ECE 4270 Fundamentals of Digital Signal Processing ECE 4270 Fundamentals of Digital Signal Processing Lecture 1 Course Logistics Introduction School of Electrical and Computer Engineering Georgia Institute of Technology Summer Semester 2004 Summer 2004 ECE 4270 B H Juang Copyright 2004 School of Electrical and Computer Engineering Georgia Institute of Technology Summer Semester 2004 Lecture 1 Slide 1 Summer 2004 Course Objectives Fundamentals of discrete time linear shift invariant signals and systems in Representation sampling and quantization Processing filtering and transform techniques Processing System Design filter processing algorithm design Efficient computational algorithms and their implementation To gain preliminary experience in computational processing of real signal and to relate the above understanding to real world scenario ECE 4270 B H Juang Copyright 2004 Copyright 2004 Lecture 1 Slide 2 Course Topics To establish the idea of using computing techniques to alter the properties of a signal for desired effects via understanding of Summer 2004 ECE 4270 B H Juang Lecture 1 Slide 3 Discrete index signals Linear systems z Transforms Sampling Quantization Frequency Response IIR and FIR Filters Filter Design Summer 2004 Discrete Fast Fourier Transform Special Filtering Topics Inverse Matched Filtering Time Frequency Analysis Non linear Filtering Techniques Symbolic Processing ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 4 Prerequisites Instructor Info Office Hours ECE3075 Random Signals probability density functions correlation power spectral densities moments Also should have prior exposure to linear systems analysis and transform analysis convolution and filtering Fourier transforms Laplace and z transforms Summer 2004 ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 5 Prof B H Juang Class Hours MWF 1200 1310 Office Hours MW 1400 1530 BH310 Or by appointment Resources http users ece gatech edu juang Contact info GCATT 341 Phone 404 894 6618 E mail juang ece gatech edu Summer 2004 Summer 2004 Quiz 2 20 Random Quizzes 10 Homework 20 Final Exam 30 ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 6 Tests 2 Random Quizzes 20 minutes each 2 Scheduled Quizzes 70 minutes each June 4 and June 30 Open book open notes Final Exam July 28 2004 1450 1740 Open book open notes Comprehensive Weight 20 Copyright 2004 Tests Homework Grading Schedule Quiz 1 ECE 4270 B H Juang Homework Textbook has basic problems with answers basic problems advanced problems and extension problems homework mostly from first 2 categories some from 3rd Weekly due 1 week after assignment Solutions posted to class web site after homework turned in Essential to good understanding and facility in the material Lecture 1 Slide 7 Summer 2004 ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 8 Textbook What is DSP Input Signal Oppenheim and Schafer DiscreteTime Signal Processing 2nd edition Prentice Hall 1999 Supplemental texts Hayes Digital Signal Processing Schaum s Outlines Series 1999 Digital McClellan Schafer Yoder DSP First Signal Computer Output Signal Digital toAnalog Conversion Method to represent a quantity a phenomenon or an event Why digital What is a signal Both on reserve in library Analog toDigital Conversion something as a sound gesture or object that conveys notice or information a detectable physical quantity as a voltage current or magnetic field strength by which messages or information can be transmitted Some class notes What are we interested in primarily for special topics nonlinear techniques Processing What kind of processing we need and encounter almost everyday Special effects Summer 2004 ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 9 Common Computing logic operations i e calculator functions Word processing Language processing Spreadsheet processing Presentation processing processing including handling of speech audio image video etc Filtering Analysis recognition synthesis and coding of real world signals Detection and estimation of signals in presence of noise or interference Copyright 2004 Input SIgnal Signal Processing a more general form of information ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 10 Advantages of Digital Representations Text processing handling of text tables basic arithmetic and Summer 2004 ECE 4270 B H Juang Summer 2004 Lecture 1 Slide 11 A to D Converter Signal Processor D to A Converter Output Signal Permanence and robustness of signal representations zerodistortion reproduction is achievable Advanced IC technology works well for digital systems Virtually infinite flexibility with digital systems Multi functionality Multi input multi output Indispensable in telecommunications which is virtually all digital at the present time Summer 2004 ECE 4270 B H Juang Copyright 2004 Lecture 1 Slide 12 Digital Processing of Analog Signals xc t A to D x n Computer y n D to A Discrete time Signal yc t x x n A to D conversion bandwidth control sampling and quantization Computational processing implemented on computers or ASICs with finite precision arithmetic Basic numerical processing add subtract multiply scaling amplification attenuation mute Algorithmic numerical processing convolution or linear filtering non linear filtering e g median filtering difference equations DFT inverse filtering MAX MIN D to A conversion re quantification and filtering or interpolation for reconstruction ECE 4270 B H Juang Summer 2004 Copyright 2004 Lecture 1 Slide 13 A sequence of numbers Mathematical representation x n xa nT T is called sampling period and its reciprocal is the sampling frequency x n may be quantized to one of a finite set of values which is then represented digitally in bits hence a digital signal course material mostly deals with discrete time signal ECE 4270 B H Juang Summer 2004 Quantization transforming a continuouslyvalued input into a representation that assumes one out of a finite set of values 0 6 4 3 Lecture 1 Slide 14 0 3 0 9 1 5 2 1 in 2 1 The finite set of output values is indexed e g the value 1 8 has an index of 6 or 110 2 in binary representation Storage or transmission uses binary representation a quantization table is needed 0 A 3 bit uniform quantizer 2 y quantize Sampled Sinusoid 5sin 2 nT 4 0 6 Analog sinusoid 5sin 2 x 4 6 2 2 6 2 0 5 10 15 6 4 4 6 20 25 30 35 40 n 0 2 Discrete sinusoid round 5sin 2 nT 4 4 y 1 2 5 sample 0 2 Quantized sinusoid round 5sin 2 x 4 2 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 6 1 x y 1 8 Copyright 2004 Discrete