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: Lectures - Course Notes/Literature Homeworks/Exercise sessions Project Exam Review of Discrete-time Signals&Systems (10-slides) Version 2006-2007 Lecture-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 would you do analog speech recognition ? analog audio compression ? …? ) IN OUT A/D D/A 2 +2 =4 IN OUT Version 2006-2007 Lecture-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 -digital communication format Version 2006-2007 Lecture-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 Receiver decision .99,.01,.96,.95,.07,… Version 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-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 (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 2006-2007 Lecture-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 !! Version 2006-2007 Lecture-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 …12MHz band (0.3…1.5km) How has this been made possible? X 1000 Version 2006-2007 Lecture-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!) Version 2006-2007 Lecture-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. ! Version 2006-2007 Lecture-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’) Version 2006-2007 Lecture-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... Version 2006-2007 Lecture-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 !! Version 2006-2007 Lecture-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, Wi-Fi, WiMax CDMA, MIMO-transmission,..) … Version 2006-2007 Lecture-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 Version 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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

Overview (II) Part II : Filter Banks & Subband Systems . 3 OUT IN + 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 H1(z) G1(z) H2(z) G2(z) H3(z) G3(z) H4(z) G4(z) + IN OUT Version 2006-2007 Lecture-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 . Version 2006-2007 Lecture-1 Introduction

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 Version 2006-2007 Lecture-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) Version 2006-2007 Lecture-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-I Part-II Part-III Version 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

Activities : Homeworks/Ex. Sessions …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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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] Version 2006-2007 Lecture-1 Introduction

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

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

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

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 2006-2007 Lecture-1 Introduction

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… u[k] y[k]=u[k-1] x + a u[k] y[k] Version 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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 2006-2007 Lecture-1 Introduction

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

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 2006-2007 Lecture-1 Introduction