dsp for engineering aplications dsp for engineering aplications eci-3-832 semester 2 2009/2010...
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DSP for Engineering DSP for Engineering AplicationsAplications
ECI-3-832
Semester 2 2009/2010
Department of Engineering and Design
London South Bank University
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Lecturer (Theoretical Lecturer (Theoretical Part)Part)
Dr. Z. Zhao Room:Room: T409 Tel:Tel: 0207 815 6340 Email: Email: [email protected]@lsbu.ac.uk
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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
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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)
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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
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Assessment 3-hour written examination: 70% Phase test (Week 7) 10% Workshop assignment: 20%
1. log book 2. formal written reports
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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).
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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
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An Example
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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
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Introduction to DSP
1.4 Disadvantages: Relatively low bandwidths Signal resolution is limited by the
D/A and A/D converters.
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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
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What is DSP Used For?
……And much more!And much more!
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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:
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JPEG ExampleOriginal
JPEG (100:1)JPEG (4:1)
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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.
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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)}]
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Some fundamental sequences Unit sample
Unit step
The exponential sequences
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Signal Duration Finite length sequence Left-sided sequence Right-sided sequence Two side sequence
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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:
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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)
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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.
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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 )()()(
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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.
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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 )()()(
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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 )(
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Convolution Sums
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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.