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FUNDAMENTAL DSP CONCEPTSC. Williams & W. AlexanderNorth Carolina State University, Raleigh, NC (USA)ECE 513, Fall 2016C. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20161 / 156Outline1Introduction2Digital Signal Processing Applications3Why Digital Signal Processing4Representation of Discrete–Time Signals5Operations on Sequences6Normalized Frequency Representation7The Z–Transform8Region of Convergence9Frequency Representation of Discrete–Time Systems10Difference Equation Representation11The Frequency Response12Pole–Zero Plots13System Response14Frequency Shifting15Inverse Z–Transform for Systems with Complex Poles16Inverse Z–Transform for Systems with Multiple Poles17Cascade Implementation of Digital Filters18Stabilization of an Unstable Filter19ReferencesC. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20162 / 156
IntroductionSignals play an important role in many activities in our daily lives.Examples include:SpeechMusicBiomedical signalsVideoDigital TelevisionC. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20163 / 156IntroductionA deterministic signalis a function of an independent variable such as time, distance,position, temperature, and pressure. Itcan be uniquely determined bya well-defined process such as a mathematical expression of one ormore independent variables,or by table look up.For example,s(t) =3 sin(2.1πt+0.3198)u(t)(1)is a deterministic signal with independent variablet.C. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20164 / 156
IntroductionA speech signal can not be described functionally by amathematical expression.However, a recorded segment of speech can be represented to ahigh degree of accuracy as the sum of several sinusoids ofdifferent amplitudes and frequencies such as s(t) =Nk=1Ak(t)sin[2πFk(t)t+θk(t)](2)A signal that is determined in a random way and can not bepredicted ahead of time is a random signal.Statistical approaches are often used to analyze random signals.C. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20165 / 156DSP ApplicationsDigital signal processing is heavily used in information technology.Information technology includes such diverse subjects asdigital signal processing,image processing,multimedia applications,computational engineering,visualization of data,database management,teleconferencing,remote operation of robots,autonomous vehicles,computer networks, etc.C. Williams & W. Alexander (NCSU)FUNDAMENTAL DSP CONCEPTSECE 513, Fall 20166 / 156
Why DSP?Many applications involving continuous–time signals use digitalsignal processing.This often involves1sampling the continuous–time signal at regular intervals,2quantizing the samples to obtain a digital sequence,3processing the digital system using a computer or a digital system,4converting the output digital sequence to a continuous–timesystem.