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Chapter 3 Signal Transmission and Filtering Outline 1 Response of lti system
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Date conversion | 18.06.2017 | Size | 19,97 Kb. |
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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 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
- 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 50t
- Figure 3.2-3
- Test signal with amplitude distortion (a) low frequency attenuated; (b) high frequency attenuated
- Figure 3.2-4
- 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
- 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
- 0.2-2 dB/km loss
- Lower than most twisted-pair 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, 11:00-12:15
- 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.
- 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
- 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
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- Correlation
- Autocorrelation Function
- Time Average vs. Ensemble Average
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- ensemble average
-
-
- time average
- Power Spectral Density
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- 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,
- Noise Equivalent Bandwidth
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