ece513chap1slides_handout - FUNDAMENTAL DSP CONCEPTS C Williams W Alexander North Carolina State University Raleigh NC(USA ECE 513 Fall 2016 C Williams

# ece513chap1slides_handout - FUNDAMENTAL DSP CONCEPTS C...

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FUNDAMENTAL DSP CONCEPTS C. Williams & W. Alexander North Carolina State University, Raleigh, NC (USA) ECE 513, Fall 2016 C. Williams & W. Alexander (NCSU) FUNDAMENTAL DSP CONCEPTS ECE 513, Fall 2016 1 / 156 Outline 1 Introduction 2 Digital Signal Processing Applications 3 Why Digital Signal Processing 4 Representation of Discrete–Time Signals 5 Operations on Sequences 6 Normalized Frequency Representation 7 The Z–Transform 8 Region of Convergence 9 Frequency Representation of Discrete–Time Systems 10 Difference Equation Representation 11 The Frequency Response 12 Pole–Zero Plots 13 System Response 14 Frequency Shifting 15 Inverse Z–Transform for Systems with Complex Poles 16 Inverse Z–Transform for Systems with Multiple Poles 17 Cascade Implementation of Digital Filters 18 Stabilization of an Unstable Filter 19 References C. Williams & W. Alexander (NCSU) FUNDAMENTAL DSP CONCEPTS ECE 513, Fall 2016 2 / 156
Introduction Signals play an important role in many activities in our daily lives. Examples include: Speech Music Biomedical signals Video Digital Television C. Williams & W. Alexander (NCSU) FUNDAMENTAL DSP CONCEPTS ECE 513, Fall 2016 3 / 156 Introduction A deterministic signal is a function of an independent variable such as time, distance, position, temperature, and pressure. It can be uniquely determined by a well-defined process such as a mathematical expression of one or more independent variables, or by table look up. For example, s ( t ) = 3 sin ( 2 . 1 π t + 0 . 3198 ) u ( t ) (1) is a deterministic signal with independent variable t . C. Williams & W. Alexander (NCSU) FUNDAMENTAL DSP CONCEPTS ECE 513, Fall 2016 4 / 156
Introduction A speech signal can not be described functionally by a mathematical expression. However, a recorded segment of speech can be represented to a high degree of accuracy as the sum of several sinusoids of different amplitudes and frequencies such as [1] s ( t ) = N k = 1 A k ( t ) sin [ 2 π F k ( t ) t + θ k ( t )] (2) A signal that is determined in a random way and can not be predicted ahead of time is a random signal. Statistical approaches are often used to analyze random signals. C. Williams & W. Alexander (NCSU) FUNDAMENTAL DSP CONCEPTS ECE 513, Fall 2016 5 / 156 DSP Applications Digital signal processing is heavily used in information technology. Information technology includes such diverse subjects as digital 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 CONCEPTS ECE 513, Fall 2016 6 / 156
Why DSP? Many applications involving continuous–time signals use digital signal processing. This often involves 1 sampling the continuous–time signal at regular intervals, 2 quantizing the samples to obtain a digital sequence, 3 processing the digital system using a computer or a digital system, 4 converting the output digital sequence to a continuous–time system.