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
      • Multipath propagation
    • 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 time-invariant system
    • impulse response and convolution integral
    • step response
    • LCCDE and LTI system
    • transfer function and frequency response
    • steady-state phasor response
    • undistorted transmission vs. distorted transmission
    • block diagram analysis: parallel, serial/cascade, feedback connection
    • Example 3.3-2 Doppler Shift
      • beating
  • 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,
          • Omni-directional 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
      • Frequency-flat channel
        • Over the desired band
        • phase
        • Frequency-selective channel
    • Distortions
      • Nonlinear distortions
      • Linear distortions
  • Example: linear distortions
  • Test signal x(t) = cos 0t + 1/5 cos 50t
  • Figure 3.2-3
    • Amplitude distortion
  • Test signal with amplitude distortion (a) low frequency attenuated; (b) high frequency attenuated
  • Figure 3.2-4
    • Phase distortion
  • Test signal with constant phase shift  = -90
  • Figure 3.2-5
    • Equalization
      • Multipath distortion
      • Intersymbol interference (ISI) in digital signal transmission
      • Linear equalization
        • Linear zero-forcing equalization (LZF): channel inversion
        • Linear minimum-mean square error equalization (LMMSE)
      • Nonlinear equalization
        • Maximum-likelihood sequence estimator (MLSE)
        • Decision-feedback equalization (DFE)
          • Feedforward (FF) filter and feedback (FB) filter
          • ZF-DFE
          • MMSE-DFE
      • CT equalizer vs. DT equalizer vs. block equalizer
        • Transversal filter, tapped-delay-line equalizer
        • Frequency-domain equalizer (FDE)
          • One-tap equalizer for OFDM
      • Adaptive equalizer
    • Nonlinear distortion and companding
      • Transfer characteristic
        • Memoryless distortion
        • Distortion with memory
      • Polynomial approximation of memoryless distortion
        • Second-harmonic 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.
          • Fiber-optic cables
          • Waveguides
        • Loss, attenuation
        • Attenuation coefficient in dB per unit length
          • Table 3.3-1
          • Frequency bands are different.
          • Fiber optic cable: 0.2-2.5 dB/km loss
          • Twisted pair: 2-6 dB/km loss
          • Coaxial cable: 1-6 dB/km loss
          • Waveguide: 1.5-5 dB/km loss
        • Repeater amplifier
          • Amplification of distortion, interference, and noise
    • Optical fiber cable
  • Light propagation down a multimode step-index fiber
  • Figure 3.3-3b
  • Light propagation down a single-mode step-index fiber
  • Figure 3.3-3a
  • Light propagation down a multimode graded-index fiber
  • Figure 3.3-3c
      • Large bandwidth and low loss
        • Carrier frequencies in the range of 200 THz
          • Max bandwidth 20 THz
        • 0.2-2 dB/km loss
          • Lower than most twisted-pair and coaxial cable systems
          • Absorption
          • Scattering
      • Less interference
        • No RF 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, 11:00-12:15
      • Ch. 1-3
      • Open book (but you will not have time to read on the site.)
      • T/F, filling blanks, Essay, Math
    • Radio Transmission
      • Line-of-sight propagation
        • Free-space path loss (FSPL)
          • The loss between two isotropic radiators in free space.
        • Formula
          • far-field
          • It is a function of frequency. However, it does not say that free space is a frequency-selective channel.
    • Example 3.3-1
  • Satellite repeater system: uplink, downlink, frequency translation, geostationary, low orbit, OBP
  • Figure 3.3-5
  • 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 3.4-1
    • Realizability, noncausality
    • Bandlimiting and timelimiting
      • It is impossible to have perfect bandlimiting and timelimiting at the same time.
  • Ideal filters are noncausal.
  • Real-World Filters
    • Half-power or 3 dB bandwidth
    • Passband, transition band/region, and stopband
  • Typical amplitude ratio of a real bandpass filter
  • Figure 3.4-3
  • 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
  • Figure 3.5-2
    • 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
  • Non-periodic signal
  • Non-energy 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
    • Definition.
    • Theorem.
  • Interpretation of spectral density functions
  • Figure 3.6-2
  • Real-Valued Wide-Sense Stationary Processes
    • Def. A real-valued random process is called WSS if following two properties are met.
  • Property 1.
  • Property 2.
  • 따라서
  • Power Spectral Density of Real-Valued WSS Random Process (Wiener-Kinchine Theorem)
  • Property 1.
  • Property 2.
  •  When X(t) and h(t) are real,



  • “uncorrelated”
  • Noise Equivalent Bandwidth


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