Tarea #3 - Procesamiento de Señales

 

]hlvmrslaba Nbtþilnb Bharìs Emiic @bnuitba am Lhfmhlmrêb Msnumib am Lhfmhlmrêb mh Qmimncjuhlnbnlchms QBUMB h¿? > Mh mstb prljmrb tbrmb sm plalþ usbr mi prcfrbjb Jbtibe pbrb mstualbr mi ncjpcrtbjlmhtc ami pmrlcacfrbjb y mi pmrlcacfrbjb prcjmalc mh smòbims am vcz, uhb jbsnuilhb y ctrb `mjmhlhb, pmrc tbjelìh gbnmr mi mstualc b bifuhb am msbs vcnms bfrmfbhac rulac eibhnc fbusslbhc am jmalb nmrc y vbrlbhzb uhltbrlb. Ibjmhtbeimjmhtm, hlhfuhc am ics lhtmfrbhtms ami frupc nchtbeb nch Jbtibe, bsê bsê qu qumm us usbj bjcs cs ib gm gmrr rrbj bjlm lmhtb htb am Cntbvm   qum ms eb ebstb stbhtm htm slj sljlib librr y mstâ mstâh h  prmsmhtms ibs `uhnlchms scilnltbabs, buhqum bifuhbs tlmhmh hcjerms al`mrmhtms  pmrc nch mi jlsjc `lh. Ib tbrmb nchstb am > pbrtms? 2.-   Frbebr acs brnglvcs am bualc, uhc `mjmhlhc, iibjbac?  bualcSjbrlb.wbv  bualcSjbrlb.wbv y  y ctr trc c jbsnuilhc iib ibj jbac ac??   pmarcSbualc.wbv pmarcSbualc.wbv.. Bjecs bualcs alnmh? ’[rcnmsbjlmhtc am smòbims‚ y bjecs aurbh 5 smfuhacs. 5.- Cetmhmr uh mstljbac am ib Amhslaba Mspmntrbi am [ctmhnlb (AM[) am nbab uhb am ibs smòbims usbhac mi pmrlcacfrbjb y mi pmrlcacfrbjb prcjmalc. >.-  B nubiqulmrb am ibs acs smòbims, sm im amem sujbr rulac eibhnc fbusslbhc am jmalb nmrc y vbrlbhzb uhltbrlb, pbrb iumfc, bi lfubi qum mh mi pbsc bhtmrlcr, sbnbrim mi pmrlcacfrbjb y mi pmrlcacfrbjb prcjmalc.

[brb pcamr ncjprmhamr ics rmsuitbacs cetmhlacs, prljmrc amemjcs am mstualbr  ibs `uhnlchms b usbr, qum smrêbh ibs slfulmhtms? ◃

  pmrlcacfrbj? ? T [xx , w Z : pmrlcacfrbjb ( x )

? T [xx , w Z : pmrlcacfrbjb ( x , wlh ) ? T [xx , w Z : pmrlcacfrbjb ( x , wlh , h``t ) ? T [xx , ` Z : pmrlcacfrbjb pmrlcacfrbjb ( x , wlh , h``t , @s ) ? T [xx , ` Z : pmrlcacfrbjb (…, " rbhfc ") ? pmrlcacfrbjb (…) Amvumivm mi pmrlcacfrbjb (amhslaba mspmntrbi am pctmhnlb) am x . Ibs pcsleims mhtrbabs sch?  W? vmntcr am abtcs. ^l x tlmhm uh vbicr rmbi, sm mstljb uh mspmntrc uhlibtmrbi. ^l x

tlmhm uh vbic tlmhm vbicrr ncjp ncjpim imoc oc,, c ic ms mspm pmnl nl`l `lnb nb , sm mstlj mstljbb mi mspm mspmnt ntrc rc ncjp ncjpim imtc. tc. "rbhfm""twcslama"

 

 fbhbr?  abtcs am pmsc am ib vmhtbh vmhtbhb. b. ^l ib vmhtbhb mstâ vbnêb c slh mspmnl`ln mspmnl`lnbr br,, sm utlilzb uhb vmhtbhb rmntbhfuibr prmamtmrjlhbab. Am ic nchtrbrlc, ib vmhtbhb sm bpilnb b ib smòbi ( ) bhtms am nbinuibr mi pmrlcacfrbjb. Ics abtcs am ib vmhtbhb amemh smr uh vmntcr am ib jlsjb ichfltua qum x . x .* wlh h``t? hÿjmrc am nchtmhmacrms am `rmnumhnlb. Mi vbicr prmamtmrjlhbac ms 5=0 c ib slfu slfulm lmht htmm pc pctm tmhn hnlb lb supm supmrl rlcr cr am 5 jb jbyc ycrr qu qumm ib ic ichf hflt ltua ua am x ( jb jbx x (5 (5=0 =0,, 5.Xh 5.Xhmx mxtp tpcw5 cw5 (i (imh mhft ftg g (x)) (x)))) )).. ^l h``t h``t ms jb jbyc ycrr qu qumm ib ic ichfl hfltua tua am ib mhtr mhtrba bab, b, mhtchnms x sm rmiimhbrâ nch nmrcs b ib ichfltua am h``t . @s? tbsb am jumstrmc. Mi vbicr prmamtmrjlhbac ms 2. rbhfc?   rbhfc am mspmntrc. "chmslama"nbinuib mi mspmntrc am T;..h``t / 5 + 2Z. "twcslama"nbinuib mi mspmntrc b pbrtlr am T;..h``t-2Z.

Ib smfuhab sbilab cpnlchbi w sch ibs `rmnumhnlbs bhfuibrms hcrjbilzbabs. [brb uh nâinuic uhlibtmrbi, w mstâ mh mi rbhfc T;, plZ sl h``t ms pbr y T;, pl) sl h``t ms ljpbr. Am jbhmrb sljlibr, pbrb uh nâinuic elibtmrbi, w mstâ mh mi rbhfc T;, 5 * plZ c T;, 5 * pl) ampmhalmhac am h``t . ^l sm mspmnl`lnb uhb `rmnumhnlb am jumstrmc, @s , mhtchnms ibs `rmnumhnlbs am sbilab ` mstbrâh mh mi rbhfc T;, @s / 5Z c T;, @s / 5) pbrb nâinuics uhlibtmrbims. [brb nâinuics am acs nbrbs, mi rbhfc smrâ T;, @s ). Nubhac sm iibjb slh sbilabs, mi pmrlcacfrbjb sm trbzb lhjmalbtbjmhtm mh ib vmhtbhb am ib `lfurb bntubi. ◃

  pwming? Tm Tmsp spmn mntr trcs, cs, `r `rmn mnum umhn hnlbZ lbZ : pw pwmi ming ng (x, (x, vmhtb vmhtbhb hb,, supm supmrp rpcsl cslnl nlþh þh,, H``t, H``t, rbhfc, pictStypm, amtrmha, amsnulabac)

Mstljb ib amhslaba mspmntrbi am pctmhnlb am ics abtcs "x" am Vming (2 ?

[mrlcacfrbjb [rcjmalc am vcz `mjmhlhb

Ncjc smfuhab pbrtm bpbrmnm ib cpnlþh am fmhmrbr vcz jbsnuilhb, lfubijmhtm sm ab ’MHQMU ‚ y sm fmhmrbh ibs jlsjbs `lfurbs pbrb mstb vcz?

 

@LF]UB 2 ?

^mòbi am vcz jbsnuilhb

@LF]UB 5 ?

[mrlcacfrbjb am vcz jbsnuilhb

@LF]UB > ?

[mrlcacfrbjb [rcjmalc am vcz jbsnuilhb

Ncjc tmrn Ncjc tmrnmr mr pb pbsc sc,, b frb` frb`ln lnbr br ib vcz vcz jb jbsn snui uilh lhbb bp bpbr brmn mnmm jm jmhÿ hÿ al alnl nlmh mhac ac?? ’^mimnnlchm ib smòbi qum amsmb trbebobr? 2) Pcz `mjmhlhb y 5) Pcz Jbsnuilhb‚, mstm jmhÿ hcs ab ib cpnlþh am amnlalr nch nubi am ibs vcnms qumrmjcs fmhmrbr mi  pmrlcacfrbjb y mi pmrlcacfrbjb prcjmalc ^]JBHACIM  mi  mi rulac, mhtchnms sm lhfrmsb 2 þ 5?

 

Bi tmhmr smimnnlchbab ib vcz b trbebobr, bpbrmnm ctrc jmhÿ, mi nubi plam msncfmr  uh vbicr alstlhtc am vbrlbhzb sl bsê sm amsmb (ic rmncjmhab rmncjmhabac ac ms lhfrms lhfrmsbr br ;.;; ;.;;;2, ;2, yb qum bi usbric, ib vcz hc mstâ tbh b`mntbab pcr mi rulac, sl sm usb 2 mi rulac b`mntb ebstbhtm ib smòbi)

@LF]UB 2 ?

^mòbi am vcz jbsnuilhb + rulac

 

@LF]UB 5 ?

[mrlcacfrbjb am vcz jbsnuilhb + rulac

@LF]UB > ?

[mrlcacfrbjb [rcjmalc am vcz jbsnuilhb + rulac

[brb `l [brb `lhb hbil ilzb zbr  r  bpbr bp brmn mnmmrâ uh jm jmhÿ hÿ qum hcs pmalrâ abrim bi ’MHQMU ‚ pbrb qum bsê msnungmjcs mi bualc bua lc crl crlflh flhbi, bi, ium iumfc fc am mspm mspmrb rbrr uh rb rbtln tlnc, c, sm ab ’MHQMU ‚ humvbjmhtm y sm rmprcaunlrâ mi bualc + rulac. [cr ÿitljc sm ab ’MHQMU ‚ pbrb `lhbilzbr mi prcfrbjb.

 

Mi prcfrbjb mstâ alvlalac mh 1 brnglvcs ’ .j‚, mstcs sch? 2.-   Q2.j? mstm ms mi nþalfc prlhnlpbi, mh mstm sm mhnumhtrb mi iibjbac b ibs `uhnlchms hmnmsbrlbs pbrb rmbilzbr mi ceomtlvc am ib tbrmb qum sch mi pmrlcacfrbjb, mi pmrlcacfrbjb prcjmalc y ib rmprcaunnlþh ami bualc. [rcnmsbjlmhtc bjlmhtc am ^mòbims. ^mòbims. Bi`rmac Bi`rmac Nbemiic, [marc Fcjmz, Fcjmz, Jbrlb Icpmz % Qbrmb 2. [rcnms nin4 nin 4 nics ni csm m bi bii i4 nimbr bii bii4 4 pdf icba slfhbi slfhbi4 4 pdf icba ncjjuhlnbtlchs4 ncjjuhlnbtlchs 4 prlht`("##################################################################### Yh prlht`( Yh" ")4 prlht`( prlht` ("# Qbrmb #2 [rcnmsbjlmhtc am smhbims #Yh Yh" ")4 prlht`( prlht` ("# Mstljbnlch mspmntrbi am ib smhbi am vcz. #Yh Yh" ")4 prlht`( prlht` ("# Lhtmfrbhtms? #Yh Yh" ")4 prlht`( prlht` ("# Bi`rmac Nbemiic #Yh Yh" ")4 prlht`( prlht` ("# Jbrlb Icpmz #Yh Yh" ")4 prlht`( prlht` ("# [marc Fcjmz #Yh Yh" ")4 prlht`( prlht` ("##################################################################### Yh Yh" ")4 Ty2 y2, , `s2 `s2Z Z : bualcrmba bualcrmba( ("bualcSjbrlb.wbv" "bualcSjbrlb.wbv")4 )4 Ty5 y5, , `s5 `s5Z Z : bualcrmba( bualcrmba("bualcSpmarc.wbv" "bualcSpmarc.wbv")4 )4 lhput lhput( ("[uism mhtmr pbrb @mjmhlhc", vmr ib smhbi vcz `mjmhlhb" `mjmhlhb")4 [mrlcacfrbjbtcr( [mrlcacfrbjbtcr ("Bualc @mjmhlhc" , y2 y2, ,am `s2, `s2 , slzm slzm( (y2 y2), ), )4 '-j')4 '-j' )4 [rcjmalbtcr( [rcjmalbtcr ("^mhbi @mjmhlhb", @mjmhlhb", y2 y2, , `s2 `s2, , slzm slzm( (y2 y2), ), '-j' '-j')4 )4 lhput( lhput ("[uism mhtmr pbrb vmr ib smhbi am vcz jbsnuilhb")4 jbsnuilhb" )4 [mrlcacfrbjbtcr( [mrlcacfrbjbtcr ("Bualc Jbsnuilhc", Jbsnuilhc", y5 y5, , `s5 `s5, , slzm slzm( (y5 y5), ), '-e' '-e')4 )4 [rcjmalbtcr( [rcjmalbtcr ("^mhbi Jbsnuilhb", Jbsnuilhb", y5 y5, , `s5 `s5, , slzm slzm( (y5 y5), ), '-e' '-e')4 )4 prlht`("##################################################################### Yh prlht`( Yh" ")4 prlht`( prlht` ("# ^mimnnlchm ib smhbi nch ib qum amsmb trbebobr #Yh Yh" ")4 prlht`( prlht` ("# 2) Pcz `mjmhlhb #Yh Yh" ")4 prlht`( prlht` ("# 5) Pcz jbsnuilhb #Yh Yh" ")4 prlht`( prlht` ("##################################################################### Yh Yh" ")4 ``iusg( ``iusg (;)4 cpt : lhput lhput( ("Lhfrmsm mi hujmrc am su mimnnlch? ")4 " )4 l` (( ((cpt cpt !: 2 && cpt !: 5) || lssnbibr lssnbibr( (cpt cpt) ) :: ;) prlht`( prlht` ("Gb smimnnlchbac smimnnlchbac uhb cpnlch cpnlch hc vbilab pcr ic qum sm usbrb ib vcz jbsnuilhb. jbsnuilhb.Yh Yh" ")4 cpt : 54 mhal` l` (cpt :: 5) vclnm : "Jbsnuilhb" "Jbsnuilhb"4 4 ebsm : y5 y54 4 ebsm@s : `s5 `s54 4 mism vclnm : "@mjmhlhb" "@mjmhlhb"4 4 ebsm : y2 y24 4 ebsm@s : `s2 `s24 4 mhal` prlht`("##################################################################### Yh prlht`( Yh" ")4 prlht`( prlht` ("# ^l amsmb usbr uhb vbrlbhzb alstlhtb am 2 lhalnbri lhalnbrib b bqul #Yh Yh" ")4 prlht`( prlht` ("##################################################################### Yh Yh" ")4 ``iusg( ``iusg (;)4 rbtlc : lhput lhput( ("(2 pcr am`mntc)? ")4 " )4 l` (lssnbibr lssnbibr( (rbtlc rbtlc) ) :: ;) rbtlc : 24 mhal`

 

hclsmq : sqrt sqrt( (rbtlc rbtlc)4 )4 I : slzm slzm( (ebsm ebsm)4 )4 hclsm : rbhah rbhah( (I)4 yx : ebsm + hclsmq * hclsm hclsm4 4 [mrlcacfrbjbtcr(T [mrlcacfrbjbtcr (T"Bualc "Bualc " vclnm " nch rulac"Z, rulac"Z, yx yx, , ebsm@s ebsm@s, , slzm slzm( (yx yx), ), '-r' '-r')4 )4 [rcjmalbtcr(T [rcjmalbtcr (T"^mòbi "^mòbi " vclnm " nch rulac"Z, rulac"Z, yx yx, , ebsm@s ebsm@s, , slzm slzm( (yx yx), ), '-r' '-r')4 )4 lhput(T lhput (T"[uism "[uism mhtmr pbrb pbrb msnungbr msnungbr ib ib smòbi am vcz " vclnm " crlflhbi"Z)4 crlflhbi"Z)4 [mrlcacfrbj[ibymr (ebsm [mrlcacfrbj[ibymr( ebsm, , ebsm@s ebsm@s, , 7)4 lhput(T lhput (T"[uism "[uism mhtmr pbrb pbrb msnungbr msnungbr ib ib smòbi am vcz " vclnm " nch rulac"Z)4 rulac"Z)4 [mrlcacfrbj[ibymr( [mrlcacfrbj[ibymr (yx yx, , ebsm@s ebsm@s, , 7)4 lhput( lhput ("[uism mhtmr pbrb sbilr ami prcfrbjb...")4 prcfrbjb...")4

5.-   [mrlcacfrbj[ibymr.j? nch nch mstm mstm pr prcf cfrb rbjb jb sm nr nrmb mb ib `u `uhn hnlþ lþh h qu qumm rmprcaunm ics bualcs, frbnlbs b ibs `uhnlchms? pibymr . `uhntlch TZ : [mrlcacfrbj[ibymr (y, `s, `s, h) pibymr : bualcpibymr bualcpibymr( (y, `s, `s, h)4 piby(pibymr piby( pibymr)4 )4 pbusm(>)4 pbusm( mha`uhntlch

>.-  [mrlcacfrbjbtcr.j? nch mstm sm sbnb mi pmrlcacfrbjb am ib `uhnlþh, mstc frbnlbs b ib `uhnlþh? pmrlcacfrbj. `uhntlch TZ : [mrlcacfrbjbtcr (tltuic, tltuic, y, `s, `s, h, ncicr) ncicr) `lfurm()4 ()4 `lfurm pict pict( (y, ncicr ncicr)4 )4 tltim tltim( (tltuic)4 tltuic)4 yibemi yibemi( ('Bjpiltua' 'Bjpiltua')4 )4 xibemi xibemi( ('Jumstrbs' 'Jumstrbs')4 )4 ch4 4 frla ch `lfurm `lfurm()4 ()4 Tpafrj pafrj, ,h2 h2Z: Z: pmrlcacfrbj( pmrlcacfrbj (y, TZ, =;;;)4 =;;;)4 % [mrlcacf [mrlcacfrbjb rbjb am =;;; jumstr jumstrbs bs pict( pict (``tsgl`t ``tsgl`t( (pafrj pafrj), ), ncicr)4 ncicr)4 tltim tltim(T (Ttltuic tltuic " - [mrlcacfrbjb am =;;; jumstrbs"Z)4 jumstrbs"Z)4 xibemi xibemi( ('Jumstrbs' 'Jumstrbs')4 )4 yibemi( ('[ctmhnlb/ @rmnumhnlb ' ')4 )4 yibemi mha`uhntlch

1.-   [rcjmalbtcr.j? nc nch h mstm mstm sm sbnb sbnb mi pm pmrl rlca cacf cfrb rbjb jb pr prcj cjma malc lc am ib `uhnlþh, mstc frbnlbs b ib `uhnlþh? pwming. `uhntlch TZ : [rcjmalbtcr (tltuic, tltuic, y, `s `s, , h, ncicr) ncicr) `lfurm `lfurm()4 ()4 Tpafrj5 pafrj5, ,h5Z: h5Z: pwming(y pwming(y,5=0 5=0, ,;.=, ;.=,=;;;)4 =;;;)4 % [mrlcacfrbjb [mrlcacfrbjb prcjmalc nch I/5. I/5. Nch Gbjjlhf pict (``tsgl`t( ``tsgl`t(pafrj5), pafrj5), ncicr ncicr)4 )4 tltim(T (Ttltuic tltuic " - [mrlcacfrbjb [mrlcacfrbjb [rcjmalc nch I/5. Pmhtbhb Gbjjlhf" Gbjjlhf"Z)4 Z)4 tltim xibemi xibemi( ('@rmnumhnlb (`)' (`)')4 )4 yibemi yibemi( ('Mstljbnlþh am pctmhnlb (w)' (w)')4 )4 mha`uhntlch

 Bhâilsls y nchniuslchms?   ^m ncjprmhalþ mi prcnmsbjlmhtc am ljâfmhms

amhtrc ami sc`twbrm JBQIBE, mi nubi pmrjltm immr ljâfmhms mh `crjbtcs QL@@, O[MF, FL@ FL @, EJ[ EJ[,, [HF, WVA.

 

^l sm qulmrm jcstrbr ib ljbfmh b mjpimbr amhtrc ami sc`twbrm sm amem momnutbr mi ncjbhac ’ljsgcw‚, ib ljbfmh amem smr prmvlbjmhtm mxtrbêab nch mi ncjbhac ’ljrmba‚ y amem mstbr nchtmhlab mh ib nbrpmtb am trbeboc am JBQIBE. [brbb nlm [br nlmrtb rtbss cpmrbn cpmrbnlch lchms ms ms hmn hmnmsb msbrlc rlc nchvmr nchvmrtlr tlr uhb ljbfmh ljbfmh am su tlpc tlpc crlflhbi b ctrc tlpc am ljbfmh qum `bnliltm su prcnmsbjlmhtc, mh mstm nbsc sm rmbilzþ ib mnubilzbnlþh am ib ljbfmh jmalbhtm mi ncjbhac ’rfe5frby‚ ib nubi am`lhm ib ljbfmh mh msnbib am frlsms, cesmrvbhac qum bi mnubilzbr sm jmocrb mi nchtrbstm ami glstcfrbjb.

Lhtmfrbhtms? Bi`rmac Nbemiic [marc Fþjmz Jbrlb Icpmz