MECE 3320 Measurements & Instrumentation. Static and Dynamic Characteristics of Signals

Transcription

1 MECE 330 MECE 330 Masurms & Isrumao Sac ad Damc Characrscs of Sgals Dr. Isaac Chouapall Dparm of Mchacal Egrg Uvrs of Txas Pa Amrca

2 MECE 330 Sgal Cocps A sgal s h phscal formao abou a masurd varabl bg rasmd bw a procss ad a masurm ssm Characrscs of Sgals Magud - grall rfrs o h maxmum valu of a sgal Rag - dffrc bw maxmum ad mmum valus of a sgal Amplud - dcav of sgal flucuaos rlav o h ma Frquc - dscrbs h m varao of a sgal

3 MECE 330 Sgal Cocps Cod. Characrscs of Sgals Cod. Damc - sgal s m varg Sac - sgal dos o chag ovr h m prod of rs Drmsc - sgal ca b dscrbd b a quao ohr ha a Fourr srs or gral approxmao o-drmsc - dscrbs a sgal whch has o dscrbl par of rpo ad cao b dscrbd b a smpl quao.

4 MECE 330 Sgal Cocps Cod. Sgal characrscs o b cosdrd a masurm ssm Rag Tmporal varao

5 MECE 330 Sgal Classfcao Aalog Sgal couous m Dscr Sgal formao avalabl a dscr pos m

6 MECE 330 Sgal Classfcao cod. Quazao: Assgg a sgl valu o a rag of maguds of a couous sgal. E.g. a dgal wach dsplas a sgl umrcal valu for h r durao of m ul s updad a h x dscr m sp.

7 MECE 330 Sgal Classfcao cod.

8 MECE 330 Couous sgal Dscr sgal Sgal Aalss Ma valu RMS valu rms d d d Ma valu RMS valu rms d Roo Ma Squar RMS valu s a dcao of h amou of varao h damc poro of h sgal.

9 MECE 330 Sgal Aalss Cosdr h fuco Th ma s gv b: 30 cos6 30 cos6 d = 30 s 6 6 = 30 s 6 s 6 6 Th RMS s gv b: rms 30 cos 6 d s 6 4 s 6 cos6 6

10 MECE 330 Effc of Tm Prod o Ma Valu for o-drmsc Sgal As h avragg m prod bcoms log rlav o sgal prod, h rsulg valus wll accural rprs h sgal. o-drmsc sgals hav a rag of frqucs ad o sgl avragg prod wll produc a xac rprsao of h sgal. I such a cas, h sgal should b avragd for a prod logr ha h logs m prod coad wh h sgal.

11 MECE 330 Effc of Subracg DC Offs for a Damc Sgal DC offs ma b rmovd from a damc sgal o accua h characrscs of h flucuag compo of h sgal.

12 MECE 330 Sgal Aalss Cod. Sourc: solarssm.asa.gov A complx wavform, rprsd b wh lgh, ca b rasformd o smplr compos, rprsd b h colors h spcrum. A vr complx sgal, v o ha s o-drmsc aur, ca b approxmad as a f srs of s ad cos fuco Fourr Srs.

13 MECE 330 Sprg-Mass Ssm Sgal Amplud & Frquc d d Govrg Equao: m 0 Soluo: Acos Bs ; / m Th soluo ca also b xprssd as: C cos C A * C s B B a A * * ; a A B Amplud of oscllao s C Frquc of oscllao s f Th m prod T s gv b: T f

14 MECE 330 Frquc Aalss A complx sgal ca b hough of as mad up of ss ad coss of dffr ampluds ad m prods, whch ar addd oghr a f rgoomrc srs Fourr Srs. 3 4 Mods of vbrao for a srg plucd a s cr

15 MECE 330 Fourr Srs ad Coffcs A fuco wh a prod T= / ca b rprsd b a rgoomrc srs, such ha for a, / / / / / / 0 0 s cos s cos T T T T T T d T B d T A d T A B A A If s v fuco, cos A If s odd fuco, s B

16 MECE 330 Fourr Srs Exampl Drm h Eulr coffcs of h Fourr srs of h fuco fx=x for - x : a0= fxdx= xdx=0 - - a fxcosxdx= xcosx dx - - x [ cos x s x] 0 b fxs xdx= xsx dx - - x [ s x cos x] cos

17 MECE 330 Fourr Srs Exampl x s f x s x s x s3 x s4 x Fv rms 00 rms f3 x f5 x f00 x fx 0 Ral fuco Thr rms x 3.4

18 MECE 330 Gbbs Phomo Th paral sum of a Fourr srs shows oscllaos ar a dscou po as show from h prvous xampl. Ths oscllaos do o fla ou v wh h oal umbr of rms usd s vr larg. As a xampl, h ral fuco fx=x has a valu of 3.4 wh x=3.4. O h ohr had, h paral sum soluo usg 00 rms has a valu of 0.38 wh x=3.4. I s drascall dffr from h ral valu. I gral, hs oscllaos wors wh h umbr of rms usd dcras. I h prvous xampl, h valu of h fv rms soluo s ol 0.06 wh x=3.4. Thrfor, xrm ao has o b pad wh usg h Fourr aalss o dscouous fucos.

19 MECE 330 Fourr Trasform ad Frquc Spcrum Th Fourr coffcs ar gv b: A T T / T / cos d B T T / T / s d If h prod T of h fuco approachs f, h spacg bw h frquc compos bcom fl small. I such a cas, h coffcs A ad B bcom couous fucos of frquc ad ca b xprssd as: A cos d B s d Sourc: Cambrdg Uvrs

20 MECE 330 Fourr Trasform ad Frquc Spcrum ow, cosdr a complx umbr dfd b. A B Iroducg cos s d cos s d Th abov quao ca b rwr as f f Th abov quao provds h wo-sdd Fourr rasform of. d Frquc spcrum Th magud of f, also calld modulus, s gv b f R f Im f Th phas of f s gv b f a Im f R f

21 MECE 330 Fourr Trasform ad Frquc Spcrum Cosdr a sgal rprsd b h Fourr srs: Th frquc spcrum s show blow: 5s 3s 6 0. s 0 0. C 5 V C 0 V C 3 V C 0 V C V f Hz f Hz f 3 Hz f 4 Hz f 5 Hz rad 0 rad 0. rad 0 rad 0. rad 3 4 5

22 MECE 330 Dscr Fourr Trasform Cosdr a dscr sgal wh daa pos wh as h sourc. So, w hav 0,,, -. ow h Fourr rasform of s ow, ach dscr po ca b rprsd b a dlad mpuls fuco,. Ths mpls ha gral abov s ol valuad a df pos. So, w ca rwr h gral as: d f f r r f f f f f d d f

23 MECE 330 Dscr Fourr Trasform Thrfor f 0 f Ths ca b valuad for a f. Bu, w wa o valua for h fudamal frquc ad s harmocs,.. f, f, 3f,.., or /, /, 3/,.., / Thrfor 0, 0,,... I marx form, ca b rprsd as whr

24 MECE 330 Dscr Fourr Trasform Exampl Cosdr a couous sgal: 5 cos 3cos4 dc Hz Hz ow, l us sampl h sgal 4 ms,.. f s = 4Hz, a = 0, ¼, ½, ¾. Pu =, = 0,,, 3

25 MECE 330 Dscr Fourr Trasform Exampl So h dscr sgal s gv b: 4 3cos cos ca wr h Fourr rasform as 0 0 I marx form, w ca rwr h rasform as: whr

26 MECE 330 Dscr Fourr Trasform Exampl Th marx hrfor bcoms: Th magud of h DFT coffcs s show blow:

27 MECE 330 Ivrs Dscr Fourr Trasform Th vrs rasform of f 0 f s 0.. h vrs marx s / ms h complx cojuga of h orgal marx. Sc h orgal marx s smmrcal, h spcrum s smmrcal abou /. Thrfor F ad F- produc wo frquc compos x /, /; ad > / o of whch s ol vald. Th hghr of hs wo frqucs s calld h alasg frquc.

28 MECE 330 Ivrs Dscr Fourr Trasform Bcaus of smmr, h corbuo o s boh from ad -. Thrfor 0 Bu, Thrfor F * = F-.. h complx cojuga.

29 MECE 330 Ivrs Dscr Fourr Trasform Subsug o quao for, ]} arg[ cos{ }s Im{ }cos R{.. * or Ths rprss a sampls s/cos wav a a frquc of / Hzad a magud of /.

30 MECE 330 Irprao of Exampl. 0 = 0 rprss a d.c valu of 0/ = 0/4 = 5.. = -4 rprss a fudamal compo wh pa amplud / = x4/4 = wh phas gv b arg[] = -90 dg,.. cos/ = = / mpls a compo -3cos. I pcal applcaos, s grall 04 or grar. - has 04 compos: 53 o 03 ar complx cojugas of o 5