Signals & Systems - Chapter 3

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Samuel Fitzgerald
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1 .EgrCS.cm, i Sigls d Sysms pg 9 Sigls & Sysms - Chpr S. Ciuus-im pridic sigl is rl vlud d hs fudml prid 8. h zr Furir sris cfficis r -, - *. Eprss i h m. cs A φ Slui: 8cs cs 8 8si cs si cs Eulrs Apply U. Ciuus-im pridic sigl is rl vlud d hs fudml prid. h zr Furir sris cfficis r, - *, - * -. Eprss i h m. cs A φ Slui: S. A discr-im pridic sigl is rl vlud d hs fudml prid 5. h zr Furir sris cffici r, - *, - * Eprss i h m A. si A φ Slui: 5 5 & i : r gr y hr is si 5 si 5 cs cs } { } { Eulrs Apply

2 U. A discr-im pridic sigl is rl vlud d hs fudml prid 9. h zr Furir sris cffici r, - *, - * - Eprss i h m A A si φ. Slui: S. Fr h ciuus-im prid sigl 5 cs si drmi h fudml frqucy d h Furir sris cfficis such h Slui: Apply Eulrs h Fudml Frqucy ; - ; 5-5 * -; U. Fr h ciuus-im prid sigl cs si 7 5 drmi h fudml frqucy d h Furir sris cfficis. Slui: S. Us h Furir sris lysis qui clcul h cfficis h ciuus-im pridic sigl.5.5 ih fudml frqucy. Slui: Ciuus-im sysm, hv: Furir Sris SyhsisEqui d d Furir Sris AlysisEqui.EgrCS.cm, i Sigls d Sysms pg

3 .5 v dd d.5 d.5 cs.5 d.5 si.5 U. Us h Furir sris lysis qui clcul h cfficis h ciuus-im pridic sigl.5 msc.5 msc msc ih fudml frqucy. Slui: 5S. Csidr hr ciuus-im pridic sigls hs Furir sris rprsis r s flls: 5 cs 5 si 5 Us Furir sris prpris hlp sr h fllig qusis: Which f h hr sigls isr rl vlud? b Which f h hr sigls isr v? Slui: if * h h sigl is rl hris i is. : cug ms h AB* A-B Furir sris cfficis r K hris W h { K } { - * -K } hr is Rl Furir sris cfficis r cs - hris W h { cs} { - * cs-} hr is Rl Furir sris cfficis r si - hris W h { si} { - * -si-} hr is Rl.EgrCS.cm, i Sigls d Sysms pg

4 b Fr sigl b v is Furir Sris Cffici mus b v I hr rds h rliship - - is ru Which ms ly is v sic ly his fuci - 5U. Csidr hr ciuus-im pridic sigls hs Furir sris rprsis r s flls: si cs5.9 si hr is igr 5 hr is rl hr is igr Us Furir sris prpris hlp sr h fllig qusis: Which f h hr sigls isr rl vlud? b Which f h hr sigls isr v? Slui: S. Us h lysis qui vlu h umricl vlus f prid f h Furir sris cfficis f h pridic sigl Slui: Fr Discr-im sysm, hv > > {δ m 8δ m}. m > > δ Furir Sris Syhsis Equi Furir Sris Alysis Equi firs udrsd h sigl { m 8 m } m usig h dfiii f impuls fuci c ri: m 8 m hris W s h h sigl is pridic ih fudml prid f. If yu d s i, us fid vlu, 8,,,, 5 8, hich rps vry fur rms δ 8 hr: >, -, -, U. Us h lysis qui vlu h umricl vlus f prid f h Furir sris cfficis f h pridic sigl Slui: {δ 5m δ 5m}. m.egrcs.cm, i Sigls d Sysms pg

5 7S. L b rl d dd pridic sigl ih prid 7 d Furir cffici. Giv h 5,, 7. Drmi h vlus f, -, - d -. Slui: Usig h prpris f Furir Sris culd s: Prid ih prid 7 7 *7 5 *7 *7 7 rl d dd is purly imgiry d dd U. L b rl d dd pridic sigl ih prid 9 d Furir cffici. Giv h 5, 7 -. Drmi h vlus f, -, - d -. Slui: 8S. Drmi h Furir sris rprsis h fllig sigls: Ech illusrd i h fllig figur b Ech illusrd i h fllig figur c Ech illusrd i h fllig figur.egrcs.cm, i Sigls d Sysms pg

6 d Ech illusrd i h fllig figur is pridic sigl ih prid d - - Slui: d Igri by pr udv uv d vdu.egrcs.cm, i Sigls d Sysms pg

7 .EgrCS.cm, i Sigls d Sysms pg 5 b dd v d d d d si si c si si d d d d d

8 d d ll 8U. Drmi h Furir Sris rprsi h sigl sh i h fllig figur: - - Slui: 9S. A discr-im pridic sigl is rl vlud d hs fudml prid 5. h zr Furir sris cfficis r, - *, * - Eprss i h m A A si φ. Slui: 5 dd 5 5 cs 5 cs8 5 cs 5 cs U. A discr-im pridic sigl is rl vlud d hs fudml prid 7. h zr Furir sris cfficis r, - *, * - Eprss i h m A A si φ. Slui: S. Drmi h Furir sris cfficis h fllig discr-im pridic sigl. Pl h mgiud d phs f ch s f cfficis..egrcs.cm, i Sigls d Sysms pg

9 Slui: firs rm scd rm hr sics prid si cs X U. Drmi h Furir sris cfficis h fllig discr-im pridic sigl. Pl h mgiud d phs f ch s f cfficis. Slui: si7 S. h sigl rprsd by h fllig Furir sris cfficis is pridic ih prid 8. Drmi h sigl Slui: 8 cs cs cs U. h sigl rprsd by h fllig Furir sris cfficis is pridic ih prid 7. Drmi h sigl Slui:.EgrCS.cm, i Sigls d Sysms pg 7

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =