
Chapter 3 Signal Transmission and Filtering Outline 1 Response of lti system

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 Chapter 3 Signal Transmission and Filtering
 Outline
 3.1 Response of LTI System
 Coherent AM reception and LPF
 3.2 Signal Distortion in Transmission
 3.3 Transmission Loss and Decibels
 Doppler frequency shift and beating
 3.4 Filters and Filtering
 Quadrature modulator and demodulator, heterodyne receiver
 3.5 Quadrature Filters and Hilbert Transform
 3.6 Correlation and Spectral Density
 3.1 RESPONSE OF LTI SYSTEMS
 Coherent AM reception and LPF
 a system
 linear timeinvariant system
 impulse response and convolution integral
 step response
 LCCDE and LTI system
 transfer function and frequency response
 steadystate phasor response
 undistorted transmission vs. distorted transmission
 block diagram analysis: parallel, serial/cascade, feedback connection
 Example 3.32 Doppler Shift
 3.2 SIGNAL DISTORTION IN TRANSMISSION
 Chapter 3 is all about the channel.
 3.1 Heterodyne quadrature modulator and demodulator have LTI filters.
 There are 4 types of channels for wireless communication using EM wave in the RF band .
 If interference and noise are ignored;
 The propagation channel is modeled by a linear channel.
 Each path has the following four characters:
 Gain, Delay
 Doppler
 Angle/Direction of Departure (AOD/DOD)
 Angle/Direction of Arrival (AOA/DOA)
 The radio channel maps the propagation channel to a CT SISO/MISO/SIMO/MIMO linear system depending on;
 antenna pattern (directivity) and
 configurations (spacing).
 Directional antenna. Ex. Horn antenna,
 Omnidirectional antenna
 uniform linear array (ULA)
 uniform circular array (UCA)
 The modulation channel may introduce nonlinear distortion incurred by amplifiers.
 The digital channel is modeled by a DT system.
 Precisely speaking, the channel becomes nonlinear with finite precision.
 Often modeled by a linear DT system corrupted by additive quantization noise.
 Distortionless Transmission
 A channel is distortionless iff it is an LTI system with impulse response
 Frequencyflat channel
 Over the desired band
 phase
 Frequencyselective channel
 Distortions
 Nonlinear distortions
 Linear distortions
 Example: linear distortions
 Test signal x(t) = cos 0t + 1/5 cos 50t
 Figure 3.23
 Test signal with amplitude distortion (a) low frequency attenuated; (b) high frequency attenuated
 Figure 3.24
 Test signal with constant phase shift = 90
 Figure 3.25
 Equalization
 Multipath distortion
 Intersymbol interference (ISI) in digital signal transmission
 Linear equalization
 Linear zeroforcing equalization (LZF): channel inversion
 Linear minimummean square error equalization (LMMSE)
 Nonlinear equalization
 Maximumlikelihood sequence estimator (MLSE)
 Decisionfeedback equalization (DFE)
 Feedforward (FF) filter and feedback (FB) filter
 ZFDFE
 MMSEDFE
 CT equalizer vs. DT equalizer vs. block equalizer
 Transversal filter, tappeddelayline equalizer
 Frequencydomain equalizer (FDE)
 Onetap equalizer for OFDM
 Adaptive equalizer
 Nonlinear distortion and companding
 Transfer characteristic
 Memoryless distortion
 Distortion with memory
 Polynomial approximation of memoryless distortion
 Secondharmonic distortion
 Intermodulation distortion
 Companding
 3.3 TRANSMISSION LOSS and DECIBELS
 Power gain
 g = P_out/P_in
 decibels
 g_dB = 10 log_10 g
 3 dB = 1/2
 G = 10^(g_dB/10)
 Serial interconnection of amplifiers and attenuators > addition, subtraction in dB
 If g = 10^m, then g_dB = m*10 dB
 dBm
 0 dBm = 1 mW
 10 dBm = 10 mW
 20 dBm = 100 mW = 0.1 W
 30 dBm = 1 W = 0 dBW
 Transmission loss and repeaters
 Loss L = 1/g
 Path loss
 Passive transmission medium
 Transmission lines
 coaxial cable: Coaxial lines confine virtually all of the electromagnetic wave to the area inside the cable.
 Twisted(wire) pair cable:
 EMI is cancelled. Invented
 by A. G. Bell.
 Fiberoptic cables
 Waveguides
 Loss, attenuation
 Attenuation coefficient in dB per unit length
 Table 3.31
 Frequency bands are different.
 Fiber optic cable: 0.22.5 dB/km loss
 Twisted pair: 26 dB/km loss
 Coaxial cable: 16 dB/km loss
 Waveguide: 1.55 dB/km loss
 …
 Repeater amplifier
 Amplification of distortion, interference, and noise
 Light propagation down a multimode stepindex fiber
 Figure 3.33b
 Light propagation down a singlemode stepindex fiber
 Figure 3.33a
 Light propagation down a multimode gradedindex fiber
 Figure 3.33c
 Large bandwidth and low loss
 Carrier frequencies in the range of 200 THz
 0.22 dB/km loss
 Lower than most twistedpair and coaxial cable systems
 Absorption
 Scattering
 Less interference
 No noise
 Low maintenance cost
 Secure
 Hybrid of electrical and optical components
 LED or laser
 Envelope detector
 Correction and Announcement
 Propagation channel: Each path has gain, …
 A channel is distortionless iff it is an LTI system with impulse response
 Nonlinear memoryless distortion has input output relation given by
 which increases bandwidth of the output because multiplication in TD corresponds to convolution in the FD.
 Exam on next Tuesday @LG104, 11:0012:15
 Ch. 13
 Open book (but you will not have time to read on the site.)
 T/F, filling blanks, Essay, Math
 Radio Transmission
 Lineofsight propagation
 Freespace path loss (FSPL)
 The loss between two isotropic radiators in free space.
 Formula
 farfield
 It is a function of frequency. However, it does not say that free space is a frequencyselective channel.
 Satellite repeater system: uplink, downlink, frequency translation, geostationary, low orbit, OBP
 Figure 3.35
 3.4 FILTERS and FILTERING
 Ideal Filters
 LPF
 BPF
 Lower and upper cutoff frequencies
 Passband and stopband
 HPF
 NF
 Transfer function of a ideal bandpass filter
 Figure 3.41
 Realizability, noncausality
 Bandlimiting and timelimiting
 It is impossible to have perfect bandlimiting and timelimiting at the same time.
 Ideal filters are noncausal.
 RealWorld Filters
 Halfpower or 3 dB bandwidth
 Passband, transition band/region, and stopband
 Typical amplitude ratio of a real bandpass filter
 Figure 3.43
 3.5 QUADRATURE FILTERS and HILBERT TRANSFORMS
 The quadrature filter is an allpass network that shifts the phase of positive frequencies by 900 and negative frequencies by +900
 Quadrature Filtering and Hilbert Transform
 Example. Hilbert transform of cosine signal
 Instead of separating signals based on frequency content we may want to separate them based on phase content. Hilbert transform
 Hilbert transform used for describing single sideband (SSB)
 signals and other bandpass signals
 Properties of the Hilbert transform
 3.6 CORRELATION AND SPECTRAL DENSITY
 Stochastic Process = signal with uncertainty described probabilistically
 Two ways to describe: 1) probability space and mapping to sample path ,2) Kolomgorov’ s extension theorem
 Nonperiodic signal
 Nonenergy signal
 Ex)Bit Stream
 Noise
 Voice Signal
Ensemble Average  Ensemble Average


 Correlation
 Autocorrelation Function
 Time Average vs. Ensemble Average

 ensemble average


 time average
 Power Spectral Density

 Interpretation of spectral density functions
 Figure 3.62
 RealValued WideSense Stationary Processes
 Def. A realvalued random process is called WSS if following two properties are met.
 Property 1.

 Property 2.
 따라서
 Power Spectral Density of RealValued WSS Random Process (WienerKinchine Theorem)
 Property 1.

 Property 2.
 When X(t) and h(t) are real,
 Noise Equivalent Bandwidth

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