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  • VLSI Digital Signal Processing Systems

    Introduction to Digital Signal Processing Systems

    Lan-Da Van (), Ph. D.Department of Computer ScienceNational Chiao Tung University

    Taiwan, R.O.C.Spring, 2007

    ldvan@cs.nctu.edu.tw

    http://www.cs.nctu.edu.tw/~ldvan/

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-2

    Outlines

    IntroductionDSP AlgorithmsDSP Applications and CMOS ICsRepresentations of DSP AlgorithmsConclusionReferences

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-3

    Why Use Digital Signal Processing?

    Robust to temperature and process variations Controlled better to accuracyNoise/interference tolerancesMathematical representationProgramming capability

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-4

    Common System Configuration

    Multimedia-Communication Applications

    VLSI Signal Processing Library Processor Software

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-5

    VLSI Signal Processing System Design Spectrum

    Computer arithmeticAdderMultiplier

    Digital filterAdaptive digital filter

    LMS/DLMS (Delay LMS) basedRLS based

    TransformMultiplier-accumulator basedRecursive-filter basedROM-based: DA, CORDICButterfly based

    ProcessorGeneral purposed processorDSP processorReconfigurable computing processor

    Non-numerical operationError control coding

    Viterbi DecoderTurbo Code

    Polynomial computationDynamic programmableEtc..

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-6

    VLSI Signal Processing System Publication Area (But not limited)

    IEEE Journal of Solid-State CircuitsIEEE Journal on Selected Areas in CommunicationsIEEE MicroIEEE Trans. on Biomedical EngineeringIEEE Trans. on Circuits and Systems I: Regular PapersIEEE Trans. on Circuits and Systems II: Express BriefsIEEE Trans. on Circuits and Systems for Video TechnologyIEEE Trans. on CommunicationsIEEE Trans. on Computer-Aided Design of Integrated CircuitsIEEE Trans. on ComputersIEEE Trans. on Image ProcessingIEEE Trans. on Information TheoryIEEE Trans. on MultimediaIEEE Trans. on NanotechnologyIEEE Trans. on Neural NetworksIEEE Trans. on Signal ProcessingIEEE Trans. on VLSI SystemsProceedings of the IEEEThe Journal of VLSI Signal Processing SystemsElsevier Integration - The VLSI Journal

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-7

    VLSI Signal Processing System Design Space

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-8

    Outlines

    Features:DSP AlgorithmsDSP Applications and CMOS ICsRepresentations of DSP Algorithms

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-9

    DSP Algorithms

    ConvolutionCorrelationDigital filtersAdaptive filtersDiscrete Fourier transformSource Coding Algorithms

    Discrete cosine transform Motion estimationHuffman codingVector quantization

    Decimator and expanderWavelet and filter banksViterbi algorithm and dynamic programming

    Algorithm: A set of rules for solving a problem in a finite number of steps.

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-10

    Signals

    Analog signalt->y: y=f(t), y:C, n:C

    Discrete-time signaln->y: y=f(nT), y:C, n:Z

    Digital signaln->y: y=D{f(nT)}, y:Z,n:Z

    2)1110(

    2)1000(2)1011( 2)1000(

    y y y)3()1(

    )2()1(

    t n nAnalog Signal Digital SignalDiscrete-Time Signal

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-11

    LTI Systems

    Linear systemsAssume x1(n)->y1(n) and x2(n)->y2(n), where -> denotes lead to. If ax1(n)+bx2(n)->ay1(n)+by2(n), then the systems is referred to as Linear System.Homogenous and additive properties

    Time-invariant (TI) systemsx(n-n0)->y(n-n0)

    LTI systemsy(n)=h(n)*x(n)

    Causal systemsy(n0) depends only on x(n), where n

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-12

    Sampling of Analog Signals

    Nyquist sampling theoremThe analog signal must be band-limitedSample rate must be larger than twice the bandwidth

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-13

    System-Equation Representation

    Impulse/unit sample response

    Transfer function / frequency response

    Difference equations

    State equations

    11

    0

    1)()()( ==

    zab

    zXzYzH

    )()1()( 01 nxbnyany +=

    ][)( 10 nuabnhn=

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-14

    Convolution & Correlation

    Convolution

    =

    ==k

    knhkxnhnxny )()()()()(

    )()()()( nxnaknxkak

    ==

    =

    =

    +=k

    knxkany )()()(

    Correlation

    )()( knxkhk

    =

    =

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-15

    Linear Phase FIR Digital Filters

    Digital filters are an important class of LTI systems.Linear phase FIR filter

    )()( nMhnh =

    0)6()0( bhh ==1)5()1( bhh ==

    2)4()2( bhh ==

    3)3( bh =

    )4()5()6()3()2()1()()(

    210

    3210

    ++++++=

    nxbnxbnxbnxbnxbnxbnxbny

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-16

    IIR Filter Structures

    22

    11

    22

    110

    1)(

    ++

    =zazazbzbbzH

    1z

    2a

    1a

    1z

    0b

    1b

    2b

    )(nx )(ny

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-17

    Introduction to an Adaptive Algorithm

    Widely used in communication, DSP, and control systemDeterministic gradient / least square algorithm

    Steepest descent algorithmRLS algorithm

    Stochastic gradient algorithmLMS algorithm, DLMS algorithmBlock LMS algorithmGradient Lattice algorithm

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-18

    Adaptive Applications

    Channel equalizerSystem identificationImage enhancementEcho cancellerNoise cancellationPredictorLine enhancementBeamformer

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-19

    Notation

    )Error: e(n Factor: Adaptationtor: W(n)Weight Vectput: d(n)Desired Ou

    al: X(n)Input Sign

    .5

    .4

    .3

    .2.1

    : .10.9.8.7

    .6

    MatrixDiagonal:Eigenvalue

    ix: Ration MatrAutocorrel: NTap Number

    ent: MMisadjustm adj

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-20

    Steepest Descent Algorithm

    )()()( nXnWny T=TNnxnxnxnXwhere )]1( ... )1( )([)( +=

    TN nwnwnwnW )]( ... )( )([)( 110 =

    )()()( )()()(

    )()()(

    nWnXndnXnWnd

    nyndne

    T

    T

    =

    =

    =The error at the n-th time is

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-21

    LMS Algorithm

    ))((21)()1( nJnWnW +=+

    )()(2)( nXnenJ =

    An efficient implementation in software of steepest descent using measured or estimated gradientsThe gradient of the square of a single error sample

    e(n)X(n)W(n))W(n +=+=> 1 Cost

    w0, w1, w0

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-22

    Summary of LMS Adaptive Algorithm (1960)

    )()()( nnny T xw=

    )()()( nyndne =

    )()( )()1( nnenn xww +=+

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-23

    Block Diagram of an Adaptive FIR Filter Driven by the LMS Algorithm

    1z)(nx 1z 1z

    )(0 nw )(2 nw)(1 nw )(1 nwN

    )1( nx )2( nx )1( + Nnx

    )(nd)(ny

    )(ne

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-24

    Unitary/Orthogonal Transform (1/4)

    Definition: (from Linear Algebra)

    Let A be nn matrix that satisfies IAAAA == .

    We call A as an unitary matrix if Ahas complex entries, and we call A an orthogonal matrix if A has real number.

  • VLSI Digital Signal Processing Systems

    Lan-Da Van VLSI-DSP-1-25

    Why Orthogonal Transformation? (2/4)

    Energy conservationEnergy compaction

    Most unitary transforms tend to pack a large fraction of the average energy of signals into a relatively few components of the transform coefficients.

    DecorrelationWhen signals are highly correlated, the transform coefficients tend to be uncorrected (or less correlated).

    Information preservationThe information carried by signals are preserved under a unitary transform.

  • VLS

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