1. Digital Signal Processing II
Marc Moonen
Dept. E.E./ESAT, K.U.Leuven
homes.esat.kuleuven.be/~moonen/

2. Digital Signal Processing II
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 Signals&Systems (10-slides)
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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 ? …? ) IN
OUT
A/D
D/A 2 +2 =4 IN
OUT
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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
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5. DSP in applications : GSM
DSP for digital communications (`physical layer’ ) :
a common misunderstanding is that digital communications
is `simple’….
While in practice…
Transmitter
1,0,1,1,0,…
Channel x + a
noise
1/a
Receiver
decision
.99,.01,.96,.95,.07,…
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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
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7. DSP in applications : GSM
GSM specs/features :
Multi-path channel is modeled with short (3…5 taps) FIR filter
H(z)= a+b.z^-1+c.z^-2+d.z-3+e.z^ (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. Algebra, 1ste kand !!!)
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’ (>100/sec)
= SPECTACULAR !!
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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 << 8*125 ! )
- Speech coding :
Original `PCM’-signal has 64kbits/sec = 8 ksamples/sec * 8bits/sample
Reduce this to <11kbits/sec, while preserving quality
Coding based on speech generation model (vocal tract,…),
least-squares paramater estimation (again!), etc.
- Etc..
= BOX FULL OF DSP/MATHEMATICS !!
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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 30kHz…1MHz band
(3,5…5km)
VDSL modems : up to 52Mbits/sec in …12MHz band
(0.3…1.5km)
How has this been made possible?
X 1000
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10. DSP in applications : ADSL
Communication Impairments :
Channel attenuation
Received signal may be attenuated by more than 60dB
ps: more attenuation 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 (>500!)
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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. !
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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’)
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13. DSP in applications : ADSL
ADSL-DMT Transmission block scheme :
DFT/IDFT (FFT/IFFT) based modulation/demodulation scheme
pointer : PS: do not try to understand details here...
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14. DSP in applications : ADSL
ADSL specs
512-point (I)FFT’s (or `similar’) for DMT-modulation
FFT-rate = kHz
(i.e. > point FFTs per second !!!!)
basic sampling rate is 2.21 MHz (=512*4.3215k)
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 MHz
filter initialization via least-squares/eigenvalue procedure
adaptive frequency-domain equalization filters (FEQ)
VDSL specs
e.g point (I)FFT’s, etc….
= BOX FULL OF DSP/MATHEMATICS !!
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15. DSP in applications : Other…
Speech (HK-17)
Speech coding (GSM, DECT, ..), Speech synthesis (text-to-speech),
Speech recognition
Audio Signal Processing (HK-17)
Audio Coding (MP3, AAC, ..), Audio synthesis
Editing, Automatic transcription, Dolby/Surround, 3D-audio,.
Image/Video (HD-05)
Digital Communications
Wireline (xDSL,Powerline), Wireless (GSM, 3G, Wi-Fi, WiMax
CDMA, MIMO-transmission,..) …
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16. DSP in applications Enabling Technology is Signal Processing
1G-SP: analog filters
2G-SP: digital filters, FFT’s, etc.
3G-SP: full of mathematics, linear algebra,
statistics, etc...
VLSI
etc...
H197 (JVDW)
DSP-I (PW)
DSP-II
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17. 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 `bird’s-eye view’
skip many mathematical details (if possible…  )
selection of topics (non-exhaustive)
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18. Overview (I) INTRO : Part I : Filter Design & Implementation Lecture-1
Lecture-2 : IIR & FIR Filter Design
Lecture-3 : Filter Realization
Lecture-4 : Filter Implementation
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19. Overview (II) Part II : Filter Banks & Subband Systems . 3 OUT IN +
Lecture-5 : Filter Banks Intro/Applications (coding/CDMA/…)
Lecture-6/7 : Filter Banks Theory
Lecture-8 : Special Topics
(Frequency-domain processing, Wavelets,…) . 3
subband processing
H1(z)
G1(z)
H2(z)
G2(z)
H3(z)
G3(z)
H4(z)
G4(z) + IN
OUT
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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 .
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21. Overview (IV) OUTRO : Lecture 14: Case study ADSL/VDSL modems DAC S/P
FFT
FEQ
IFFT
P/S
Tx clock
Discrete
equivalent
channel
Rx clock
p(t)
Tx filter
Channel
Rx filter
ch(t)
r(t)
ADC
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22. Prerequisites H197: `Systeemtheorie en Regeltechniek’ (JVDW)
HJ09: `Digitale Signaalverwerking I’ (PW)
signaaltransformaties, bemonstering, multi-rate, DFT, …
H001: `Toegepaste Algebra en
Analytische Meetkunde’ (JVDW)
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23. Literature / Arenberg Library
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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24. Literature / DSP-II Library
Collection of books is available to support course material
List/info/reservation via DSP-II webpage
contact: (E)
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25. Activities : Lectures Lectures: 14 * 2 hrs Course Material:
Part I-II-III : Slides (use version !!)
...download from DSP-II webpage
Part III : `Introduction to Adaptive Signal Processing’,
Marc Moonen & Ian.K. Proudler
= bijkomende info, geen examenstof !
…(if needed) download from DSP-II webpage
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26. Activities : Homeworks/Ex. Sessions
…to support course material
6 Matlab/Simulink Sessions
…to support homeworks
…come prepared !!
contact:
(E)
(E/F)
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27. 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.4 to
Study & internet surfing
Build demonstration model & experiment in Matlab/Simulink
Deliverable :
Intermediate presentation (.ppt or similar) : Oct. 24/27
Final presentation, incl. Matlab/Simulink demonstration : Dec.
(20 mins per group)
Software
Groups of 2
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28. Activities : Project Topics/Papers
List available under DSP-II web page
Other topics : subject to approval !
( 1/2-page description to before Oct. 4)
Tutoring
+ 14 other research assistants/postdocs
All .PPT presentations will be made available
(www), maar behoren niet tot examen-leerstof
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29. Activities : Examen Mondeling, schriftelijk voorbereiding Open boek
Inzicht-/denkvragen, geen rekenoefeningen
5 for question-1
5 for question-2
5 for question-3
5 for project (software/presentation)
___
= 20
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30. homes.esat.kuleuven.be/~rombouts/dspII
Contact:
Slides
Homeworks
Projects info/schedule
Examenvragen , ..
DSP-II Library
FAQs (send questions to or )
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31. Review of discrete-time systems 1/10
Discrete-time (DT) system is `sampled data’ system:
Input signal u[k] is a sequence of samples (=numbers)
..,u[-2],u[-1],u[0],u[1],u[2],…
System then produces a sequence of output samples y[k]
..,y[-2],y[-1],y[0],y[1],y[2],…
Will consider linear time-invariant (LTI) DT systems:
Linear :
input u1[k] -> output y1[k]
input u2[k] -> output y2[k]
hence a.u1[k]+b.u2[k]-> a.y1[k]+b.y2[k]
Time-invariant (shift-invariant)
input u[k] -> output y[k], hence input u[k-T] -> output y[k-T]
u[k]
y[k]
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32. Review of discrete-time systems 2/10
Causal systems:
iff for all input signals with u[k]=0,k<0 -> output y[k]=0,k<0
Impulse response:
input …,0,0,1,0,0,0,...-> output …,0,0,h[0],h[1],h[2],h[3],...
General input u[0],u[1],u[2],u[3]: (cfr.linearity!)
`Toeplitz’ matrix
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33. Review of discrete-time systems 3/10
Convolution:
u[0],u[1],u[2],u[3]
y[0],y[1],...
h[0],h[1],h[2],0,0,...
= `convolution sum’
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34. Review of discrete-time systems 4/10
Z-Transform:
H(z) is `transfer function’
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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 u[k] -> bounded output y[k]
--iff
--iff poles of H(z) inside the unit circle
(for causal,rational systems)
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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,a^2,a^3…
u[k]
y[k]=u[k-1] x + a
u[k]
y[k]
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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
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38. Review of discrete-time systems 8/10
Special case is
N poles at the origin z=0 (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
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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
u[0]=1
u[2]
u[1] Im Re
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40. Review of discrete-time systems 10/10
H(z) & frequency response:
periodic : period =
for a real impulse response h[k]
Magnitude response is even function
Phase response is odd function
example (`low pass filter’):
Nyquist frequency
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