Digital Signal Processing II Advanced Topics

1
Digital Signal Processing IIAdvanced Topics

• Marc Moonen
• Dept. E.E./ESAT, K.U.Leuven
• marc.moonen_at_esat.kuleuven.be
• www.esat.kuleuven.be/scd/

2
Lecture-1 Introduction

• General Intro
• Aims/Scope
• Why study DSP ?
• DSP in applications GSM, ADSL
• Overview
• Activities
• Lectures - Course Notes/Literature
• Homeworks/Exercise sessions
• Project
• Exam
• Review of Discrete-time SignalsSystems
  (10-slides)

3
Why study DSP ?

• Analog Systems vs. Digital Systems
• - translate analog (e.g. filter) design into
  digital
• - going digital allows to expand
  functionality/flexibility/
• (e.g. how would you do analog speech
  recognition ? analog audio compression ? ? )

4
DSP in applications GSM

• Cellular mobile telephony (e.g. GSM)
• Basic network architecture
• -country covered by a grid of cells
• -each cell has a base station
• -base station connected to land telephone
  network and
• communicates with mobiles via a radio
  interface
• -digital communication format

5
DSP in applications GSM

• DSP for digital communications (physical layer
  )
• a common misunderstanding is that digital
  communications
• is simple.
• While in practice

6
DSP in applications GSM

• DSP for digital communications (physical layer
  )
• In practice
• This calls for channel modeling compensation
  (equalization)

!!
.59,.41,.76,.05,.37,
Transmitter 1,0,1,1,0,
Multipath Channel
Receiver
??

1,0,1,1,0,
noise
7
DSP in applications GSM

• GSM specs/features
• Multi-path channel is modeled with short (35
  taps) FIR filter
• H(z) ab.z-1c.z-2d.z-3e.z-4
  (interpretation?)
• Channel is highly time-varying (e.g. terminal
  speed 120 km/hr !)
• Channel coefficients (cfr. a,b,c,d,e) are
  identified in receiver based on
• transmission of pre-defined training
  sequences, in between data bits
• (problem to be solved is given channel
  input and channel output,
• compute channel coefficients)
• This leads to a least-squares parameter
  estimation procedure
• (cfr. Linear Algebra course!)
• Channel model is then used to design suitable
  equalizer (channel inversion), or (better) for
  reconstructing transmitted data bits based on
  Maximum-likelihood sequence estimation (Viterbi
  decoding)
• All this is done at burst-rate (gt100/sec)

SPECTACULAR !!
8
DSP in applications GSM

• GSM specs/features (continued)
• - Multiplexing
• Capacity increase by time frequency
  multiplexing
• FDMA e.g. 125 frequency channels for
  GSM/900MHz
• TDMA 8 time slots(users) per channel,
  burst mode communication
• (PS in practice, capacity per cell ltlt
  8125 ! )
• - Speech coding
• Original PCM-signal has 64kbits/sec
  8 ksamples/sec 8bits/sample
• Reduce this to lt11kbits/sec, while
  preserving quality
• Coding based on speech generation model
  (vocal tract,), where
• model coefficient are identified for
  each new speech segment (e.g.
• 20 msec) (i.e. least-squares parameter
  estimation, again).
• Then transmit model coefficients instead
  of signal samples...
• - Etc..

BOX FULL OF DSP/MATHEMATICS !!
9
DSP in applications ADSL

• Telephone Line Modems
• voice-band modems up to 56kbits/sec in 0..4kHz
  band
• ADSL modems up to 8Mbits/sec in 30kHz1MHz band
• (3,55km)
• VDSL modems up to 52Mbits/sec in 12MHz
  band
• (0.31.5km)
• How has this been made possible?

X 1000
10
DSP in applications ADSL

• Communication Impairments
• Channel attenuation
• Received signal may be attenuated by more than
  60dB
• (attenuation increases with line length
  larger at high (MHz) frequencies)
• PS this is why for a long time, only the
  voiceband (up to 4kHz) was used
• Frequency-dependent attenuation introduces
  inter-symbol interference (ISI). ISI channel
  can (again) be modeled with an FIR filter. Number
  of taps will be much larger here (gt500!)

11
DSP in applications ADSL

• Communication Impairments
• Coupling between wires in same or adjacent
  binders introduces crosstalk
• Near-end Xtalk (NEXT) (upstream in
  downstream, downstream in upstream)
• Far-end Xtalk (FEXT) (upstream in
  upstream, downstream in downstream)
• Meaning that a useful signal may be drowned in
  (much larger) signals from other users..
• leading to signal separation and spectrum
  management problems
• Other
• Radio Frequency Interference
• (AM broadcast, amateur radio)
• Echo due to impedance mismatch
• Etc..

Conclusion Need advanced modulation, DSP,etc. !
12
DSP in applications ADSL

• ADSL spectrum divide available transmission
  band in 256 narrow bands (tones), transmit
  different sub-streams over different sub-channels
  (tones) (DMT, Discrete
  Multi-tone Modulation)

13
DSP in applications ADSL

• ADSL-DMT Transmission block scheme
• DFT/IDFT (FFT/IFFT) based modulation/demodulation
  scheme
• pointer www.adslforum.com PS do
  not try to understand details here...

14
DSP in applications ADSL

• ADSL specs
• 512-point (I)FFTs (or similar) for
  DMT-modulation
• FFT-rate 4.3215 kHz
• (i.e. gt4000 512-point FFTs per second
  !!!!)
• basic sampling rate is 2.21 MHz
  (5124.3215k)
• 8.84 MHz A/D or D/A (multi-rate
  structure)
• fixed HP/LP/BP front-end filtering for frequency
  duplex
• adjustable time-domain equalization filter (TEQ)
• e.g. 32 taps _at_ 2.21 MHz
• filter initialization via
  least-squares/eigenvalue procedure
• adaptive frequency-domain equalization filters
  (FEQ)
• VDSL specs
• e.g. 4096-point (I)FFTs, etc.

BOX FULL OF DSP/MATHEMATICS !!
15
DSP in applications Other

• Speech
• Speech coding (GSM, DECT, ..), Speech
  synthesis (text-to-speech),
• Speech recognition
• Audio Signal Processing
• Audio Coding (MP3, AAC, ..), Audio
  synthesis
• Editing, Automatic transcription,
  Dolby/Surround, 3D-audio,.
• Image/Video
• Digital Communications
• Wireline (xDSL,Powerline), Wireless (GSM,
  3G, Wi-Fi, WiMax
• CDMA, MIMO-transmission,..)

16
DSP in applications

• Enabling Technology is
• Signal Processing
• 1G-SP analog filters
• 2G-SP digital filters, FFTs, etc.
• 3G-SP full of mathematics, linear algebra,
  
• statistics, etc...
• VLSI
• etc...

SignalsSystems course (JVDW)
DSP-I (PW)
DSP-II
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DSP-II Aims/Scope

• Basic signal processing theory/principles
• filter design, filter banks, optimal
  filters adaptive filters
• Recent/advanced topics
• robust filter realization, perfect
  reconstruction filter banks,
• fast adaptive algorithms, ...
• Often birds-eye view
• skip many mathematical details (if
  possible ? )
• selection of topics (non-exhaustive)

18
Overview (I)

• INTRO
• Lecture-1
• Part I Filter Design Implementation
• Lecture-2 IIR FIR Filter Design
• Lecture-3 Filter Realization
• Lecture-4 Filter Implementation

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Overview (II)

• Part II Filter Banks Subband Systems
• Lecture-5 Filter Banks Intro/Applications
  (audio coding/CDMA/)
• Lecture-6/7 Filter Banks Theory
• Lecture-8 Special Topics
• (Frequency-domain
  processing, Wavelets,)
• .

20
Overview (III)

• Part III Optimal Adaptive Filtering
• Lecture-9 Optimal/Wiener Filters
• Lecture-10 Adaptive Filters/Recursive Least
  Squares
• Lecture-11 Adaptive Filters/LMS
• Lecture-12 Fast Adaptive Filters
• Lecture-13 Kalman Filters
• .

21
Overview (IV)

• OUTRO Lecture 14 - Case study ADSL/VDSL

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Prerequisites

• Systeemtheorie en Regeltechniek (JVDW)
• Digitale Signaalverwerking I (PW)
• signaaltransformaties, bemonstering,
  multi-rate, DFT,
• Toegepaste Algebra en
• Analytische Meetkunde (JVDW)

23
Literature / Campus Library Arenberg

• A. Oppenheim R. Schafer
• Digital Signal Processing (Prentice Hall
  1977)
• L. Jackson
• Digital Filters and Signal Processing
  (Kluwer 1986)
• P.P. Vaidyanathan
• Multirate Systems and Filter Banks
  (Prentice Hall 1993)
• Simon Haykin
• Adaptive Filter Theory (Prentice Hall
  1996)
• M. Bellanger
• Digital Processing of Signals (Kluwer
  1986)
• etc...

Part-I
Part-II
Part-III
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Literature / DSP-II Library

• Collection of books is available to support
  course material
• List/info/reservation via DSP-II webpage
• contact Vincent.LeNir_at_esat (E)

25
Activities Lectures

• Lectures 14 2 hrs
• Course Material
• Part I-II-III Slides (use version 2008-2009
  !!)
• ...download from DSP-II webpage
• Part III Introduction to Adaptive Signal
  Processing,
• Marc Moonen Ian.K. Proudler
• support material, not mandatory !
  
• (if needed) download from DSP-II webpage

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Activities Homeworks/Ex. Sessions

• Homeworks
• to support course material
• 6 Matlab/Simulink Sessions
• to support homeworks
• come prepared !
• contact Sylwester.Szczepaniak_at_esat
  (EnglishPolish)
• Vincent.LeNir_at_esat
  (EnglishFrench)
• Prabin.Kumarpandey_at_esat
  (EnglishNepali)
• Pepe.Gilcacho_at_esat
  (EnglishSpanish)

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Activities Project

• Discover DSP technology in present-day systems
• examples 3D-audio, music synthesis,
  automatic
• transcription, speech
  codec, MP3, GSM, ADSL,
• Select topic/paper from list on DSP II webpage
  (submit 1st/2nd choice by Oct.5 to
  sylwester.szczepaniak_at_esat)
• Study www surfing
• Build demonstration model experiment in
  Matlab/Simulink
• Deliverable
• Intermediate presentation (.ppt or similar)
  Oct..
• Final presentation, incl. Matlab/Simulink
  demonstration Dec..
• (20 mins per group)
• Software
• Groups of 2

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Activities Project

• Topics/Papers
• List available under DSP-II web page
• Other topics subject to approval !
• (email 1/2-page description to
  sylwester.szczepaniak_at_esat
• before Oct. 5)
• Tutoring
• 14 research assistants/postdocs
• All PPT presentations will be made available,
  for ref.

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Activities Exam

• Oral exam, with preparation time
• Open book
• Grading
• 5 pts for question-1
• 5 pts for question-2
• 5 pts for question-3
• 5 pts for project (software/presentation)
• ___
• 20 pts

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homes.esat.kuleuven.be/sszczepa/dspII

• Contact sylwester.szczepaniak_at_esat
• Slides
• Homeworks
• Projects info/schedule
• Exams 2000-2001, ..
• DSP-II Library
• FAQs (send questions to
• sylwester.szczepaniak_at_esat
• or marc.moonen_at_esat )

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Review of discrete-time systems 1/10

• Discrete-time (DT) system is sampled data
  system
• Input signal uk is a sequence of samples
  (numbers)
• 
  ..,u-2,u-1,u0,u1,u2,
• System then produces a sequence of output
  samples yk
• 
  ..,y-2,y-1,y0,y1,y2,
• Will consider linear time-invariant (LTI) DT
  systems
• Linear
• input u1k -gt output y1k
• input u2k -gt output y2k
• hence a.u1kb.u2k-gt a.y1kb.y2k
• Time-invariant (shift-invariant)
• input uk -gt output yk, hence input
  uk-T -gt output yk-T

32
Review of discrete-time systems 2/10

• Causal systems
• iff for all input signals with uk0,klt0 -gt
  output yk0,klt0
• Impulse response
• input ,0,0,1,0,0,0,...-gt output
  ,0,0,h0,h1,h2,h3,...
• General input u0,u1,u2,u3 (cfr.
  linearity shift-invariance!)

33
Review of discrete-time systems 3/10

• Convolution

convolution sum
34
Review of discrete-time systems 4/10

• Z-Transform

H(z) is transfer function
35
Review of discrete-time systems 5/10

• Z-Transform
• input-output relation
• may be viewed as shorthand notation
• (for convolution operation/Toeplitz-vector
  product)
• stability
• bounded input uk -gt bounded output yk
• --iff
• --iff poles of H(z) inside the unit circle
• (for causal,rational systems)

36
Review of discrete-time systems 6/10

• Example-1 Delay operator
• Impulse response is ,0,0,0, 1,0,0,0,
• Transfer function is
• Example-2 Delay feedback
• Impulse response is ,0,0,0, 1,a,a2,a3
• Transfer function is

37
Review of discrete-time systems 7/10

• Will consider only rational transfer functions
• In general, these represent infinitely long
  impulse response (IIR) systems
• N poles (zeros of A(z)) , N zeros (zeros of B(z))
• corresponds to difference equation
• Hence rational H(z) can be realized with finite
  number of delay elements, multipliers and adders

38
Review of discrete-time systems 8/10

• Special case is
• N poles at the origin z0 (hence guaranteed
  stability)
• N zeros (zeros of B(z)) all zero
  filters
• corresponds to difference equation
• 
  moving average (MA) filters
• impulse response is
• 
  finite impulse response (FIR) filters

39
Review of discrete-time systems 9/10

• H(z) frequency response
• given a system H(z)
• given an input signal complex sinusoid
• output signal
• frequency
  response
• H(z) evaluated on
  the unit circle

40
Review of discrete-time systems 10/10

• H(z) frequency response
• periodic period
• for a real impulse response hk
• Magnitude response is
  even function
• Phase response
  is odd function
• example (low pass filter)

Nyquist frequency