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1
Advanced Digital Signal Processing
Abdellatif Zaidi †
Department of Electrical Engineering
University of Notre Dame
azaidi@nd.edu
Outline:
1. Introduction
2. Digital processing of continuous-time signals
• Retition: Sampling and sampling theorem
• Quantization
• AD- and DA-conversion
3. DFT and FFT
• Leakage effect
• Windowing
• FFT structure
4. Digital filters
• FIR-filters: Structures, linear phase filters, least-squares
frequency domain design, Chebyshev approximation
• IIR-filters: Structures, classical analog lowpass filter
approximations, conversion to digital transfer functions
• Finite word-length effects
5. Multirate digital signal processing
• Decimation and interpolation
• Filters in sampling rate alteration systems
• Polyphase decomposition and efficient structures
• Digital filter banks
6. Spectral estimation
• Periodogram, Bartlett’s method, Welch’s method,
Blackman-Tukey method
• ARMA modeling, Yule-Walker equation and solution
Literature
• J. G. Proakis, D. G. Manolakis: Digital Signal Processing: Principles, Algorithms, and Applications, Prentice
Hall, 2007, 4th edition
• S. K. Mitra: Digital Signal Processing: A ComputerBased Approach, McGraw Hill Higher Education, 2006,
3rd edition
• A. V. Oppenheim, R. W. Schafer: Discrete-time signal
processing, Prentice Hall, 1999, 2nd edition
• M. H. Hayes: Statistical Signal Processing and Modeling, John Wiley and Sons, 1996 (chapter 6).
Parts of this textbook have been realized in close collaboration with Dr. Joerg Kliewer whom I warmly thank.
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– Numerical integration and differentiation
– Determination of mean value, correlation, p.d.f., . . .
1. Introduction
1.1 Signals, systems and signal processing
What does “Digital Signal Processing” mean?
Signal:
• Physical quantity that varies with time, space or any other
independent variable
• Mathematically: Function of one or more independent
variables, s1(t) = 5 t, s2(t) = 20 t2
• Examples: Temperature over time t, brightness (luminance) of
an image over (x, y), pressure of a sound wave over (x, y, z)
or (x, y, z, t)
Speech signal:
Amplitude →
1
x 10
4
0.5
0
0.1
0.2
0.3
0.4
t [s] →
0.5
0.6
Digital signal processing: Processing of signals by digital means
(software and/or hardware)
Includes:
• Conversion from the analog to the digital domain and back
(physical signals are analog)
• Mathematical specification of the processing operations ⇒
Algorithm: method or set of rules for implementing the system
by a program that performs the corresponding mathematical
operations
• Emphasis on computationally efficient algorithms, which are
fast and easily implemented.
−0.5
−1
• Properties of the system (e.g. linear/nonlinear) determine the
properties of the whole processing operation
• System: Definition also includes:
– software realizations of operations on a signal, which
are carried out on a digital computer (⇒ software
implementation of the system)
– digital hardware realizations (logic circuits) configured
such that they are able to perform the processing operation,
or
– most general definition: a combination of both
0.7
Signal Processing:
• Passing the signal through a system
• Examples:
– Modification of the signal (filtering, interpolation, noise
reduction, equalization, . . .)
– Prediction, transformation to another domain (e.g. Fourier
transform)
3
4

Basic elements of a digital signal processing system
1.2 Digital signal processors (DSPs)
Analog signal processing:
• Programmable microprocessor (more flexibility), or hardwired
digital processor (ASIC, application specific integrated circuit)
(faster, cheaper)
Analog
input
signal
Analog
signal
processor
Analog
output
signal
Often programmable DSPs (simply called ”DSPs”) are used for
evaluation purposes, for prototypes and for complex algorithms:
Digital signal processing:
(A/D: Analog-to-digital, D/A: Digital-to-analog)
Analog
input
signal
A/D
converter
Digital
input
signal
Digital
signal
processor
Digital
output
signal
D/A
converter
Analog
output
signal
• Fixed-point processors: Twos-complement number representation.
• Floating-point processors: Floating point number representation (as for example used in PC processors)
Why has digital signal processing become so popular?
Overview over some available DSP processors see next page.
Digital signal processing has many advantages compared to
analog processing:
Performance example: 256-point complex FFT
Property
Digital
Analog
Dynamics
only
limited
by
complexity
generally
unlimited
(costs, complexity ∼
precision)
without problems
low
generally limited
Precision
Aging
Production
costs
Frequency
range
Linear-phase
frequency
responses
Complex
algorithms
generally limited (costs
increase drastically with
required precision)
problematic
higher
ωdmin ≪ ωamin , ωdmax ≪ ωamax
exactly realizable
approximately realizable
realizable
strong limitations
(from [Evaluating DSP Processor Performance, Berkeley Design Technology, Inc., 2000])
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Some currently available DSP processors and their properties (2006):
Manufacturer
Family
Arithmetic
Data
width (bits)
BDTImark
2000(TM)
Core
clock speed
Unit price
qty. 10000
Analog Devices
ADSP-219x
ADSP-2126x
ADSP-BF5xx
ADSP-TS20x
DSP563xx
DSP568xx
MSC71xx
MSC81xx
TMS320C24x
TMS320C54x
TMS320C55x
TMS320C64x
TMS320C67x
fixed-point
floating-point
fixed-point
floating/fixed-point
fixed-point
fixed-point
fixed-point
fixed-point
fixed-point
fixed-point
fixed-point
fixed-point
floating-point
16
32/40
16
8/16/32/40
24
16
16
16
16
16
16
8/16
32
410
1090
4190
6400
820
110
3370
5610
n/a
500
1460
9130
1470
160 MHz
200 MHz
750 MHz
600 MHz
275 MHz
80 MHz
300 MHz
500 MHz
40 MHz
160 MHz
300 MHz
1 GHz
300 MHz
$11-26
$5-15
$5-32
$131-205
$4-47
$3-12
$13-35
$77-184
$2-8
$3-54
$4-17
$15-208
$12-31
Freescale
Texas-Instuments
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