Signals and Noise Communications System PDF

SIGNALS AND NOISE Communications system sinusoid ✗ (t)...

SIGNALS AND NOISE Communications system sinusoid ✗ (t) = Asin ( Zitft + to ) values we can use for modulation / Keying Nyquist Sampling Theorem extracts f- s 2 Zfm → to avoid aliasing transforms energy modulator %" " multiplexer bounded unbounded Functions to electrical demod singularity encrypt. wired - wireless / demon waveguide Impulse / radio unit Dirac Delta Function decrypt signals ↳ contains information about nature of phenomenon unit step / Heaviside Function Analog signal ↳ continuous in both time and amplitude ↳ free space only signal that can travel through as EM Waves via wave propagation ↳ electrical properties used are voltage frequency , , current , charge Digital signal ↳ discrete in both time and amplitude ↳ sampling + quantizing ( disaetize in time + in amplitude ) unit Ramp / Ray luke function - bit Binary digit = Time shifting how the Fidelity - qualitatively describes signal is replicated classifications of signals continuous - time and Discrete - Time -.. a) - 81^+3 ] + 38 In +2 ] + 28 Intl ] + 38 In ] -28 [ n I] + 8 [n 2 ] + 2g [ n z] domain - - cont in -. and range b) 2u(t ) - 2 ult 1)- c) - rlt ) 1- Zuct ) + rft 2) -  SIGNALS AND NOISE Real and complex Causal , Anti causal - , Non causal - Past future , present { present past & future Deterministic and Random / Stochastic Time Reversal Time Scaling Even and Odd Even : ✗ C- t ) = ✗ (t ) or ✗ [ - n ] = ✗ [n ] Odd : ✗ C- t ) = - ✗ (t ) or ✗ [ - n ] = - ✗ [n ] ^ a ✗ (-1-+1) shift ( + +1 , ✗ first Flip ~ ~ c ) C. v v system ↳ physical device that performs an operation on a given signal periodic and Aperiodic Linear time-Invariant Systems Linear Systems Homogeneous : f- ( Kx ) = kfcx ) continuous functions periodic but Additive : f- ( × Xz ) f- ( × ) + f- (x2 ) trigonometric + = All are , , all trigonometric discrete functions are aperiodic Test if additive 4×1-2 homogeneous : y. or = and Power Energy f- ( x ) ( X.tn/z)t2--4X,t2t4Xzt24KXt2--?k H : = 4×+2 A! 4 ? (4×+2) 4×1 t 4×21-2 = 4×11-4×2 +4 not not additive homogeneous o< Eco Time Invariance OL PL N p=o E = @ ↳ shift in input corresponds to a shift in output 9 if 2, then ✗ ( tt ) power ! s = yctts) Determine if power energy or. ✗ (f) = e- " tact) , a > 0 ✗ In ] = u[n ] ° ' 9999 "t ' I ✗ In ] / : 121-22+3 't f (e- ) dt = 0 → finite 0 0 = to Power ' i. Energy.. h is the one / being shifted t f. flt )g(t - I )dI  SIGNALS AND NOISE External Noise { 3 2,1 } , { 3 1,2 } , q q K) { 2,3 } Flip : hl 1. - = 4 ✗(K) = 93 , 1,2 } q Align for shifting : ✗ : 93 , 1,2 ) 93 , 1,2 } 93 , 1,2 ) q q q h :{ 112,3 } { 2,3 } 2,3 } Internal Noise 1. { i. T T T 9 61-3=9 Multiply : 31-21-6=11 Add 9 d d d y[ u ] y[ I ] y 12 ] ? vn { 311,2 } Pn { 3 , 1,2 } = ER q 9 " " pinakataba { } n { 1,2 3 } 1,2 , 3 " " Bernardo , T T 4nA Kathryn 1+4=5 2 BW noise = BW d d } dB - 3] y[ y[ 2) yin ] = { 9. 9.11.5.2 } q e- charge of Ndf N ✗ ¥ " " pink noise hln ) = { 3 -2,2 } , → hl - ) n = { 2 , -2,3 } q p ( ) ✗ n = { 2,2 , 2 , 2,2 } 1 vn : 4K ( 300 )(4MHz )( 1000) Un 8.14µV : ✗ : { 2,2 , 2 , 2,2 } q h : > { 2 -2,3 } 1- , then align p move BN = 412C Bn = 125 Hz y[ n ] : { 6,2 , 6,6 6,0 4 } , , Noise ↳ unwanted Noise and calculations signal Analysis Distortion : deviation by imperfect response : Interference addition of extraneous signals of Noise General category signal-to-Noise Ratio CSNR) SNR = signal power noise power Noise Factor & Noise Figure harmonic external internal F = %i Te intermodulation noise noise f- = It distortion distortion from outside the within the system % % If ,3f , 4f Zf , Ifz , 2fz±f , system ↳ 290K ↳ NF = 1010g (F) atmospheric noise ↳ less severe above noise Losses in Antenna system sky ← attenuation in dB 30MHz t (L 1) 290 Tsky %) 1- - - Ta = L Ts = Tm (1 - to Tant = k b 6 ✓ mean absorption temp. CONST [ 25 ] effective noise temp of. antenna + fieldline  SIGNALS AND NOISE Noise Measuring dB rn C =D Bmt 90 dB = dBm + 30 TLP = dBrnC - dB rn CO ↳ transmission level point Excess Noise Ratio TH Tc ENR 1010g - = Tc Double-Tuned Amplifier Peak Envelope power Frequency-Deviation Constant for a Clapp Oscillator Frequency- Modulated Modulation Index  RADIO WAVE PROPAGATION Wave Propagation Em Wave Quantities t disturbance is in motion t movement through a medium Wavefront ↳ set of where the has the points wave same phase 1 I 1 Source Medium Detector Classification of waves - Transverse disturbance is 1 to direction leg light radio ) I - , Longitudinal disturbance is 11 to direction ( e. g. sound ) Power Density How much power is present in a given space or region - - Mechanical requires a medium PT { - P, = Electromagnetic - does not need a medium 411-122 , spherical → isotropic antenna ( density ) Heavier atoms is bigger → sound travels slower wave Impedance sounds travel faster ↳ ratio between through solids than gases. electric and magnetic field intensities on a L since elastic they are more certain medium " Permeability - Magnetic Flux 133 ] [ 1m ] µ i µoµr Zo = E Eo Er ' Permittivity - Electric Flux 132] [ Hm ] For free : Zo 1201T r = 377 A space = Electromagnetic Wave TR , T V I = YI if free space I use c in f = 7 d R , TI % Electromagnetic spectrum E EHF 30 to 300 V Voice 300 to 3000 VLF V 3 to 30 kHz Surface AM Electric Field strength L LF 30 to 300 kHz 30ps E = M MF 300 to 3000 kHz R -11 HF 3 to 30 MHz FM Curr E over the Rockets Sky Nagscore ng 30 points si - V VHF 30 to 300 MHz Effect of Environment of EM Waves U UHF 300 to 3000 MHz Absorption s SHF 3 to 30 GHz Wave Space µ ↳ EM waves are transferred to atoms and molecules of space E EHF 30 to 300 GHz Interference 1 Infrared 300 to 3000GHz b two waves collide / combine visible spectrum light ROYGBV ↳ may be constructive or destructive , If Sunspot Cycles Every very very loving mother has very ugly ↳ 27 - day or 11 - year ( latest at 2019 ) son except I Optical Properties Reflection Polarization - bouncing of waves ↳ based Refraction E- field bending of passing through on - waves when mediums HLA LHT Vertical - electric field is perpendicular, magnetic field parallel Linear Horizontal - electric field is parallel, magnetic field perpendicular - frequency remains constant ! circular Diffraction - tendency to bend around slits Elliptical Random  RADIO WAVE PROPAGATION Wave Propagation Methods Sky ↳ to ionosphere then back to refraction Ground Wave ground via ↳ travels curvature of earth h uses HF too high f- → prone to absorption along range ↳ lost to some energy is absorption ↳ eventually disappears due to tilting space wave ↳ travels in the troposphere ↳ conditions depends on Los maximum distance that a radio signal can travel before it encounters an obstacle, such as the earth's curvature or other physical barriers. Radio Horizon Ionization ↳ dmi = 2hft.tt 2h ft, r occurs when high energy ultraviolet light waves from the sun enter the ionosphere → strike a atom literally knock an electron free gas → dkm = 17hm.tt 17hm , r survival : CONV 03 or 04 : in ← ft 07 or 08 : mi km tropospheric scattering D- Layer ↳ lowest , least important for HF propagation , least ionized ↳ reflects LF and MF ( absorbs radio waves due to ionization ) Ducting - when radiowave signals follow the curvature of the earth E- Layer / Kennelly - Heaviside Layer ↳ aids in MF here propagation auroral activity - occurs , temperature f. inversion ↳ reflects some HF waves , 150 MHz above is unaffected Es - Layer (sporadic E- layer ) ↳ ionization density very high ↳ persists during the night appears sporadically , satellites Propagation by F1 Layer ↳ for combines with Fa used more absorption , at night LOS ! 1=2 Layer ↳ for HF most important  RADIO WAVE PROPAGATION Fading ↳ variations in signal strength by atmospheric conditions virtual Height ↳ apparent height of incident reflected back to wave ground d hu. - Hanoi Skip Distance ↳ distance between Tx and the first point where the sky wave returns to the earth - dead zone or quiet zone, outer limit of the ground wave range. skip Zone - no reception ↳ of silence zone ↳ too far from and ground wave skip distance Maximum Usable Frequency MUF = fc Sec Qi MUF = fc iff a = 90° 1 critical frequency f-c = 9 Nmax ↳ Max # of free e- per m3 Optimum Working Frequency OWF = 0.85 MUF ↳ this when MUF is not explicitly asked always use Er Resulting Field Strength , 4 depends on freq , direct field strength Ed , Scatter Angle difference between direct geometrical path Actual Surface Refractivity and reflected paths 8 2 Ed sin it 8 Er = × hard 8 = 2 hat Atmospheric Layers than 1. Troposhere - Lowest, Weather Disturbances takes place, 8 - 10 miles * Raindrops cause greater attenuation by scattering by absorption above 100 MHz at frequencies 2. Stratosphere- no weather, circulation does occur, 40 miles * Ionospheric reflection is more likely to occur at long wavelengths. 3. Ionosphere- ionized layer, sun’s radiant energy, 30 to 250 miles, D,E and F later * Radiation is less affected by reflections from aircraft flying over transmission path when vertical polarization is used.  ANALOG MODUL ATION Recall : Types of wave Propagation s - Surface → LF , vertical 9 Ground Terrestrial ( Los ) @ < 1). gpdace undermodulation Trans ionospheric ( sat Comm ) Sky ionospheric - - crossover 6 distortion / ↳ D , E , F (F & , Fz ) Kendall effect to E- sporadic ( Kennelly - Heaviside layer ) Perfect modulation ( m =D over modulation (m > 1) ' t d wall freq , - penetrating power t ionosphere AM penetrating power Frequency Spectrum Modulation BW 1 I f- spy = fc ± fun ↳ alters characteristic of carrier according to message 's instantaneous A. BW f- usps f- LSB - - - value-Based f, f- m Froot fctfm ) - Vlt) ( wtt 0 = Vp sin to 1 ¥M I AM PM side frequency Amplitude why do we need to modulate ? Mvc ↳ reach VSB = V2 = 2 farther distances 4 practical size of antenna conventional AM system ( DSBFC ) ↳ length ✗ ✗ a f- ↳ double side band - full carrier ↳ fc >> f- m → smaller antenna Pt = Pct PSB t PSB " ↳ frequency selection / can choose to Pc = Vrms ' = ( " / 2) = Vi R R 212 How does modulation work ? vet ☐V ( 21T£ t ) ' ' carrier: Clt ) V. f. ± Of sin Vm (MK) MZ VCZ : pm = = = = MZP, 0-1=00 QR 212 2,2 Message : mlt ) Vmsin (2ñfmt ) -. " types of Modulation PSB VSBZ ( mvyz ) M " Pc = = = Linear amplitude ZR 2,2 4 continuous frequency Angular phase :. P , = Pet MF Pc If Pc + " ( It m / Pt ± Pc Discrete - pulse amplitude / position width / code 2 Amplitude Modulation For SSBFC : For SSBRC (90% suppression ) Pt Pc P, 0.1 Pc Psp 1-