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

2. DSP-II p. 2 Version 2005-2006 Chapter-1 Introduction 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)

3. DSP-II p. 3 Version 2005-2006 Chapter-1 Introduction 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 could analog speech recognition be done? analog….?) INOUT INOUT A/DD/A 2 +2 =4

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

5. DSP-II p. 5 Version 2005-2006 Chapter-1 Introduction 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 x Receiver decision.99,.01,.96,.95,.07,… 1,0,1,1,0,…

6. DSP-II p. 6 Version 2005-2006 Chapter-1 Introduction DSP in applications : GSM 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,… !!

7. DSP-II p. 7 Version 2005-2006 Chapter-1 Introduction 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 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 !!

8. DSP-II p. 8 Version 2005-2006 Chapter-1 Introduction 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 !!

9. DSP-II p. 9 Version 2005-2006 Chapter-1 Introduction 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 …10MHz band (0.3…1.5km) How has this been made possible? X 1000

10. DSP-II p. 10 Version 2005-2006 Chapter-1 Introduction 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!)

11. DSP-II p. 11 Version 2005-2006 Chapter-1 Introduction 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-II p. 12 Version 2005-2006 Chapter-1 Introduction 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-II p. 13 Version 2005-2006 Chapter-1 Introduction 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...www.adslforum.com

14. DSP-II p. 14 Version 2005-2006 Chapter-1 Introduction DSP in applications : ADSL 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 !!

15. DSP-II p. 15 Version 2005-2006 Chapter-1 Introduction 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, WLAN, CDMA, MIMO-transmission,..) …

16. DSP-II p. 16 Version 2005-2006 Chapter-1 Introduction 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

17. p. 17 Version 2005-2006 Chapter-1 Introduction 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)

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

19. DSP-II p. 19 Version 2005-2006 Chapter-1 Introduction 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,…). 3 subband processing 3 H1(z) G1(z) 3 subband processing 3 H2(z) G2(z) 3 subband processing 3 H3(z) G3(z) 3 subband processing 3 H4(z) G4(z) + IN OUT

20. DSP-II p. 20 Version 2005-2006 Chapter-1 Introduction 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. DSP-II p. 21 Version 2005-2006 Chapter-1 Introduction Prerequisites H197: `Systeemtheorie en Regeltechniek’ (JVDW) HJ09: `Digitale Signaalverwerking I’ (PW) signaaltransformaties, bemonstering, multi-rate, DFT, … H001: `Toegepaste Algebra en Analytische Meetkunde’ (JVDW)

22. DSP-II p. 22 Version 2005-2006 Chapter-1 Introduction Lectures/Course Notes Lectures: 14 * 1,5 hrs (8h50-10h20) 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

23. DSP-II p. 23 Version 2005-2006 Chapter-1 Introduction 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

24. DSP-II p. 24 Version 2005-2006 Chapter-1 Introduction 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)imad.barhumi@esat

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

26. DSP-II p. 26 Version 2005-2006 Chapter-1 Introduction Project Discover DSP technology in present-day systems examples: 3D-audio, music synthesis, automatic transcription, speech codec, MP3, 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 !!

27. DSP-II p. 27 Version 2005-2006 Chapter-1 Introduction 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

28. DSP-II p. 28 Version 2005-2006 Chapter-1 Introduction 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

29. DSP-II p. 29 Version 2005-2006 Chapter-1 Introduction Tijdsbesteding Budget = 157.5u Besteding les: 14 * 1.5u = 21u Matlab/Simulink exercises : 6* 2.5= 15u Matlab/Simulink exercises prep: 6* 2= 12u project : 40u project presentations : 2* 2.5u = 5u belasting: 21*4 + 15 + 12+ 40 + 5 = 156.0u 8u50-10u20 !!

30. DSP-II p. 30 Version 2005-2006 Chapter-1 Introduction homes.esat.kuleuven.be/~rombouts/dspII Contact: geert.rombouts@esatgeert.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 )geert.rombouts@esatmarc.moonen@esat

31. DSP-II p. 31 Version 2005-2006 Chapter-1 Introduction Review of discrete-time systems (1) Will consider linear time-invariant (LTI) systems.. Linear : input u1[k] -> output y1[k] input u2[k] -> output y2[k] hence input 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] PS: may be obtained by sampling continuous-time signals/systems (cfr. Nyquist) u[k]y[k]

32. DSP-II p. 32 Version 2005-2006 Chapter-1 Introduction Review of discrete-time systems (2) Linear time-invariant (LTI) systems Causal systems: for all input u[k]=0, k 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’ u[k]y[k]

33. DSP-II p. 33 Version 2005-2006 Chapter-1 Introduction 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

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

35. DSP-II p. 35 Version 2005-2006 Chapter-1 Introduction 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 --iff poles of H(z) inside the unit circle (for causal,rational systems)

36. DSP-II p. 36 Version 2005-2006 Chapter-1 Introduction 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

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

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

39. DSP-II p. 39 Version 2005-2006 Chapter-1 Introduction 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

40. DSP-II p. 40 Version 2005-2006 Chapter-1 Introduction 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