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

• 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
• Amplitude distortion
• Phase distortion

• 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
• Compressing + expanding

• 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
• Total reflection, refraction index

• 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 lowpass filter (a) Transfer function (b) Impulse response
• Figure 3.4-2

• 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

• Example. Hilbert transform of a rectangular pulse
• (a) Convolution; (b) Result

• 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,



• White Noise
• 따라서
• Noise : White & Gaussian
•  practically non-white
•  온도의 함수

• “uncorrelated”

• Noise Equivalent Bandwidth