General Intro Digital Signal Processing IIdspuser/DSP-CIS/2007-2008/lecture… · Digital Signal Processing II Marc Moonen Dept. E.E./ESAT, K.U.Leuven [email protected]

p. 1 DSP-II

Digital Signal Processing II

Marc Moonen

Dept. E.E./ESAT, K.U.Leuven

[email protected]

homes.esat.kuleuven.be/~moonen/

DSP-II Version 2007-2008 Lecture-1 Introduction p. 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)


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 IN OUT

A/D D/A

2 +2

=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



• 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

x

Receiver

decis

ion

.99,.01,.96,.95,.07,…

1,0,1,1,0,…



• DSP for digital communications (`physical layer’ ) :

– In practice…

– This calls for channel modeling + compensation (equalization)

Transmitter

1,0,1,1,0,…

+

Receiver

1,0,1,1,0,… ?? noise

`Multipath’

Channel

.59,.41,.76,.05,.37,… !!



• 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^-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’ (>100/sec)

= SPECTACULAR !! DSP-II Version 2007-2008 Lecture-1 Introduction p. 8


• 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,…), 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 !!


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



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 `ìnter-symbol interference’’

(ISI). ISI channel can (again) be modeled with an FIR filter. Number of taps

will be much larger here (>500!)



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. !



• 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’)



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...



ADSL specs • 512-point (I)FFT’s (or `similar’) for DMT-modulation

FFT-rate = 4.3215 kHz

(i.e. >4000 512-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. 32 taps @ 2.21 MHz

filter initialization via least-squares/eigenvalue procedure

• adaptive frequency-domain equalization filters (FEQ)

VDSL specs • e.g. 4096-point (I)FFT’s, etc….

= BOX FULL OF DSP/MATHEMATICS !!


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,..)

• …


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...

Signals&Systems course (JVDW)

DSP-I (PW)

DSP-II


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… J )

selection of topics (non-exhaustive)

DSP-II Version 2007-2008 Lecture-1 Introduction p. 18 0 0 .5 1 1 .5 2 2 .5 3

0

0 .2

0 .4

0 .6

0 .8

1

1 .2

P a s sb a nd R ip p le

S to p b a nd R ip p le

P a s sb a nd C uto f f -> < - S to p b a nd C uto ff

Overview (I)

• INTRO : Lecture-1

• Part I : Filter Design & Implementation Lecture-2 : IIR & FIR Filter Design

Lecture-3 : Filter Realization

Lecture-4 : Filter Implementation


Overview (II)

• Part II : Filter Banks & Subband Systems 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 3 H1(z) G1(z)




+ IN

OUT


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

.


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


Prerequisites

`Systeemtheorie en Regeltechniek’ (JVDW)

`Digitale Signaalverwerking I’ (PW)

signaaltransformaties, bemonstering, multi-rate, DFT, …

`Toegepaste Algebra en

Analytische Meetkunde’ (JVDW)


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

Àdaptive Filter Theory’ (Prentice Hall 1996)

• M. Bellanger

`Digital Processing of Signals’ (Kluwer 1986)

• etc...

Part-III

Part-II

Part-I


Literature / DSP-II Library

• Collection of books is available to support course material

• List/info/reservation via DSP-II webpage

• contact: Vincent.LeNir@esat (E)


Activities : Lectures

Lectures: 14 * 2 hrs

Course Material:

• Part I-II-III : Slides (use version 2007-2008 !!)

...download from DSP-II webpage

• Part III : Ìntroduction to Adaptive Signal Processing’,

Marc Moonen & Ian.K. Proudler

= support material, not mandatory !

…(if needed) download from DSP-II webpage


Activities : Homeworks/Ex. Sessions

• `Homeworks’

…to support course material

• 6 Matlab/Simulink Sessions

…to support homeworks

…come prepared !!

• contact: Geert.Rombouts@esat

Sam.Corveleyn@esat

Sylwester.Szczepaniak@esat (E)

Vincent.LeNir@esat (E/F)


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 geert.rombouts@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


Activities : Project

Topics/Papers

• List available under DSP-II web page

• Other topics : subject to approval !

(email 1/2-page description to geert.rombouts@esat before Oct. 5)

Tutoring

geert.rombouts@esat

+ 14 other research assistants/postdocs

All PPT presentations will be made available, for ref.


Activities : Examen

• Oral exam, with preparation time

• Open book

• Grading :

5 pts for question-1



5 pts for project (software/presentation)

___

= 20 pts


homes.esat.kuleuven.be/~rombouts/dspII

• Contact: geert.rombouts@esat

• Slides

• Homeworks

• Projects info/schedule

• Exams 2000-2001, ..

• DSP-II Library

• FAQs (send questions to geert.rombouts@esat or marc.moonen@esat )


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]



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 & shift-invariance!)

=

]3[

]2[

]1[

]0[

.

]2[000

]1[]2[00

]0[]1[]2[0

0]0[]1[]2[

00]0[]1[

000]0[

]5[

]4[

]3[

]2[

]1[

]0[

u

u

u

u

h

hh

hhh

hhh

hh

h

y

y

y

y

y

y

`Toeplitz’ matrix



Convolution:

=

]3[

]2[

]1[

]0[

.

]2[000

]1[]2[00

]0[]1[]2[0

0]0[]1[]2[

00]0[]1[

000]0[

]5[

]4[

]3[

]2[

]1[

]0[

u

u

u

u

h

hh

hhh

hhh

hh

h

y

y

y

y

y

y

u[0],u[1],u[2],u[3] y[0],y[1],...

h[0],h[1],h[2],0,0,...

][*][][.][][ kukhiuikhkyi

=−= ∑ = `convolution sum’



Z-Transform:

∑ −∆

=i

izihzH ].[)(

[ ] [ ]

=

−−−−−−−−−−

−−−

]3[

]2[

]1[

]0[

.

]2[000

]1[]2[00

]0[]1[]2[0

0]0[]1[]2[

00]0[]1[

000]0[

.1

]5[

]4[

]3[

]2[

]1[

]0[

.1

3211).()(

5432154321

u

u

u

u

h

hh

hhh

hhh

hh

h

zzzzz

y

y

y

y

y

y

zzzzz

zzzzHzY4444444444 34444444444 21444444 3444444 21

∑ −∆

=i

iziyzY ].[)(∑ −∆

=i

iziuzU ].[)(

)().()( zUzHzY =⇒ H(z) is `transfer function’



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)

)().()( zUzHzY =

∞∑ pk

kh ][



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… Transfer function is

1)(

−= zzH

u[k]

∆

y[k]=u[k-1]

x

+

a

u[k]

∆

y[k]

1

1

11

433221

.1)(

)(.)(

......)(

−

−

−−

−−−−

−=⇒

=−⇒

++++=

za

zzH

zzHzazH

zazazazzH



Will consider only rational transfer functions:

• In general, these represent ìnfinitely long impulse response’ (ÌIR’)

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

N

N

N

N

N

NN

N

NN

zaza

zbzbb

zazaz

bzbzb

zA

zBzH

−−

−−

−

−

+++

+++=

+++

+++==

...1

...

...

...

)(

)()(

1

1

1

10

1

1

1

10

][....]1[.][....]1[.][.][110

NkyakyaNkubkubkubky NN −−−−−−++−+=

...)().()().()().()( ⇒=⇒= zUzBzYzAzUzHzY



Special case is

• N poles at the origin z=0 (hence guaranteed stability)

• N zeros (zeros of B(z)) = àll zero’ filters

• corresponds to difference equation

=`moving average’ (MA) filters

• impulse response is

= `finite impulse response’ (`FIR’) filters

][....]1[.][.][)().()( 10 NkubkubkubkyzUzHzY N −++−+=⇒=

,...0,0,0,,,...,,,0,0,0110 NN bbbb

−

N

NNzbzbb

z

zBzH

−−+++== ...

)()(

1

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

∞−∞= pp kekukj,][

ω

ω

ωωωj

ezi

ijkj

i

ikj

i

zHkueiheeihikuihky=

−− ∑∑∑ ===−= )(].[].[].[][].[][)(

)(ωj

eH


ω

u[0]=1

u[2] u[1]

Im

Re


-4 -2 0 2 40

0.5

1

-4 -2 0 2 4-5

0

5


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’):

)(ωj

eH

)(ωj

eH∠

Nyquist frequency

,...1,1,1,1,1..., −−=kj

eπ

π

π2

π− ω

Documents

General Intro Digital Signal Processing IIdspuser/DSP-CIS/2007-2008/lecture… · Digital Signal Processing II Marc Moonen Dept. E.E./ESAT, K.U.Leuven [email protected]