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Advanced Digital Signal Processing

by Abhishek Apoorv
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Advanced Digital Signal Processing by Abhishek Apoorv

Abhishek Apoorv
Abhishek Apoorv

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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. 2
– 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]) 5 6
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 7 8

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