signal is any kd o physical quaniy ha conveys/ ransmis/sores ormaion Medical signal processg eg () elecrical volage, ha can be measured on he surace o he sk/head as a resul o he hear-/muscle-/bra aciviies (ECG/EMG/EEG) eg () gamma phoon deecion radioisoope diagnosics () () mv/cm KD 59 5 mm/s mv/cm Classiicaion o signals saic ime-dependen periodic non-periodic random deermisic pulsed conuous elecric non-elecric analog digial elecric signals non-elecric signals are ranserred o elecric ones a very special role advanages o elecric signals: hey are easy o ransorm, ampliy, ransmi digial signals analog signals are ranserred o digial ones advanages o digial signals: hey are easy o sore, he noise can be engeered and luence can be reduced 5 mm/s 3 4
quaniy ha compares he magniudes o wo signals: Signal level or Bel-number (or Decibel-number): n (named aer Bell) uni o n : Bel (B) or decibel (db) c radian arc radius m rad m radius arc c ph (power o Hydrogen) H ph lg M e g : H ph lg -7-7 M ( 7) 7 n lg J B lg J E B lg E B sead o Bel number we are usg decibel-number decimal logarihm o raio o wo powers (ensiies, energies) n lg db (d = ) 5 6 he characerisic uni: power (or ensiy/energy), he pracical uni: (elecric) volage he relaion beween power and volage: I signal level wih volages: n lg lg (Ohm : I) db lg db lg db db 7 lg db,3 db 3dB 3dB lg db db db c hal lie, hal value hickness lg db db db 8
empirical densiy Densiy Specrum n: number o daa n h cm H h body heigh, H area under he curve: n area under he curve: H h body heigh, specrum, as a special densiy 9 6 7 8 9 6 7 8 9 Fourier s heorem or periodic s (signals) specrum all (usual) periodic s can be expressed as a sum o se (and cose) s rom he undamenal requency and he overones periodic : here is a period,, where is he requency he se, which has he same requency as he periodic : undamenal requency, 3, 4, : overones (le specrum) square pulse ra undamenal r(equency) undamenal r+ 3rd overone undamenal r+ 3rd overone + 5h overone undamenal r+ 3rd overone + 5h overone + 7h overone 5 5 5 5 5 5 5 5
undamenal r+ 3rd overone + 9h overone undamenal r+ 3rd overone + h overone undamenal r+ 3rd overone + 3h overone 5 5 specrum 5 5 5 5 undamenal r+ 5 5 3rd overone + 5h overone 4 5 5 3 undamenal r+ 3rd overone + 7h overone undamenal r+ 3rd overone + 7h overone + + 5 5 specrum c ie series k k 3 4 8 Creag an ECG signal rom se s 3 5 exbook, Figure VII3 6
Measured specra Fourier heorem or non-periodic s (signals) lue clare all (usual) s can be expressed as a sum o se (and cose) s specrum: conuous J c emission specra o candescen ligh sources 7 8 se =/ specrum le specrum ( le) Music ime-requency represenaion periodic B B =/ le specrum se a ew periods C C d/d =/ band specrum D D eg pulsed ulrasound more periods d/d =/ band specrum non-periodic E E d/d conuous specrum 9
Voicepr Hear beas ime-requency represenaion (+ oscillogram) oscillogram (sound ensiy vs ime) (s) se (Hz) ime requency represenaion (s) hp://wwwnripsgojp/org/ourh/o3/dex-ehml pronounced consonans and vowels sysole diasole Frequency and ampliude ranges o biological signals Frequency dependen uni: Elecronic ampliier () () ou and ou : same s same: undamenalis requiremen similar: realisic requiremen ( ) () ( ) ou( ), where ou ou,, power ga (ampliicaion) volage ga (ampliicaion) racical manual, iel page o meas 7 3 4
(requency dependen) volage-divider ou ou ou requency dependen volage-divider: wih capacior 5 ou C C C C a high requencies he capacior is a shorcu ou High-pass/low-cu iler a very low requencies: a low requencies: because o he phase dierence, he sum should be calculaed as vecors C C i ( ), ou i a high requencies : i,, ou n(db) ou C log 6 db/ocave 6 ou C C C a low requencies: Low-pass/high-cu iler ou a high requencies: C C he capacior a low requencies is a disconuiy n(db) C i ( ), i, ou a very high requencies : i ( ), ou C ou log -6 db/ocave 7 n(db) n max n max -3 or (): >, n= lg = lg > db or (): requency characerisics l : lower requency limi l u ranser band (passband) ideal ampliier (logarihmic scale) u : upper requency limi 8
mpliier wih eedback, : : volage ga wih eedback volage ga wihou eedback >, posiiv eedback (same phase), > (advanage) ( a) ( c) ( ( b) ) Wihou appropriae perspecive we may no recognize our real posiion <, negaiv eedback ( opposie phase), < (disadv) posiiv eedback: (a) =, ampliicaion: ie se wave oscillaor eg: ulrasound generaor, hea heraphy (b), ampliicaion: very big regeneraive ampliier eg: hearg, ouer haircells 9 negaiv eedback: all ampliier 3 n(db) posiiv eedback 3 db wihou eedback 3 nalog signal digial signal 3 negaiv eedback log 3 4 5 3 analog signal: ime- and value-con 3 4 5 6 7 8 9 3 4 5 3 ime-discree value-con ranser band posiiv eedback: ranser band narrrower (big disadvanage) higher ga (advanage) negaiv eedback: ranser band broader (advanage) less ga (small disadvanage) 3 3 4 5 ime-con value-discree 3 4 5 6 7 8 9 3 4 5 digial signal: ime- and value-discree 3
ime-discree: he value o he signal is no known or all momens ime highes requency componen o he signal sampl = max, reconsruced signal is consan sampl = 5 max, req o reconsruced signal is wrong samp = max, req o reconsruced signal is correc Nyquis Shannon samplg heorem: or complee reconsrucion he mimum samplg requency should be wice he requency o he highes overone o he signal eg: hii, max = khz sampl = 44 khz > khz value discree: he value o he signal can no be arbirary eg: hii, 6 bi = 6 = 65 536 (CD sandard) 4 bi = 4 = 6 777 6 ( bes audio card) 33 discr ou egral discrimaion ulse processg o selec only hose pulses ha are larger han a prese ampliude exbook, Figure VII3 dierenial discrimaion ou o selec only hose pulses whose ampliudes lie wih a prese wdow 34 N h Disribuion s and ID/DD specra densiy cm M=N -N cumulaivedisribuion cumulaivedisribuion N 6 5 4 3 5 6 7 8 9 4 8 6 4 5 6 7 8 9 4 8 6 4 5 6 7 8 9 DD- specrum ID- specrum how many pulses are larger han h? how many pulses are smaller han h? 35 Concenraion o whie blood cells Couler couner 36