Applications of Linear Algebra in Signal Sampling and Modeling
|
|
- August Higgins
- 6 years ago
- Views:
Transcription
1 Applications of Linear Algebra in Signal Sampling and Modeling by Corey Brown Joshua Crawford Brett Rustemeyer and Kenny Stieferman Abstract: Many situations encountered in engineering require sampling a signal to determine a model of that signal. Such a signal could have its source in temperature probes antennas or virutally any real time scenario. This paper examines the fundamental theory behind signal processing works an example problem based on a suggested algorithm and briefly discusses other possible applications. INTRODUCTION: A signal is a time dependent numerical representation of events in the physical world. In typical applications the signal is in the form of a current or a voltage. For the signal to be useful it must be modeled. Signal processing takes time dependent data and manipulates it to create a mathematical model useful to practical problem solvers. Many techniques for signal processing exist including Fourier Transforms moving averages filtering and spectral analysis. Spectral analysis uses sampled data to reconstruct a given signal. Though conceptually simple sampling is typically impractical for most applications due to the large quantity of data involved in the calculations. However the fundamental concepts behind signal processing are better demonstrated with this method than with more advanced techniques. THEORY AND DEFINITIONS: A signal can be many different things depending on the application. An example of ideal signal would be s= k which alternates across the time axis and resembles a clock signal in a digital circuit. Typical signals are not so simple.
2 A complex continuous signal can be modeled by sampling the data at uniform discrete time intervals. The number of samples taken in each second is the sample rate or sampling frequency. Continuous signals can not be effectively utilized however the sampled data allows for the construction of a functional model which can be used in calculations. For the purposes of modeling the signal can be viewed as some combination of sine and cosine waves. Fourier Series require an infinite number of frequencies but the sampling frequency is subdivided into a finite number of frequency ranges to reduce calculations. One cosine and one sine function is needed to represent the signal for each subdivision of the sampling frequency. If the sampled data is represented by a vector it can be written as a linear combination of two vectors each composed of the appropriate sinusoidal entries. Let b m contain the cosine entries at frequency subdivision m and c m contain the sine entries at subdivision m. Then B b b m ] C c c m ] D B C ] and the columns of D form a basis for the vector space V. It can be shown that the columns of D are in fact an orthogonal basis because the dot product of any two vectors in D is zero. The signal s V and s=b u C v. This can be rewritten as s=d w where w= [ u v]. Given that the columns of D form an orthogonal basis the weights can be calculated using the following relation: u s b m m] m b m b v s c m m] m c m c. This discussion forms the foundation for the calculations in the following example.
3 EXAMPLE: SAMPLING AT 6 HZ Take the following signal: s={ 5 9 } where s is sampled at at a rate of 6 Hz. Subdividing into 6 equal frequency ranges yields the following sinusoidal vectors: b ] c ] ] cos 3 cos b 3 cos cos 4 3 c ] sin 3 sin 3 sin sin 4 3 cos 5 sin ] cos 3 cos 4 b 3 cos cos 8 3 c ] sin 3 sin 4 3 cos sin cos sin b 3 cos 3 and 3. sin 8 3 cos 4 cos 5 ] c3 sin 4 sin 5 ] cos sin 3 3 Note that only four sets of vectors are required since the upper half of the frequency ranges are a reflection of the lower half. This phenomenon is known as aliasing. Putting these vectors together yields matrix B and matrix C. The sampled signal then is composed of the linear combination of these vectors: s=b u C v. As stated previously s=d w where D B C ] and w= [ u v].
4 ] 3 3 Now D um s bm m] b m b and v s c m m] m c m c. So u = 9 6 u = 5 6 u = 3 6 u 3 = 5 6 v = v = 3 6 v = 3 v 3 =. The amplitude for each frequency subdivision then is found by A= u m v m. A graph of these amplitudes with respect to frequency is referred to as the signal's spectrum. (Reference personal website for spreadsheet and graphs.) The spectrum allows reconstruction of the original signal. Since the number of possible frequencies is infinite six sampled points is inadequate to form an accurate model of the signal. However in real applications many more points are sampled allowing for a closer representation of the signal. CONCLUSIONS: Signal processing can use linear algebra in combination with sampling techniques to create a mathematical representation of a complete analog signal. As mentioned before there are many other methods for analyzing signals. One such algorithm uses a formula involving a covariance matrix whose entries are calculated by Laplace Transforms. A simpler but highly effective signal processing technique for filtering out noise takes a moving average of the points to eliminate irregular spikes and isolate the primary signal. In spectral analysis the
5 chosen sample rate is an important factor for the calculations (since it is the starting point for the algorithm) and depends primarily on the media involved. For example sounds of frequencies greater than.5 khz are not audible to the average human. So for accurate sound reproduction a sample rate of approximately 44. khz is appropriate since the upper half of this range is not present in the model due to aliasing. A large number of subdivisions would be required to create this signal model making calculation an enormous task. So to avoid tedious and prolonged hand calculations engineers assign the task of signal processing to devices such as multiplexers FPGAs and processors. These devices are hard coded with algorithms applied in similar ways as the example to create an accurate representation of the signal based on the spectrum. Regardless of which technique is used signal processing is a common and critical task in modern engineering. REFERENCES. C. Brown J. Crawford B. Rustemeyer and K. Stieferman. < Freeman Randy A. Linear Algebra in Digital Audio. (Accessed on /4/4) < 3. Johnson Don. A Signal's Spectrum. (Accessed on //4) < 4. Lay David C. Linear Algebra and Its Applications. -3 rd Edition Pearson Education Madisetti Vijay K. and Williams Douglas B. The Digital Signal Processing Handbook. CRC Press 998.
Lecture 2: SIGNALS. 1 st semester By: Elham Sunbu
Lecture 2: SIGNALS 1 st semester 1439-2017 1 By: Elham Sunbu OUTLINE Signals and the classification of signals Sine wave Time and frequency domains Composite signals Signal bandwidth Digital signal Signal
More informationThe Discrete Fourier Transform. Claudia Feregrino-Uribe, Alicia Morales-Reyes Original material: Dr. René Cumplido
The Discrete Fourier Transform Claudia Feregrino-Uribe, Alicia Morales-Reyes Original material: Dr. René Cumplido CCC-INAOE Autumn 2015 The Discrete Fourier Transform Fourier analysis is a family of mathematical
More informationENGR 210 Lab 12: Sampling and Aliasing
ENGR 21 Lab 12: Sampling and Aliasing In the previous lab you examined how A/D converters actually work. In this lab we will consider some of the consequences of how fast you sample and of the signal processing
More informationMichael F. Toner, et. al.. "Distortion Measurement." Copyright 2000 CRC Press LLC. <
Michael F. Toner, et. al.. "Distortion Measurement." Copyright CRC Press LLC. . Distortion Measurement Michael F. Toner Nortel Networks Gordon W. Roberts McGill University 53.1
More informationIntroduction to signals and systems
CHAPTER Introduction to signals and systems Welcome to Introduction to Signals and Systems. This text will focus on the properties of signals and systems, and the relationship between the inputs and outputs
More informationSound is the human ear s perceived effect of pressure changes in the ambient air. Sound can be modeled as a function of time.
2. Physical sound 2.1 What is sound? Sound is the human ear s perceived effect of pressure changes in the ambient air. Sound can be modeled as a function of time. Figure 2.1: A 0.56-second audio clip of
More informationSAMPLING THEORY. Representing continuous signals with discrete numbers
SAMPLING THEORY Representing continuous signals with discrete numbers Roger B. Dannenberg Professor of Computer Science, Art, and Music Carnegie Mellon University ICM Week 3 Copyright 2002-2013 by Roger
More informationPART I: The questions in Part I refer to the aliasing portion of the procedure as outlined in the lab manual.
Lab. #1 Signal Processing & Spectral Analysis Name: Date: Section / Group: NOTE: To help you correctly answer many of the following questions, it may be useful to actually run the cases outlined in the
More informationFrequency Division Multiplexing Spring 2011 Lecture #14. Sinusoids and LTI Systems. Periodic Sequences. x[n] = x[n + N]
Frequency Division Multiplexing 6.02 Spring 20 Lecture #4 complex exponentials discrete-time Fourier series spectral coefficients band-limited signals To engineer the sharing of a channel through frequency
More informationDr. Cahit Karakuş ANALOG SİNYALLER
Dr. Cahit Karakuş ANALOG SİNYALLER Sinusoidal Waveform Mathematically it is represented as: Sinusoidal Waveform Unit of measurement for horizontal axis can be time, degrees or radians. Sinusoidal Waveform
More information5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs
Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2
More informationSampling and Reconstruction of Analog Signals
Sampling and Reconstruction of Analog Signals Chapter Intended Learning Outcomes: (i) Ability to convert an analog signal to a discrete-time sequence via sampling (ii) Ability to construct an analog signal
More informationIntroduction (concepts and definitions)
Objectives: Introduction (digital system design concepts and definitions). Advantages and drawbacks of digital techniques compared with analog. Digital Abstraction. Synchronous and Asynchronous Systems.
More informationPhysics 115 Lecture 13. Fourier Analysis February 22, 2018
Physics 115 Lecture 13 Fourier Analysis February 22, 2018 1 A simple waveform: Fourier Synthesis FOURIER SYNTHESIS is the summing of simple waveforms to create complex waveforms. Musical instruments typically
More informationAnalog-Digital Interface
Analog-Digital Interface Tuesday 24 November 15 Summary Previous Class Dependability Today: Redundancy Error Correcting Codes Analog-Digital Interface Converters, Sensors / Actuators Sampling DSP Frequency
More informationLecture 7 Frequency Modulation
Lecture 7 Frequency Modulation Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/3/15 1 Time-Frequency Spectrum We have seen that a wide range of interesting waveforms can be synthesized
More informationBiomedical Signals. Signals and Images in Medicine Dr Nabeel Anwar
Biomedical Signals Signals and Images in Medicine Dr Nabeel Anwar Noise Removal: Time Domain Techniques 1. Synchronized Averaging (covered in lecture 1) 2. Moving Average Filters (today s topic) 3. Derivative
More informationDFT: Discrete Fourier Transform & Linear Signal Processing
DFT: Discrete Fourier Transform & Linear Signal Processing 2 nd Year Electronics Lab IMPERIAL COLLEGE LONDON Table of Contents Equipment... 2 Aims... 2 Objectives... 2 Recommended Textbooks... 3 Recommended
More informationModulation. Digital Data Transmission. COMP476 Networked Computer Systems. Analog and Digital Signals. Analog and Digital Examples.
Digital Data Transmission Modulation Digital data is usually considered a series of binary digits. RS-232-C transmits data as square waves. COMP476 Networked Computer Systems Analog and Digital Signals
More informationECEGR Lab #8: Introduction to Simulink
Page 1 ECEGR 317 - Lab #8: Introduction to Simulink Objective: By: Joe McMichael This lab is an introduction to Simulink. The student will become familiar with the Help menu, go through a short example,
More informationSignals A Preliminary Discussion EE442 Analog & Digital Communication Systems Lecture 2
Signals A Preliminary Discussion EE442 Analog & Digital Communication Systems Lecture 2 The Fourier transform of single pulse is the sinc function. EE 442 Signal Preliminaries 1 Communication Systems and
More informationHarmonic Analysis. Purpose of Time Series Analysis. What Does Each Harmonic Mean? Part 3: Time Series I
Part 3: Time Series I Harmonic Analysis Spectrum Analysis Autocorrelation Function Degree of Freedom Data Window (Figure from Panofsky and Brier 1968) Significance Tests Harmonic Analysis Harmonic analysis
More information3.2 Measuring Frequency Response Of Low-Pass Filter :
2.5 Filter Band-Width : In ideal Band-Pass Filters, the band-width is the frequency range in Hz where the magnitude response is at is maximum (or the attenuation is at its minimum) and constant and equal
More informationIslamic University of Gaza. Faculty of Engineering Electrical Engineering Department Spring-2011
Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Spring-2011 DSP Laboratory (EELE 4110) Lab#4 Sampling and Quantization OBJECTIVES: When you have completed this assignment,
More informationBasic Signals and Systems
Chapter 2 Basic Signals and Systems A large part of this chapter is taken from: C.S. Burrus, J.H. McClellan, A.V. Oppenheim, T.W. Parks, R.W. Schafer, and H. W. Schüssler: Computer-based exercises for
More informationFAST Fourier Transform (FFT) and Digital Filtering Using LabVIEW
FAST Fourier Transform (FFT) and Digital Filtering Using LabVIEW Instructor s Portion Wei Lin Department of Biomedical Engineering Stony Brook University Summary Uses This experiment requires the student
More informationFigure 1: Block diagram of Digital signal processing
Experiment 3. Digital Process of Continuous Time Signal. Introduction Discrete time signal processing algorithms are being used to process naturally occurring analog signals (like speech, music and images).
More informationDigital Video and Audio Processing. Winter term 2002/ 2003 Computer-based exercises
Digital Video and Audio Processing Winter term 2002/ 2003 Computer-based exercises Rudolf Mester Institut für Angewandte Physik Johann Wolfgang Goethe-Universität Frankfurt am Main 6th November 2002 Chapter
More informationLecture 3 Complex Exponential Signals
Lecture 3 Complex Exponential Signals Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/3/1 1 Review of Complex Numbers Using Euler s famous formula for the complex exponential The
More informationSpectrum Analysis: The FFT Display
Spectrum Analysis: The FFT Display Equipment: Capstone, voltage sensor 1 Introduction It is often useful to represent a function by a series expansion, such as a Taylor series. There are other series representations
More informationYEDITEPE UNIVERSITY ENGINEERING FACULTY COMMUNICATION SYSTEMS LABORATORY EE 354 COMMUNICATION SYSTEMS
YEDITEPE UNIVERSITY ENGINEERING FACULTY COMMUNICATION SYSTEMS LABORATORY EE 354 COMMUNICATION SYSTEMS EXPERIMENT 3: SAMPLING & TIME DIVISION MULTIPLEX (TDM) Objective: Experimental verification of the
More informationSignal Characteristics
Data Transmission The successful transmission of data depends upon two factors:» The quality of the transmission signal» The characteristics of the transmission medium Some type of transmission medium
More informationLaboratory Assignment 2 Signal Sampling, Manipulation, and Playback
Laboratory Assignment 2 Signal Sampling, Manipulation, and Playback PURPOSE This lab will introduce you to the laboratory equipment and the software that allows you to link your computer to the hardware.
More informationECE 2111 Signals and Systems Spring 2012, UMD Experiment 9: Sampling
ECE 2111 Signals and Systems Spring 2012, UMD Experiment 9: Sampling Objective: In this experiment the properties and limitations of the sampling theorem are investigated. A specific sampling circuit will
More informationObjectives. Abstract. This PRO Lesson will examine the Fast Fourier Transformation (FFT) as follows:
: FFT Fast Fourier Transform This PRO Lesson details hardware and software setup of the BSL PRO software to examine the Fast Fourier Transform. All data collection and analysis is done via the BIOPAC MP35
More informationProf. Feng Liu. Fall /04/2018
Prof. Feng Liu Fall 2018 http://www.cs.pdx.edu/~fliu/courses/cs447/ 10/04/2018 1 Last Time Image file formats Color quantization 2 Today Dithering Signal Processing Homework 1 due today in class Homework
More informationExercise 2-2. Spectral Characteristics of PAM Signals EXERCISE OBJECTIVE DISCUSSION OUTLINE DISCUSSION. Sampling
Exercise 2-2 Spectral Characteristics of PAM Signals EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the spectral characteristics of PAM signals. You will be able to
More informationESE 150 Lab 04: The Discrete Fourier Transform (DFT)
LAB 04 In this lab we will do the following: 1. Use Matlab to perform the Fourier Transform on sampled data in the time domain, converting it to the frequency domain 2. Add two sinewaves together of differing
More informationG(f ) = g(t) dt. e i2πft. = cos(2πf t) + i sin(2πf t)
Fourier Transforms Fourier s idea that periodic functions can be represented by an infinite series of sines and cosines with discrete frequencies which are integer multiples of a fundamental frequency
More informationCSCD 433 Network Programming Fall Lecture 5 Physical Layer Continued
CSCD 433 Network Programming Fall 2016 Lecture 5 Physical Layer Continued 1 Topics Definitions Analog Transmission of Digital Data Digital Transmission of Analog Data Multiplexing 2 Different Types of
More informationThe Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D.
The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. Home The Book by Chapters About the Book Steven W. Smith Blog Contact Book Search Download this chapter in PDF
More informationECE 556 BASICS OF DIGITAL SPEECH PROCESSING. Assıst.Prof.Dr. Selma ÖZAYDIN Spring Term-2017 Lecture 2
ECE 556 BASICS OF DIGITAL SPEECH PROCESSING Assıst.Prof.Dr. Selma ÖZAYDIN Spring Term-2017 Lecture 2 Analog Sound to Digital Sound Characteristics of Sound Amplitude Wavelength (w) Frequency ( ) Timbre
More informationChapter 4. Digital Audio Representation CS 3570
Chapter 4. Digital Audio Representation CS 3570 1 Objectives Be able to apply the Nyquist theorem to understand digital audio aliasing. Understand how dithering and noise shaping are done. Understand the
More informationEE390 Final Exam Fall Term 2002 Friday, December 13, 2002
Name Page 1 of 11 EE390 Final Exam Fall Term 2002 Friday, December 13, 2002 Notes 1. This is a 2 hour exam, starting at 9:00 am and ending at 11:00 am. The exam is worth a total of 50 marks, broken down
More informationEE 422G - Signals and Systems Laboratory
EE 422G - Signals and Systems Laboratory Lab 3 FIR Filters Written by Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 September 19, 2015 Objectives:
More informationEngineering Thesis. The use of Synchronized Phasor Measurement to Determine Power System Stability, Transmission Line Parameters and Fault Location
Engineering Thesis The use of Synchronized Phasor Measurement to Determine Power System Stability, Transmission Line Parameters and Fault Location By Yushi Jiao Presented to the school of Engineering and
More informationGraphs of sin x and cos x
Graphs of sin x and cos x One cycle of the graph of sin x, for values of x between 0 and 60, is given below. 1 0 90 180 270 60 1 It is this same shape that one gets between 60 and below). 720 and between
More informationSection 8.4: The Equations of Sinusoidal Functions
Section 8.4: The Equations of Sinusoidal Functions In this section, we will examine transformations of the sine and cosine function and learn how to read various properties from the equation. Transformed
More informationLAB #7: Digital Signal Processing
LAB #7: Digital Signal Processing Equipment: Pentium PC with NI PCI-MIO-16E-4 data-acquisition board NI BNC 2120 Accessory Box VirtualBench Instrument Library version 2.6 Function Generator (Tektronix
More informationSection 2.4 General Sinusoidal Graphs
Section. General Graphs Objective: any one of the following sets of information about a sinusoid, find the other two: ) the equation ) the graph 3) the amplitude, period or frequency, phase displacement,
More informationOrthonormal bases and tilings of the time-frequency plane for music processing Juan M. Vuletich *
Orthonormal bases and tilings of the time-frequency plane for music processing Juan M. Vuletich * Dept. of Computer Science, University of Buenos Aires, Argentina ABSTRACT Conventional techniques for signal
More informationTerminology (1) Chapter 3. Terminology (3) Terminology (2) Transmitter Receiver Medium. Data Transmission. Direct link. Point-to-point.
Terminology (1) Chapter 3 Data Transmission Transmitter Receiver Medium Guided medium e.g. twisted pair, optical fiber Unguided medium e.g. air, water, vacuum Spring 2012 03-1 Spring 2012 03-2 Terminology
More informationSystem analysis and signal processing
System analysis and signal processing with emphasis on the use of MATLAB PHILIP DENBIGH University of Sussex ADDISON-WESLEY Harlow, England Reading, Massachusetts Menlow Park, California New York Don Mills,
More informationEEE 309 Communication Theory
EEE 309 Communication Theory Semester: January 2016 Dr. Md. Farhad Hossain Associate Professor Department of EEE, BUET Email: mfarhadhossain@eee.buet.ac.bd Office: ECE 331, ECE Building Part 05 Pulse Code
More informationProblem Set 1 (Solutions are due Mon )
ECEN 242 Wireless Electronics for Communication Spring 212 1-23-12 P. Mathys Problem Set 1 (Solutions are due Mon. 1-3-12) 1 Introduction The goals of this problem set are to use Matlab to generate and
More informationCHAPTER 4 IMPLEMENTATION OF ADALINE IN MATLAB
52 CHAPTER 4 IMPLEMENTATION OF ADALINE IN MATLAB 4.1 INTRODUCTION The ADALINE is implemented in MATLAB environment running on a PC. One hundred data samples are acquired from a single cycle of load current
More informationExperiment 8: Sampling
Prepared By: 1 Experiment 8: Sampling Objective The objective of this Lab is to understand concepts and observe the effects of periodically sampling a continuous signal at different sampling rates, changing
More informationAliasing. Consider an analog sinusoid, representing perhaps a carrier in a radio communications system,
Aliasing Digital spectrum analyzers work differently than analog spectrum analyzers. If you place an analog sinusoid at the input to an analog spectrum analyzer and if the frequency range displayed by
More informationNyquist's criterion. Spectrum of the original signal Xi(t) is defined by the Fourier transformation as follows :
Nyquist's criterion The greatest part of information sources are analog, like sound. Today's telecommunication systems are mostly digital, so the most important step toward communicating is a signal digitization.
More informationLaboratory Assignment 4. Fourier Sound Synthesis
Laboratory Assignment 4 Fourier Sound Synthesis PURPOSE This lab investigates how to use a computer to evaluate the Fourier series for periodic signals and to synthesize audio signals from Fourier series
More informationLab Report #10 Alex Styborski, Daniel Telesman, and Josh Kauffman Group 12 Abstract
Lab Report #10 Alex Styborski, Daniel Telesman, and Josh Kauffman Group 12 Abstract During lab 10, students carried out four different experiments, each one showing the spectrum of a different wave form.
More informationRepresenting Images and Sounds
11-755 Machine Learning for Signal Processing Representing Images and Sounds Class 4. 2 Sep 2010 Instructor: Bhiksha Raj 2 Sep 2010 1 Administrivia Homework up Basics of probability: Will not be covered
More informationLinguistic Phonetics. Spectral Analysis
24.963 Linguistic Phonetics Spectral Analysis 4 4 Frequency (Hz) 1 Reading for next week: Liljencrants & Lindblom 1972. Assignment: Lip-rounding assignment, due 1/15. 2 Spectral analysis techniques There
More informationComputer Networks. Practice Set I. Dr. Hussein Al-Bahadili
بسم االله الرحمن الرحيم Computer Networks Practice Set I Dr. Hussein Al-Bahadili (1/11) Q. Circle the right answer. 1. Before data can be transmitted, they must be transformed to. (a) Periodic signals
More informationDepartment of Electronic Engineering NED University of Engineering & Technology. LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202)
Department of Electronic Engineering NED University of Engineering & Technology LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202) Instructor Name: Student Name: Roll Number: Semester: Batch:
More informationThe Fast Fourier Transform
The Fast Fourier Transform Basic FFT Stuff That s s Good to Know Dave Typinski, Radio Jove Meeting, July 2, 2014, NRAO Green Bank Ever wonder how an SDR-14 or Dongle produces the spectra that it does?
More informationLecture Schedule: Week Date Lecture Title
http://elec3004.org Sampling & More 2014 School of Information Technology and Electrical Engineering at The University of Queensland Lecture Schedule: Week Date Lecture Title 1 2-Mar Introduction 3-Mar
More informationSignal Sampling. Sampling. Sampling. Sampling. Sampling. Sampling
Signal Let s sample the signal at a time interval o Dr. Christopher M. Godrey University o North Carolina at Asheville Photo: C. Godrey Let s sample the signal at a time interval o Reconstruct the curve
More informationAlgebra and Trig. I. The graph of
Algebra and Trig. I 4.5 Graphs of Sine and Cosine Functions The graph of The graph of. The trigonometric functions can be graphed in a rectangular coordinate system by plotting points whose coordinates
More informationDOWNLOAD PDF THEORY AND AUDIO APPLICATION OF DIGITAL SIGNAL PROCESSING
Chapter 1 : Rabiner & Schafer, Theory and Applications of Digital Speech Processing Pearson Paused You're listening to a sample of the Audible audio edition. Learn more. See all 2 images. Theory And Application
More informationME 365 EXPERIMENT 8 FREQUENCY ANALYSIS
ME 365 EXPERIMENT 8 FREQUENCY ANALYSIS Objectives: There are two goals in this laboratory exercise. The first is to reinforce the Fourier series analysis you have done in the lecture portion of this course.
More informationPYKC 27 Feb 2017 EA2.3 Electronics 2 Lecture PYKC 27 Feb 2017 EA2.3 Electronics 2 Lecture 11-2
In this lecture, I will introduce the mathematical model for discrete time signals as sequence of samples. You will also take a first look at a useful alternative representation of discrete signals known
More informationSignals and Systems Using MATLAB
Signals and Systems Using MATLAB Second Edition Luis F. Chaparro Department of Electrical and Computer Engineering University of Pittsburgh Pittsburgh, PA, USA AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK
More informationIntroduction. Chapter Time-Varying Signals
Chapter 1 1.1 Time-Varying Signals Time-varying signals are commonly observed in the laboratory as well as many other applied settings. Consider, for example, the voltage level that is present at a specific
More informationEEL 4350 Principles of Communication Project 2 Due Tuesday, February 10 at the Beginning of Class
EEL 4350 Principles of Communication Project 2 Due Tuesday, February 10 at the Beginning of Class Description In this project, MATLAB and Simulink are used to construct a system experiment. The experiment
More informationChapter 7. Introduction. Analog Signal and Discrete Time Series. Sampling, Digital Devices, and Data Acquisition
Chapter 7 Sampling, Digital Devices, and Data Acquisition Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Introduction Integrating analog electrical transducers with
More informationThe Electroencephalogram. Basics in Recording EEG, Frequency Domain Analysis and its Applications
The Electroencephalogram Basics in Recording EEG, Frequency Domain Analysis and its Applications Announcements Papers: 1 or 2 paragraph prospectus due no later than Monday March 28 SB 1467 3x5s The Electroencephalogram
More informationSpeech Coding in the Frequency Domain
Speech Coding in the Frequency Domain Speech Processing Advanced Topics Tom Bäckström Aalto University October 215 Introduction The speech production model can be used to efficiently encode speech signals.
More informationSampling Theory. CS5625 Lecture Steve Marschner. Cornell CS5625 Spring 2016 Lecture 7
Sampling Theory CS5625 Lecture 7 Sampling example (reminder) When we sample a high-frequency signal we don t get what we expect result looks like a lower frequency not possible to distinguish between this
More informationspeech signal S(n). This involves a transformation of S(n) into another signal or a set of signals
16 3. SPEECH ANALYSIS 3.1 INTRODUCTION TO SPEECH ANALYSIS Many speech processing [22] applications exploits speech production and perception to accomplish speech analysis. By speech analysis we extract
More informationModulation analysis in ArtemiS SUITE 1
02/18 in ArtemiS SUITE 1 of ArtemiS SUITE delivers the envelope spectra of partial bands of an analyzed signal. This allows to determine the frequency, strength and change over time of amplitude modulations
More informationChapter 1. Electronics and Semiconductors
Chapter 1. Electronics and Semiconductors Tong In Oh 1 Objective Understanding electrical signals Thevenin and Norton representations of signal sources Representation of a signal as the sum of sine waves
More informationAmplitude and Phase Modulation Effects of Waveform Distortion in Power Systems
Electrical Power Quality and Utilisation, Journal Vol. XIII, No., 007 Amplitude and Phase Modulation Effects of Waveform Distortion in Power Systems Roberto LANGELLA and Alfredo ESA Seconda Università
More informationChapter 3 Data and Signals 3.1
Chapter 3 Data and Signals 3.1 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Note To be transmitted, data must be transformed to electromagnetic signals. 3.2
More informationESE 150 Lab 04: The Discrete Fourier Transform (DFT)
LAB 04 In this lab we will do the following: 1. Use Matlab to perform the Fourier Transform on sampled data in the time domain, converting it to the frequency domain 2. Add two sinewaves together of differing
More informationDATA INTEGRATION MULTICARRIER REFLECTOMETRY SENSORS
Report for ECE 4910 Senior Project Design DATA INTEGRATION IN MULTICARRIER REFLECTOMETRY SENSORS Prepared by Afshin Edrissi Date: Apr 7, 2006 1-1 ABSTRACT Afshin Edrissi (Cynthia Furse), Department of
More informationLab 8. Signal Analysis Using Matlab Simulink
E E 2 7 5 Lab June 30, 2006 Lab 8. Signal Analysis Using Matlab Simulink Introduction The Matlab Simulink software allows you to model digital signals, examine power spectra of digital signals, represent
More information8.2 Common Forms of Noise
8.2 Common Forms of Noise Johnson or thermal noise shot or Poisson noise 1/f noise or drift interference noise impulse noise real noise 8.2 : 1/19 Johnson Noise Johnson noise characteristics produced by
More informationCSC475 Music Information Retrieval
CSC475 Music Information Retrieval Sinusoids and DSP notation George Tzanetakis University of Victoria 2014 G. Tzanetakis 1 / 38 Table of Contents I 1 Time and Frequency 2 Sinusoids and Phasors G. Tzanetakis
More informationMel Spectrum Analysis of Speech Recognition using Single Microphone
International Journal of Engineering Research in Electronics and Communication Mel Spectrum Analysis of Speech Recognition using Single Microphone [1] Lakshmi S.A, [2] Cholavendan M [1] PG Scholar, Sree
More informationSuggested Solutions to Examination SSY130 Applied Signal Processing
Suggested Solutions to Examination SSY13 Applied Signal Processing 1:-18:, April 8, 1 Instructions Responsible teacher: Tomas McKelvey, ph 81. Teacher will visit the site of examination at 1:5 and 1:.
More informationUNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering
UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering EXPERIMENT 9 FOURIER SERIES OBJECTIVES After completing this experiment, the student will have Compose arbitrary
More informationData Communication. Chapter 3 Data Transmission
Data Communication Chapter 3 Data Transmission ١ Terminology (1) Transmitter Receiver Medium Guided medium e.g. twisted pair, coaxial cable, optical fiber Unguided medium e.g. air, water, vacuum ٢ Terminology
More informationIn this lecture. System Model Power Penalty Analog transmission Digital transmission
System Model Power Penalty Analog transmission Digital transmission In this lecture Analog Data Transmission vs. Digital Data Transmission Analog to Digital (A/D) Conversion Digital to Analog (D/A) Conversion
More informationPulse Code Modulation
Pulse Code Modulation Modulation is the process of varying one or more parameters of a carrier signal in accordance with the instantaneous values of the message signal. The message signal is the signal
More informationFFT Analyzer. Gianfranco Miele, Ph.D
FFT Analyzer Gianfranco Miele, Ph.D www.eng.docente.unicas.it/gianfranco_miele g.miele@unicas.it Introduction It is a measurement instrument that evaluates the spectrum of a time domain signal applying
More informationUNIT I FUNDAMENTALS OF ANALOG COMMUNICATION Introduction In the Microbroadcasting services, a reliable radio communication system is of vital importance. The swiftly moving operations of modern communities
More informationReal Analog - Circuits 1 Chapter 11: Lab Projects
Real Analog - Circuits 1 Chapter 11: Lab Projects 11.2.1: Signals with Multiple Frequency Components Overview: In this lab project, we will calculate the magnitude response of an electrical circuit and
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY /6.071 Introduction to Electronics, Signals and Measurement Spring 2006
MASSACHUSETTS INSTITUTE OF TECHNOLOGY.071/6.071 Introduction to Electronics, Signals and Measurement Spring 006 Lab. Introduction to signals. Goals for this Lab: Further explore the lab hardware. The oscilloscope
More informationAnalyzing A/D and D/A converters
Analyzing A/D and D/A converters 2013. 10. 21. Pálfi Vilmos 1 Contents 1 Signals 3 1.1 Periodic signals 3 1.2 Sampling 4 1.2.1 Discrete Fourier transform... 4 1.2.2 Spectrum of sampled signals... 5 1.2.3
More information