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Digital Signal Processing II

Digital Signal Processing II. Marc Moonen Dept. E.E./ESAT, K.U.Leuven marc.moonen@esat.kuleuven.be homes.esat.kuleuven.be/~moonen/. Digital Signal Processing II. General Intro Aims/Scope: Why study DSP ? DSP in applications : GSM, ADSL… Overview Activities:

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Digital Signal Processing II

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  1. Digital Signal Processing II Marc Moonen Dept. E.E./ESAT, K.U.Leuven marc.moonen@esat.kuleuven.be 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) Version 2006-2007Lecture-1 Introduction

  3. IN OUT IN 2 OUT +2 A/D D/A =4 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 ? …? ) Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  5. .99,.01,.96,.95,.07,… Transmitter 1,0,1,1,0,… Channel Receiver decision x + x 1,0,1,1,0,… 1/a a noise DSP in applications : GSM • DSP for digital communications (`physical layer’ ) : • a common misunderstanding is that digital communications is `simple’…. • While in practice… Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  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^-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 !! Version 2006-2007Lecture-1 Introduction

  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 !! Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  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!) Version 2006-2007Lecture-1 Introduction

  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. ! Version 2006-2007Lecture-1 Introduction

  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’) Version 2006-2007Lecture-1 Introduction

  13. 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... Version 2006-2007Lecture-1 Introduction

  14. 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 !! Version 2006-2007Lecture-1 Introduction

  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,..) • … Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  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) Version 2006-2007Lecture-1 Introduction

  18. Overview (I) • INTRO : Lecture-1 • Part I : Filter Design & Implementation Lecture-2 : IIR & FIR Filter Design Lecture-3 : Filter Realization Lecture-4 : Filter Implementation Version 2006-2007Lecture-1 Introduction

  19. 3 subband processing 3 G1(z) H1(z) OUT IN 3 subband processing 3 G2(z) H2(z) + 3 subband processing 3 G3(z) H3(z) 3 subband processing 3 G4(z) H4(z) 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,…) . Version 2006-2007Lecture-1 Introduction

  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 . Version 2006-2007Lecture-1 Introduction

  21. IFFT P/S S/P Discrete equivalent channel FFT FEQ r(t) ADC DAC p(t) ch(t) Tx filter Channel Rx filter Tx clock Rx clock Overview (IV) • OUTRO : Lecture 14: Case study ADSL/VDSL modems Version 2006-2007Lecture-1 Introduction

  22. Prerequisites H197: `Systeemtheorie en Regeltechniek’ (JVDW) HJ09: `Digitale Signaalverwerking I’ (PW) signaaltransformaties, bemonstering, multi-rate, DFT, … H001: `Toegepaste Algebra en Analytische Meetkunde’ (JVDW) Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  24. 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) Version 2006-2007Lecture-1 Introduction

  25. 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 Version 2006-2007Lecture-1 Introduction

  26. 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) Version 2006-2007Lecture-1 Introduction

  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 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 Version 2006-2007Lecture-1 Introduction

  28. 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 Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  30. 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 ) Version 2006-2007Lecture-1 Introduction

  31. u[k] y[k] 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] Version 2006-2007Lecture-1 Introduction

  32. `Toeplitz’ matrix 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 inputu[0],u[1],u[2],u[3]:(cfr.linearity!) Version 2006-2007Lecture-1 Introduction

  33. u[0],u[1],u[2],u[3] y[0],y[1],... h[0],h[1],h[2],0,0,... Review of discrete-time systems 3/10 Convolution: = `convolution sum’ Version 2006-2007Lecture-1 Introduction

  34. Review of discrete-time systems 4/10 Z-Transform: H(z) is `transfer function’ Version 2006-2007Lecture-1 Introduction

  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) Version 2006-2007Lecture-1 Introduction

  36. u[k] y[k]=u[k-1] u[k] y[k] + a x 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… Transfer function is Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

  39. Im u[2] u[1] Re u[0]=1 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 Version 2006-2007Lecture-1 Introduction

  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 Version 2006-2007Lecture-1 Introduction

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