et dt wey 1 4y 4) ~& Reamer: 5 Tre revesol operction on discrefe tyre signet atn) lepree-tt csith following ratternctteal expression Yn) =LEn) > Tre yevescl signe of Aiscrete’ te. Signal con be obtoin by Pligusing -he Given Stgroh about N=0 ; at) %& Swtlching from 0 tp | ond. Sualchicg $on 1-0 ot +=2 : > 11) rrognibade ts eq uol to | et t=o0 ad +--2- Afton Scaling aU) by foctm 2. : yl) = xP) ee The yt Switches Bom Ot | aad ot 20S and Soi fiom \4p 0 et 218 eguat to | at t=o ond t=1. Ts Aches 4) megnitude is behovinut® grows thet lt) compressed tn tine. | of | othemeticol represen tortion of -the scaling operation discrete ime Sigel - tr)= + (Co) : * Scalin 9 yln) 3 Thre Scoling ecole of utr) bby the factR a=2 let OQ=2 U(r) = tl) alo) 22 N20 = ytn} bs nei ze yin) = 42) 1S n=r = Xn) > “y= rs N=3 = Yln) = U6) = Note = Ylnde & (ay =o Net = Yla) =*6Y =O ' uM Oo -2h i} yld= KEY) 20 Amplitude Scaling _opexetion Amplitude Scaling Operation moy enlarge a Comp ress given Signo! OQ ampbhude | AmpU tide Stabing On Cantnu time. Signol Coq be represe ntad by Followsteg mathe expression are Os fdllovs Ya = axlt) thee Qz Omplitude Scaling Rei I Signod mul pli co-tion operotion Multiplication of -heo signels ban toe! S8sbante ai bg rouhiplic Ag dhe Volue ot eney froboat : Gs) yO)= mA) st : salt) = | 7 ytay = 7,00-> 22.8) at eter x = 1 Lilt) s0F 4C4) = x W-x, ty oF xt <3 *U) =o Nolt) = NG: x,t) nay = OSKIT 2 O04T ulbiplicetion of boo discrete ultiding tree value Signal can be ‘pbtomed by ot every Sampling stent Soy YoY =%, (Cn): ann) yatn) Aln) = v1, 2, ~2,3J mb) = L105, oS,1} Ylo) = xn) - arto) 5 {1 x1, 2x05, yin) = ft u-t33 ~rx0S; axtj Papen tL yt >| \ rs | ;pead cal | | F = aa ee ae nt Wy ; {= | | [est 2, o;-———_|- —— Wi A eo AKON 2 | ee | ve nt il ssi \ t O These Ore used as building blocks Po. raodelling comple Stans. Unit step Signet Cbocbon) ull] \ ule! fa £20 | |+——— 20 fa te 0 -|-——— 5} Bee: te a Ole) sz) PR azo rot FOE al utr) 20 fx 98 | | 14 pots CE : Unit Romp Sig nol Chunccion) cc, de® OR, . WOE Eph rs W . oe 3 7{ 2 : JE ! Yt et fy +56 - { a n =O fx +o : . U = are