Digital Signal Processing II Marc Moonen Dept E

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Digital Signal Processing II Marc Moonen Dept. E. E. /ESAT, K. U. Leuven marc.

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

Digital Signal Processing II • General Intro – Aims/Scope: Why study DSP ? DSP

Digital Signal Processing II • General Intro – Aims/Scope: Why study DSP ? DSP in applications : GSM, ADSL… – – – Overview Lectures/Course Notes/Literature Homeworks/Exercise session Project Exam • Review of Discrete-time Signals&Systems (10 -slides) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 2

Why study DSP ? • Analog Systems IN vs. OUT Digital Systems IN A/D

Why study DSP ? • Analog Systems IN vs. OUT Digital Systems IN A/D 2 +2 =4 OUT D/A - translate analog (e. g. filter) design into digital - going `digital’ allows to expand functionality/flexibility/… (e. g. how could analog speech recognition be done? analog…. ? ) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 3

DSP in applications : GSM Cellular mobile telephony (e. g. GSM) • Basic network

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 DSP-II Version 2005 -2006 Chapter-1 Introduction p. 4

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

DSP in applications : GSM • DSP for digital communications (`physical layer’ ) : – a common misunderstanding is that digital communications is `simple’…. . 99, . 01, . 96, . 95, . 07, … Channel x a Receiver + noise x 1/a decision Transmitter 1, 0, 1, 1, 0, … – While in practice… DSP-II Version 2005 -2006 Chapter-1 Introduction p. 5

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

DSP in applications : GSM • DSP for digital communications (`physical layer’ ) : – In practice… . 59, . 41, . 76, . 05, . 37, … Transmitter `Multipath’ 1, 0, 1, 1, 0, … Channel + !! Receiver ? ? 1, 0, 1, 1, 0, … noise – This calls for channel modeling + compensation (equalization) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 6

DSP in applications : GSM • GSM specs/features : – Multi-path channel is modeled

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^-4 (interpretation? ) – Channel is highly time-varying (e. g. terminal speed 120 km/hr !) – Channel coefficients are identified in receiver based on transmission of predefined 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, 1 ste 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) DSP-II Version 2005 -2006 = SPECTACULAR !! Chapter-1 Introduction p. 7

DSP in applications : GSM • GSM specs/features (continued): - Multiplexing: Capacity increase by

DSP in applications : GSM • GSM specs/features (continued): - Multiplexing: Capacity increase by time & frequency `multiplexing’ FDMA : e. g. 125 frequency channels for GSM/900 MHz TDMA : 8 time slots(=users) per channel, `burst mode’ communication (PS: in practice, capacity per cell << 8*125 ! ) - Speech coding : Original `PCM’-signal has 64 kbits/sec = 8 ksamples/sec * 8 bits/sample Reduce this to <11 kbits/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-II Version 2005 -2006 Chapter-1 Introduction p. 8

DSP in applications : ADSL Telephone Line Modems – voice-band modems : up to

DSP in applications : ADSL Telephone Line Modems – voice-band modems : up to 56 kbits/sec in 0. . 4 k. Hz band – ADSL modems : up to 8 Mbits/sec in 30 k. Hz… 1 MHz band (3, 5… 5 km) – VDSL modems : up to 52 Mbits/sec in (0. 3… 1. 5 km) … 10 MHz band X 1000 How has this been made possible? DSP-II Version 2005 -2006 Chapter-1 Introduction p. 9

DSP in applications : ADSL Communication Impairments : • Channel attenuation – Received signal

DSP in applications : ADSL Communication Impairments : • Channel attenuation – Received signal may be attenuated by more than 60 d. B ps: more attenuation at high (MHz) frequencies ps: this is why for a long time, only the voiceband (up to 4 k. Hz) 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!) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 10

DSP in applications : ADSL Communication Impairments : • Coupling between wires in same

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. ! DSP-II Version 2005 -2006 Chapter-1 Introduction p. 11

DSP in applications : ADSL • ADSL spectrum : divide available transmission band in

DSP in applications : ADSL • ADSL spectrum : divide available transmission band in 256 narrow bands (`tones’), transmit different sub-streams over different subchannels (tones) (=DMT, `Discrete Multi-tone Modulation’) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 12

DSP in applications : ADSL-DMT Transmission block scheme : DFT/IDFT (FFT/IFFT) based modulation/demodulation scheme

DSP in applications : ADSL-DMT Transmission block scheme : DFT/IDFT (FFT/IFFT) based modulation/demodulation scheme pointer : www. adslforum. com DSP-II Version 2005 -2006 PS: do not try to understand details here. . . Chapter-1 Introduction p. 13

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

DSP in applications : ADSL specs • 512 -point (I)FFT’s (or `similar’) for DMT-modulation FFT-rate = 4. 3215 k. Hz (i. e. >4000 512 -point FFTs per second !!!!) • basic sampling rate is 2. 21 MHz (=512*4. 3215 k) 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-II Version 2005 -2006 Chapter-1 Introduction p. 14

DSP in applications : Other… • Speech (HK-17) Speech coding (GSM, DECT, . .

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 (MP 3, AAC, . . ), Audio synthesis Editing, Automatic transcription, Dolby/Surround, 3 D-audio, . • Image/Video (HD-05) • Digital Communications Wireline (x. DSL, Powerline), Wireless (GSM, 3 G, WLAN, CDMA, MIMO-transmission, . . ) • … DSP-II Version 2005 -2006 Chapter-1 Introduction p. 15

DSP in applications Enabling Technology is H 197 (JVDW) DSP-I (PW) • Signal Processing

DSP in applications Enabling Technology is H 197 (JVDW) DSP-I (PW) • Signal Processing DSP-II 1 G-SP: analog filters 2 G-SP: digital filters, FFT’s, etc. 3 G-SP: full of mathematics, linear algebra, statistics, etc. . . • VLSI • etc. . . DSP-II Version 2005 -2006 Chapter-1 Introduction p. 16

Aims/Scope • Basic signal processing theory/principles filter design, filter banks, optimal filters, adaptive filters

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 mathematical details (if possible) selection of topics (non-exhaustive) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 17

Overview (I) • Part I : Filter Design & Implementation Lecture-2 : IIR &

Overview (I) • Part I : Filter Design & Implementation Lecture-2 : IIR & FIR Filter Design Lecture-3 : Filter Realization Lecture-4 : Filter Implementation DSP-II Version 2005 -2006 Chapter-1 Introduction p. 18

Overview (II) • Part II: Filter Banks & Subband Systems Lecture-5 : Filter Banks

Overview (II) • Part II: Filter Banks & Subband Systems Lecture-5 : Filter Banks Intro/Applications Lecture-6 : Filter Banks Theory Lecture-7/8 : Special Topics (Frequency-Domain processing Wavelets, …) IN . DSP-II H 1(z) 3 subband processing 3 G 1(z) H 2(z) 3 subband processing 3 G 2(z) H 3(z) 3 subband processing 3 G 3(z) H 4(z) 3 subband processing 3 G 4(z) Version 2005 -2006 Chapter-1 Introduction OUT + p. 19

Overview (III) • Part III : Optimal & Adaptive Filtering Lecture-9 : Optimal/Wiener Filters

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 . DSP-II Version 2005 -2006 Chapter-1 Introduction p. 20

Prerequisites H 197: `Systeemtheorie en Regeltechniek’ (JVDW) HJ 09: `Digitale Signaalverwerking I’ (PW) signaaltransformaties,

Prerequisites H 197: `Systeemtheorie en Regeltechniek’ (JVDW) HJ 09: `Digitale Signaalverwerking I’ (PW) signaaltransformaties, bemonstering, multi-rate, DFT, … H 001: `Toegepaste Algebra en Analytische Meetkunde’ (JVDW) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 21

Lectures/Course Notes Lectures: 14 * 1, 5 hrs (8 h 50 -10 h 20)

Lectures/Course Notes Lectures: 14 * 1, 5 hrs (8 h 50 -10 h 20) Course Notes: • Part I-II-III : Slides (use version 2005 -2006!). . . 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 DSP-II Version 2005 -2006 Chapter-1 Introduction p. 22

Literature / Arenberg Library Part-I • A. Oppenheim & R. Schafer `Digital Signal Processing’

Literature / Arenberg Library Part-I • 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) Part-II • Simon Haykin `Adaptive Filter Theory’ (Prentice Hall 1996) • M. Bellanger Part-III `Digital Processing of Signals’ (Kluwer 1986) • etc. . . DSP-II Version 2005 -2006 Chapter-1 Introduction p. 23

Literature / DSP-II Library • Collection of books is available to support course notes/slides

Literature / DSP-II Library • Collection of books is available to support course notes/slides • List/info/reservation via DSP-II webpage • contact: imad. barhumi@esat (E) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 24

Homeworks/Exercise Sessions • `Homeworks’ …to support slides/course notes • 6 Matlab/Simulink Sessions …to support

Homeworks/Exercise Sessions • `Homeworks’ …to support slides/course notes • 6 Matlab/Simulink Sessions …to support homeworks …come prepared !! • contact: geert. rombouts@esat imad. barhumi@esat (E) sam. corveleyn@esat vincent. lenir@esat (E/F) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 25

Project • Discover DSP technology in present-day systems examples: 3 D-audio, music synthesis, automatic

Project • Discover DSP technology in present-day systems examples: 3 D-audio, music synthesis, automatic transcription, speech codec, MP 3, GSM, ADSL, … commercial products and/or academic research and/or. . . • Build/experiment with Matlab/Simulink (or similar) demonstration model • Deliverable : presentation (. ppt or similar), incl. Matlab/Simulink demonstration (20 mins per group) • Groups of 2 persons • 2 presentation sessions : ? ? and ? ? December. !! aanwezigheid verplicht !! DSP-II Version 2005 -2006 Chapter-1 Introduction p. 26

Project Topics • List 2002/2003/2004 available under DSP-II web page • Any other topic….

Project Topics • List 2002/2003/2004 available under DSP-II web page • Any other topic…. ! (subject to our approval) • Email 1/2 -page description your topic to geert. rombouts@esat before October 10 (list group members!) Contact geert. rombouts@esat + 14 other research assistants/postdocs All. PPT presentations will be made available (www), maar behoren niet tot examen-leerstof DSP-II Version 2005 -2006 Chapter-1 Introduction p. 27

Examen • Mondeling, schriftelijk voorbereiding • Open boek • Inzicht-/denkvragen, geen rekenoefeningen 5 for

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 presentation ___ = 20 DSP-II Version 2005 -2006 Chapter-1 Introduction p. 28

Tijdsbesteding • Budget = 157. 5 u • Besteding les: 14 * 1. 5

Tijdsbesteding • Budget = 157. 5 u • Besteding les: 14 * 1. 5 u = 21 u 8 u 50 -10 u 20 !! Matlab/Simulink exercises : 6* 2. 5= 15 u Matlab/Simulink exercises prep: 6* 2= 12 u project : 40 u project presentations : 2* 2. 5 u = 5 u belasting: 21*4 + 15 + 12+ 40 + 5 = 156. 0 u DSP-II Version 2005 -2006 Chapter-1 Introduction p. 29

homes. esat. kuleuven. be/~rombouts/dsp. II • Contact: geert. rombouts@esat • Slides/lecture notes • Homeworks

homes. esat. kuleuven. be/~rombouts/dsp. II • Contact: geert. rombouts@esat • Slides/lecture notes • Homeworks • Projects info/schedule • Examenvragen 2000 -2001, . . • DSP-II Library • FAQs (send questions to geert. rombouts@esat or marc. moonen@esat ) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 30

Review of discrete-time systems (1) Will consider linear time-invariant (LTI) systems. . • Linear

Review of discrete-time systems (1) Will consider linear time-invariant (LTI) systems. . • Linear : u[k] input u 1[k] -> output y 1[k] input u 2[k] -> output y 2[k] hence input a. u 1[k]+b. u 2[k]-> a. y 1[k]+b. y 2[k] y[k] • Time-invariant (shift-invariant) input u[k] -> output y[k] hence input u[k-T] -> output y[k-T] • PS: may be obtained by sampling continuous-time signals/systems (cfr. Nyquist) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 31

Review of discrete-time systems (2) Linear time-invariant (LTI) systems u[k] y[k] • Causal systems:

Review of discrete-time systems (2) Linear time-invariant (LTI) systems u[k] y[k] • Causal systems: for all input u[k]=0, k<0 -> output y[k]=0, k<0 • Impulse response : input 1, 0, 0, 0, . . . -> output h[0], h[1], h[2], h[3], . . . input u[0], u[1], u[2], u[3] -> output y[0], y[1], y[2], y[3], . . . = `convolution’ DSP-II Version 2005 -2006 Chapter-1 Introduction p. 32

Review of discrete-time systems (3) • Impulse response/convolution: …, 0, 0, u[0], u[1], u[2],

Review of discrete-time systems (3) • Impulse response/convolution: …, 0, 0, u[0], u[1], u[2], u[3], 0, 0…. …, 0, 0, y[0], y[1], . . . h[0], h[1], h[2], 0, 0, . . . `Toeplitz’ matrix DSP-II Version 2005 -2006 Chapter-1 Introduction p. 33

Review of discrete-time systems (4) • Z-Transform: DSP-II Version 2005 -2006 Chapter-1 Introduction p.

Review of discrete-time systems (4) • Z-Transform: DSP-II Version 2005 -2006 Chapter-1 Introduction p. 34

Review of discrete-time systems (5) Z-Transform : • compact i/o-relation • may be viewed

Review of discrete-time systems (5) Z-Transform : • compact i/o-relation • may be viewed as `shorthand’ notation for convolution operation/Toeplitz-vector product • stability bounded input u[k] -> bounded output y[k] (`BIBO’) --iff poles of H(z) inside the unit circle (for causal, rational systems) DSP-II Version 2005 -2006 Chapter-1 Introduction p. 35

Review of discrete-time systems (6) Frequency response : • given a system with impulse

Review of discrete-time systems (6) Frequency response : • given a system with impulse response h[k] • given an input signal = complex sinusoid • output signal : = `frequency response’ = H(z) evaluated on the unit circle DSP-II Version 2005 -2006 Chapter-1 Introduction p. 36

Review of discrete-time systems (7) Frequency response : • periodic : period = •

Review of discrete-time systems (7) Frequency response : • periodic : period = • for a real impulse response h[k] Magnitude response Phase response • example : is even function is odd function Nyquist frequency DSP-II Version 2005 -2006 Chapter-1 Introduction p. 37

Review of discrete-time systems (8) `Popular’ frequency responses for filter design : low-pass (LP)

Review of discrete-time systems (8) `Popular’ frequency responses for filter design : low-pass (LP) band-stop DSP-II high-pass (HP) multi-band Version 2005 -2006 band-pass (BP) … Chapter-1 Introduction p. 38

Review of discrete-time systems (9) Rational transfer functions (`IIR filters’): • N poles (zeros

Review of discrete-time systems (9) Rational transfer functions (`IIR filters’): • N poles (zeros of A(z)) , N zeros (zeros of B(z)) • corresponds to difference equation DSP-II Version 2005 -2006 Chapter-1 Introduction p. 39

Review of discrete-time systems (10) `FIR filters’ (finite impulse response): • • `Moving average

Review of discrete-time systems (10) `FIR filters’ (finite impulse response): • • `Moving average filters’ (MA) N poles at the origin z=0 (hence guaranteed stability) N zeros (zeros of B(z)), `all zero’ filters corresponds to difference equation • impulse response DSP-II Version 2005 -2006 Chapter-1 Introduction p. 40