[ ] Amplitude Modulation AM with Envelope Detector. Large S/N limit m. c c c c s c. slowly varying. y, low-pass filtered (envelope)

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Diane Thornton
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1 Amplitude Modulation AM with Envelope Detetor Large S/N limit m < 1 (t) in ω t 1 m [ ] Reeived = y(t) = A 1 + m ( t) o ω t + n ( t)o ω t + n ( t)in ω t { j ω t (t)e } = Re Y lowly varying y, low-pa filtered (envelope) overmodulation = ditortion ( undermodulation = wated power) Le 16b.6-1 T1

t)in ω t { j ω t (t)e } = Re Y lowly varying y, low-pa filtered

2 Amplitude Modulation AM with Envelope Detetor [ ] Reeived = y(t) = A 1 + m ( t) o ω t + n ( t)o ω t + n ( t)in ω t { j ω t (t)e } = Re Y lowly varying { (t)} Im Y Y(f ) 0 A Y(t) [1 + m (t)] n(t) n (t) n (t) R e { Y(t) } W 0 f N o = kt f Le 16b.6- T

3 Amplitude Modulation AM with Envelope Detetor { (t)} Im Y Y(f ) 0 A Y(t) [1 + m (t)] n(t) n (t) n (t) R e { Y(t) } W 0 f N o = kt f N [ m ] Y(t) A 1 + (t) + n (t) envelope = deteted ignal + noie Note: 4WN o = n o ω t + n in ω t = n Le 16b.6-3 S N out out A m ( t) n (t) = m A (t) 4WN o T3

4 Amplitude Modulation AM with Envelope Detetor S N out out A m ( t) n (t) = m A (t) 4WN o S N in in ( A )( 1+ m (t) ) y ignal o where S in = 4WN (t) S i N i 1+ m (t) + o o 1 1 Noie figure F AM = = = 3 FAM 3 S N m 1 provided that A >> n (large S/N limit) Le 16b.6-4 T4

5 AM Performane (mall S/N limit) { } Im Y φ n (t) A [ 1 + m (t) ] n(t) [ ] A 1 + m ( t) o φ (t) n φ n (t) R e { Y } Y(t) n(t) + A o φ n (t) + A m ( t)o φ n(t) multipliative noie! Want S N 10 for fully intelligible AM "AM threhold" in in ( i.e. A ( 1 + m (t) ) > 3 n(t) ) Le 16b.6-5 T5

6 Frequeny and Phae Modulation (FM, PM) = [ ] Tranmitted: x(t) A o ω t +φ (t) Phae Modulation ("PM"): φ (t) = K'(t) Frequeny Modulation ("FM"): d φ dt ( -1) = π K r < 1, or φ = t = ω (t) (t) for (t) (t) ( τ )dτ +A -A 0 x(t) FM ignal t v o ω v(t) frequeny-enitive diriminator output funtion ω v o reeiver: y(t) Le 16b.6-6 filter, limiter diriminator envelope detetor low pa filter, DC blok output V1

for (t) (t) ( τ )dτ +A -A 0 x(t) FM ignal t v o ω v(t) frequeny-enitive diriminator output funtion

7 FM Bandwidth Expanion Fator β * d dt φ -1 = ω (t) = π K (t) r for (t) < 1 S(f) β = KW -W 0 W f intrini bandwidth P B W 1+β, o W < B K + W ( ) Y(f ) 0 B K f For PM: B ( ' + ) ( ( K 1 W not proven here) if β >> 1) Le 16b.6-7 V

8 Vetor Signal Analyi of PM/FM ( ) { j } t +ψ Reeived ignal y(t) = x(t) + n(t) = r( t)o ω t (t) = Re Y(t)e ω Im { Y (t)} r n (t) Y(t) x (t) >> n (t) r(t) n (t) φ n - φ(t) φ n 0 η(t) φ(t) A ψ(t) { (t)} Re Y Le 16b.6-8 n ( n φ ) n (t ψ (t) φ (t) + r (t)in φ A = φ (t) + ) A Diriminator output: PM: FM: v(t) =ψ (t) =φ (t) +η (t) = K ' (t ) + n (t ) A v(t) =ψ (t) π= K(t ) + n (t ) π A where ψ = d ψ dt V3

9 Calulation of PM S out /N out Reall n(t) = n ( t) o ω t n ( t) in ω t lowly varying lowly varying output N(f) kt R ) = ) = ) = o n (t n (t n (t N B kt R 0 B f PM: v(t) =ψ (t) =φ (t) +η (t) = K ' (t ) + n (t ) A Therefore PM: S (want large K ' (t), but approahe FM) K' (t) A o N out = = K ' (t) n (t) A N ow N o B 4N CNR ow for ae B = W(K <<1) Le 16b.6-9 V4

(t) =φ (t) +η (t) = K ' (t ) + n (t ) A Therefore PM: S (want large K ' (t), but

10 FM: Calulation of FM S out /N out v(t) =ψ (t) π= K(t ) + n (t ) π A where ψ = d ψ dt n (t) N (f ) n (t) j ω N(f ) N o = N R ( τ) n ω N(f = ω ) N o FM : S ( A ) out N out = K (t) n (t) π 4 egment S out W 0 W f ( ) W 4N 3 o 4 ( π f ) N o df = 0 A 1 W π A 3 Le 16b.6-10 V5

11 Calulation of FM S Therefore S out/n out A 3 out N out = K FM 3 N o W 3P = β = 6[ CNR] β N o W (K/W) 3 where CNR ( Carrier-to-Noie Ratio) = P N B = P N W β P o o "Wi de-band FM" (WBFM) S N out out WBFM P N W o S = o N 3β * o DSBSC Le 16b.6-11 FM advantage for β 5 ( FM radio, ( β + 1)W 00 khz); 3 β 19 db! V6

β P o o "Wi de-band FM" (WBFM) S N out out WBFM P N W o S = o N 3β * o DSBSC

12 Calulation of FM S out/n out FM pre-emphai & de-emphai filter Sine FM noie ) N(t f 0 f Pre-emphai ignal f pre-tranmiion and de-emphaize ignal + noie at reeiver; thi an yield ~10 db improvement (depending ) Le 16b.6-1 V7

pre-tranmiion and de-emphaize ignal + noie at reeiver;

13 Le 16b.6-13 { (t)} Im Y r n (t) φ n (t) FM Threhold (low SNR limit) ψ(t) A Y(t) (analogou to oding gain via bandwidth) φ n (t) -φ(t) ψ (t) φ n A + in ( φ φ n ) igna l obliteration r n { (t)} 5 1 baeband S/N in threhold (baeline) (db) typial FM threhold Re Y range over π Therefore mut have A >> r n to avoid multipliative noie 40 0 FM SNR OUT for automobile dropout in null, paed ~λ/ t V8

14 Iue In Chooing Modulation Type 1) Deired output SNR ) Cot of bandwidth ($, availability) (for ommuniation or torage) 3) Standard impoed on hannel, inexpenive equipment 4) Potential for oure oding 5) Charateriti (noie, fading), potential for hannel oding 6) Cot, power, weight, ize, thermal ontraint on ytem Le 16b.6-14 X1

inexpenive equipment 4) Potential for oure oding 5) Charateriti (noie, fading),

15 Output SNR Requirement CD-quality audio: ay 40 db dynami range (loudet power/ quiet power) +55 db SNR 95 db o 0 LOG 10 L 95 Therefore L = 56,000 level of σ < 3,000 digital level, 15-bit FM-quality audio: ay β * = 5 ~50 db (~35 db available above ~15-dB threhold) Intelligible peeh: > 10dB Video: Video: tudio-quality ~40 + db home-quality ~ db Le 16b.6-15 X

15-bit FM-quality audio: ay β * = 5 ~50 db (~35 db available above ~15-dB threhold)

16 Nominal Bandwidth Requirement 1) Voie: ~3 khz (6kHz exellent) ) Mui ~15 + khz 3) Video ~6 MHz (NTSC), 0 MHz (HDTV) 4) Data ~ bit/e; 10 4 OK often Le 16b.6-16 X3

17 State-Of-The-Art Soure Coding 1) Voie ~1.,.4, 4.8, 9.6 kbp; OK good 3 64 kbp ~ unompreed e.g. 8 khz at 8 bit ~ 58 db SNR ) Mui kbp for ~ CD quality, tereo 3) Video 4) Data Le 16b kbp jerky, blurred, or little hange kbp ~10 fp, 56 pixel (lip-read threhold) and artifat (moving detail) 384 kbp good video onferene quality 1.5 Mbp VCR NTSC TV 6 Mbp good NTSC TV 0 Mbp HDTV divide by 4 for typial miellaneou data, lole oding X4

18 FM Hybrid Analog Communiation Sytem Laer Example 1 FM Modulation x(t) Laer 0 ω (t) x(t) (t) 0 t (t) t Here we ue the tandard definition of CNR for a uperheterodyne reeiver. ( ) 3 S OUT / N = [ ] β β = B / OUT CNR 6 where W Baeband Optial uperheterodyne are limited by photon noie that flutuate with S(t), o the expreion here i approximate. Sine optial link have great bandwidth, β* an be very large. Le 16b.6-18 Y1

( ) 3 S OUT / N = [ ] β β = B / OUT CNR 6 where W Baeband Optial uperheterodyne are limited by photon

19 AM Hybrid Analog Communiation Sytem AM Modulation Laer Example S(t 1 ) Laer x(t) 0 x(t) t The CNR applie to the unmodulated laer and it detetor within the paband of the detetor output orreponding to the petrum of the ignal (t). Thi CNR mut be above the AM threhold of 10 db in order for to apply. S OUT / N OUT = [ CNR ] m Le 16b.6-19 Y

the detetor output orreponding to the petrum of the ignal (t).

20 Le 16b.6-0 FM/AM Analog Communiation Sytem Laer Example 3 FM/AM Modulation (t) AM near f 1 Hz Laer Sm t 1 (t) 0 (t) [FM] f (t) varie with ( t) [FM] 3 [ ] S / N CNR m 6 β where B = W β for (t) OUT OUT 1 AM FM Aume avalanh photo diode: g ( ) P D kthf [CNR] APD = η P / hf W β G P RL ηp ( ) eg P D = dark urrent + bakground power (W). Want [CNR] m 1 AM to be over FM threhold 15 db; then hooe β to yield deired S / N ( ay 50 db total) 0 O f Y3

[FM] f (t) varie with ( t) [FM] 3 [ ] S / N CNR m 6 β where B = W β for (t) OUT OUT 1 AM FM Aume avalanh photo

Digital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System

Digital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System Digital Modulation David Tipper Associate Professor Department of Information Science and Telecommunications University of Pittsburgh http://www.tele.pitt.edu/tipper.html Typical Communication System Source