p. 1 dsp-ii digital signal processing ii marc moonen dept. e.e./esat, k.u.leuven...

p. 1DSP-II

Digital Signal Processing II

Marc Moonen

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

[email protected]

homes.esat.kuleuven.be/~moonen/

DSP-IIVersion 2006-2007 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 OUTA/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 noise1/a

x

Receiver

dec

isio

n

.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. 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 !!



• 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 !!


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

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!)



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 (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,..)

• …


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


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)

DSP-IIVersion 2006-2007 Lecture-1 Introduction p. 180 0.5 1 1.5 2 2.5 3

0

0.2

0.4

0.6

0.8

1

1.2

Passband Ripple

Stopband Ripple

Passband Cutoff -> <- Stopband Cutoff

Overview (I)

• INTRO : Lecture-1

• Part I : Filter Design & ImplementationLecture-2 : IIR & FIR Filter Design

Lecture-3 : Filter Realization

Lecture-4 : Filter Implementation


Overview (II)

• Part II : Filter Banks & Subband SystemsLecture-5 : Filter Banks Intro/Applications (coding/CDMA/…)

Lecture-6/7 : Filter Banks Theory

Lecture-8 : Special Topics

(Frequency-domain processing, Wavelets,…)

.

3 subband processing 3H1(z) G1(z)




+IN OUT


Overview (III)

• Part III : Optimal & Adaptive FilteringLecture-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

Discreteequivalent

channel

Rx clock

p(t)

Tx filter Channel Rx filter

ch(t) r(t) ADC


Prerequisites

H197: `Systeemtheorie en Regeltechniek’ (JVDW)

HJ09: `Digitale Signaalverwerking I’ (PW) signaaltransformaties, bemonstering, multi-rate, DFT, …

H001: `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

`Adaptive 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 2006-2007 !!)

...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


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.4 to geert.rombouts@esat) • 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


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. 4)

Tutoring

geert.rombouts@esat

+ 14 other research assistants/postdocs

All .PPT presentations will be made available (www), maar behoren niet tot examen-leerstof


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


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

• Contact: geert.rombouts@esat

• Slides• Homeworks • Projects info/schedule

• Examenvragen 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!)

]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

zzzzHzY

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

k

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 `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

NN

NN

NNN

NNN

zaza

zbzbb

zazaz

bzbzb

zA

zBzH

...1

...

...

...

)(

)()(

11

110

11

110

][....]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)) = `all 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,,,...,,,0,0,0 110 NN bbbb

NNNzbzbb

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

keku kj ,][

jezi

ijkj

i

ikj

i

zHkueiheeihikuihky

)(].[].[].[][].[][ )(

)( jeH


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’):

)( jeH

)( jeH

Nyquist frequency

,...1,1,1,1,1..., kje

2

p. 1 dsp-ii digital signal processing ii marc moonen dept. e.e./esat, k.u.leuven...

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