What is Digital Signal Processing?
                                         Digital Signal Processing
                                                      Lecture # 2                                                                         First, let’s ask ourselves: What is a signal?
                               Discrete-Time Signals and Systems                                                                                  In the fields of communications, signal processing, and in electrical
                                                                                                                                                  engineering more generally, a signal is any time-varying or
                                                                                                                                                  spatial-varying quantity.
                                                    Monson H. Hayes                                                                                   ◮ Current, voltage, acoustic waveform, light intensity across the focal
                                                    mhh3@gatech.edu                                                                                      plane of a camera, ...
                                                       ∞                                                                                          In the physical world, any quantity measurable through time or over
                                                    X                                                                                             space can be taken as a signal.
                             x(n) =                               x(k)δ(n −k)                                                                         ◮ Temperature distribution over an area or a volume or as a function of
                                                                                                                                                         time, wide velocity, rainfall, ...
                                                  k=−∞                                                                                            Within a complex society, any set of human information or machine
                                                                                                                                                  data can be taken as a signal.
                                                                                                                                                      ◮ Stock market prices, number of bytes transmitted across a channel
                                                                                                                                                         versus time, human population as a function of time, ...
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       What is a Digital Signal?                                                                                                          What is Digital Signal Processing?
               Asignal that is a function of a discrete variable, such as x(n) or z(k),                                                   Digital Signal Processing
               is a discrete-time signal                                                                                                  DSP is concerned with the representation of signals as sequences of
               When a discrete-time signal is quantized in amplitude,                                                                     numbers and with methods of processing those numbers to achieve some
               xq(n) = Q{x(n)} then we have a digital signal.                                                                             desired goal.
               M.Hayes (CAU-GT)                             Lecture # 2                           September 1, 2011     3 / 37                    M.Hayes (CAU-GT)                             Lecture # 2                          September 1, 2011     4 / 37
       Examples of Processing Tasks                                                                                                       Digital Signal Processing Applications
                                                                                                                                              General-Purpose DSP                  Graphics/Imaging                        Instrumentation
                                                                                                                                            Digital filtering                       3-D rotation                            Spectrum Analysis
               Information extraction                                                                                                       Convolution                            Robot vision                            Function generation
                   1   Trends in data (forcasting and control)                                                                              Correlation                            Image transmission                      Pattern matching
                   2   Target detection (radar and sonar)                                                                                   Hilbert transforms                     Image compression                       Seismic processing
                   3   Single speaker in a crowd (surveillance)                                                                             Fast Fourier transforms                Pattern recognition                     Transient analysis
               Signal restoration and enhancement                                                                                           Adaptive filtering                      Image enhancement                       Digital filtering
                                                                                                                                            Windowing                              Homomorphic processing                  Phase-locked loops
                   1   Deconvolution (deblurring, channel equalization)                                                                     Waveform generation                    Workstations
                   2   Noise reduction (CD’s?)
               Signal representation                                                                                                          Voice/Speech                         Control                                 Military
                   1   Signal modeling (speech synthesis)                                                                                   Voice mail                             Disk control                            Secure communications
                   2   Signal coding (Transmission and storage)                                                                             Speech vocoding                        Servo control                           Radar processing
                   3   Signal restoration, Spectral analysis                                                                                Speech recognition                     Robot control                           Sonar processing
                                                                                                                                            Speaker verification                    Engine control                          Image processing
                                                                                                                                            Speech enhancement                     Laser printer control                   Navigation
                                                                                                                                            Speech synthesis                       Motor control                           Missile guidance
                                                                                                                                            Text to speech                                                                 Radio frequency modems
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       Digital Signal Processing Applications                                                                                             Objectives
           Telecommunications                                                                   Automotive
          Echo cancellation                          FAX                                        Engine control                                    Our approach, for the most part, concerns the description, analysis,
          ADPCMtranscoders                           Cellular telephone                         Vibration analysis                                and design of digital systems.
          Digital PBX’s                              Speaker phones                             Antiskid brakes
          Line repeaters                             Digital speech interpolation               Adaptive ride control
          Channel multiplexing                       X.25 packet switching                      Global positioning                                                                x(n)       ✲ Digital                        y(n)       ✲
          1200 to 19200 bps modems                   Video conferencing                         Navigation                                                                                            System
          Adaptive equalizers                        Spread spectrum                            Voice commands
          DTMFencoding/decoding                      Workstations                               Digital radio                                     Wewill look at
          Data encryption                                                                       Cellular telephones                                  1   Types of digital systems.
           Consumer                                  Industrial                                 Medical                                                      ⋆ Characterizations and properties
                                                                                                                                                     2   Analysis of digital systems.
          Radar detectors                            Robotics                                   Hearing aids                                                 ⋆ Finding responses to given inputs
          Power tools                                Numeric control                            Patient monitoring                                   3   Design of digital systems.
          Digital audio/tv                           Security access                            Ultrasound equipment                                         ⋆ Algorithms, filters, computer programs
          Music synthesizer                          Power line monitors                        Diagnostic tools
          Educational toys                                                                      Prosthetics
                                                                                                Fetal monitors
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       Digital Signal Processing Systems                                                                                                  Discrete-Time Signals
                                                                                                                                                  Adiscrete-time signal is an indexed set of real or complex numbers:
                                            x(n)       ✲ Digital                        y(n)       ✲                                                                         x = {x(n)}                     −∞