DSP for Engineering DSP for Engineering AplicationsAplications

ECI-3-832

Semester 2 2009/2010

Department of Engineering and Design

London South Bank University

Lecturer (Theoretical Lecturer (Theoretical Part)Part)

Dr. Z. Zhao Room:Room: T409 Tel:Tel: 0207 815 6340 Email: Email: zhaoza@lsbu.ac.ukzhaoza@lsbu.ac.uk

TextbookTextbook

Alan V. Oppenheim, Ronald W. Schafer, Discrete-time Signal Processing, 2ed, Prentice Hall, ISBN: 0-13-083443-2

Monson H. Hayes, Digital Signal Processing, McGraw-Hill, ISBN 0-07-027389-8

Unit Structure (Theoretical

Part) Introduction to DSP Discrete-time signals and Systems the Fourier transforms of discrete-time

signals (DTFT) The z-transform The discrete Fourier transform (DFT) and

its efficient computation (FFT)

Teaching and Learning Methods

Lecture: 2 hour each week Tutorial: 1 hour in even weeks Laboratory work (Matlab

exercises):2 hour in odd weeks Self learning: 102 hours

Assessment 3-hour written examination: 70% Phase test (Week 7) 10% Workshop assignment: 20%

1. log book 2. formal written reports

Introduction to DSP1.1 What is DSP?

DSP, or Digital Signal Processing, is concerned with the use of programmable digital software and/or hardware (digital systems) to perform mathematical operations on a sequence of discrete numbers (a digital signal).

Introduction to DSP

1.2 A General (Engineering) DSP SystemAnti-

aliasing filter

A/D DSP

D/AReconstructi

on filter

Analog

signal

Analog

signal

Analog

signal

Analog

signal

Digital

signal

Digital

signal

An Example

Introduction to DSP1.3 Advantages: Programmable Well-defined, stable, and repeatable Manipulating data in the digital domain

provides high immunity from noise Use of computer algorithms allows

implementation of functions and features that are impossible with analog methods

Introduction to DSP

1.4 Disadvantages: Relatively low bandwidths Signal resolution is limited by the

D/A and A/D converters.

Introduction to DSP1.5 Applications: digital sound recording such as CD and

DAT speech and compression for

telecommunications and storage implementation of wire-line and radio

modems image enhancement and compression speech synthesis and speech recognition Stock Market information processing

What is DSP Used For?

……And much more!And much more!

Speech Coding – Vo-coder

Pulse Train

Random Noise

Vocal TractModel

V/U

Synthesized Speech

Decoder

Original Speech

Analysis:• Voiced/Unvoiced decision• Pitch Period (voiced only)• Signal power (Gain)

Signal PowerPitch

Period

Encoder

LPC-10:

JPEG ExampleOriginal

JPEG (100:1)JPEG (4:1)

Discrete time Signals and Systems Discrete-time signal and its

classification What is discrete-time signal? Special sequences used in DSP Signal properties and and basic operations

Discrete-time systems and properties Properties of discrete-time systems

Convolution sum and methods for performing convolution

LCCDE Linear Constant Coefficient Difference Equation.

Discrete time Signals A discrete-time signal is an indexed sequence

of real or complex numbers.It is a functions of an integer-valued variable, n, that is, often, denoted by x(n).

Complex Sequencesz(n) = a(n)+jb(n) = Re{z(n)}+jIm{z(n)}

= |z(n)|exp[jarg{z(n)}]Where |z(n)| is the magnitude and arg{z(n)} is the

phase angleThe conjugate of z(n) isz*(n) = a(n)-jb(n) = Re{z(n)}-jIm{z(n)}

= |z(n)|exp[-jarg{z(n)}]

Some fundamental sequences Unit sample

Unit step

The exponential sequences

Signal Duration Finite length sequence Left-sided sequence Right-sided sequence Two side sequence

Periodic and Aperiodic Sequences

A signal x(n) is said to be periodic if, for some positive real integer N,x(n) = x(n+N)

Fundamental period – N is smallest integer of the last equation.

Examples:

Symmetric Sequences A real valued signal is said to be even if, for all n:

x(n) = x(-n) Whereas a signal is said to be odd if, for all n:

x(n) =- x(-n) Any signal can be decomposed as a combination

of even and odd signal:x(n) = xe(n) + xo(n)xe(n) = ½ [(x(n) + x(-n) ]xo(n) = ½ [(x(n) - x(-n) ]

Complex value sequence:It is said to be conjugate symmetric if, for all nx(n) = x*(-n)

It is said to be conjugate asymmetric if, for all nx(n) = - x*(-n)

Signal Manipulations Shifting Reversal Scaling Addition Multiplication Time-scaling y(n) = x(mn)

y(n)=x(n/N) Shifting, reversal and time-scaling

operation are order dependent.

Signal Decomposition: The unit sample may be used to

decompose an arbitrary signal x(n) into a sum of weighted and shifted unit sample as follows

k

knkxnx )()()(

Discrete-time Systems and properties

A discrete-time system is a mathematical operator or mapping that transforms one signal ( the input) into another signal ( the output) by means of a fixed set of rules or operation.

System Properties Memory-less system

Definition: A system is said to be memoryless if the output at any time n=n0 depends only on the input at time n=n0.

Ex: y(n) = x2(n)Y(n) = x(n)+x(n-1)

Additive systems:T[x1(n) + x2(n)] = T[x1(n)] + T[x2(n)]

Homogeneity:T[cx(n)] =c T[x(n)]

Linear system:T[a1x1(n) + a2x2(n)] =a1 T[x1(n)] + a2T[x2(n)]h(n) = T[δ(n)]hk(n) = T[δ(n-k)]

Examples

k

k nhkxny )()()(

System Properties (Cont’d) Shift Invariant System:

For y(n)=T[x(n), the system is said to be shift invariant if, for any delay n0, the response to x(n-n0) is y(n-n0).

LSI ( Linear Shift Invariant) System:For LSI : hk(n) = h(n-k)

For LSI system, any input x(n) will have output: = x(n)*h(n)

CausalityA system is said to be causal if, for any n0 the response of the system at time n0 depends only on the input to time n= n0.

StabilityA sytem is said to be stable in the bounded input-bounded output sense if, for any input that is bounded , the output will be bounded,

k

knhkxny )()()(

Anx )(

Bny )(

Convolution Sums

Difference Equations

Difference equation provide a method for computing the response of a system, y(n), to an arbitrary input x(n).

Approaches to solve LCCDE: Classical approach of finding homogeneous and particular

solution. Using z-transform.