Sistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2015/16 Aula 3-29 de Setembro
|
|
- Herbert Oliver
- 6 years ago
- Views:
Transcription
1 Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 2015/16 Aula 3-29 de Setembro
2 Aliasing Example fsig=101khz fsig=899 khz All sampled signals are equal! fsig=1101 khz 2
3 How to describe time sampling using Math? -> Dirac Pulses Amostragem de sinais: X = Signal f(t) T = Dirac Comb n= X = n= Sampled Signal (t n T ) f a (t) By definition of Delta function f(t 0 ) = f(t) (t t 0 )dt Sampled signal (continuous time) f a (t) = T f(t) 3
4 The Reconstruction Problem: The sampled signal f a (t) information about the original? (i.e. Is it possible to recover from the sampled version?) carries ALL the f(t) f a (t) Rephrasing the question in the Frequency Domain: Is it possible to recover the original signal s Spectrum??? 4
5 Fourier Transform F (w) = f(t)e iwt dt f(t) = 1 2 F (w)e iwt dw FT Properties: 1) If f(t) is Real 2) Convolution FT g(t) = f 1 (t) f 2 (t) F ( w) = F (w) (Symmetry of FT) f 1 (t) f 2 (t) T F F 1 (w) F 2 (w) (Inverse) f 1 (t) f 2 (t) T F 1 2 F 1(w) F 2 (w) f 1 ( )f 1 (t )d 5
6 Fourier Transform of the Sampled Signal F a (w) = n= n= f a (t) = T f(t) T F (w n ) F (w) = F a (w) = 1 2 T F { T }(w) F (w) n= n= n= n= ( n ) F (w )d F (w n ) F (w) F a (W ) w * =... 2 w... 6
7 Can we recover the original F(w) Spectrum from Fa(w)? F (w) Low Pass Filter F a (W ) w =... 2 w... YES! Sampling Freq F (w) w =... F a (W ) 2 w... NO! In the last case it is impossible to recover the original spectrum 7
8 Frequency Aliasing The frequencies fsig and N fs ± fsig (N integer), are indistinguishable in the discrete time domain 8
9 Nyquist Shannon sampling theorem The frequency spectrum is periodized by the sampling process, and it can overlap: (period WT=2π/Ta) - ALIASING A real signal with a frequency range DC -> Fmax must be sampled at a minimum frequency Fa 2 Fmax To avoid ALIASING for signals with an unknown frequency spectrum we need to eliminate frequency components Fa / 2 by Analog Filters before sampling In a more general way, for real signals with frequency spectrum limited to an bandwidth F= Fmax - Fmin, the minimum sampling frequency, is n: Fa 2 F 9
10 Sampling Limited Bandwidth Signals When fmax M Δf Example: 3 Δ fext = fmax F a (W ) f sam =2 Δf = 2 f max /M When fmax = M Δf ( M integer) F a (W ) Example M= 4 3 f 4 Δf = f max samp = 2 Δf = f max /2 f sam =2 Δ f ext = 2/3 f max 3 Δf ext = f max w -f samp f samp = 2 Δf ext = 2 f max /3 w 3 10
11 Sampling Theorem DC->f max Signals In order to prevent aliasing, we need f sig,max < f s /2 The sampling rate fs=2*f sig,max is called the Nyquist rate Two possibilities: Sample fast enough to cover all spectral components,including "parasitic" ones outside band of interest Limit f sig,max through filtering 11
12 Ideal Brick Wall Anti-Alias Filter There is no Ideal Filters 12
13 Practical Anti-Alias Filters 13
14 Anti-Aliasing Analog Filters Ideal Filter A=1 A=0 Signal with unknown Spectrum Bandwidth LP Filter ADC F (w) Correctly Sampled signal PRATICAL ANALOG! Filter 14
15 Anti-Aliasing Filters For a correct sampling we need to be sure that the image spectrum overlaps only at amplitudes lower than the ADC resolution log( F(w) ) Cutoff of Filter The Bandwidth of the LPF + ADC system will always be inferior to the Nyquist Limit Fsamp /2 Nth-Order LPF Slope = 6 N db/oct = 20 N db/dec Dynamic range of ADC (db) Banda Passante log(w) 15
16 Anti-Aliasing Filter Examples ADC with fsamp= 1 bit Resolution: 60dB (see table in lesson 2) 3rd Order Low Pass Filter: 18 db/oct, 60 db/dec fsamp/2=500 khz System s Analog Bandwidth BW= 50 khz 16
17 Reconstruction of the analog signal from the samples ADC t t t Filter Low-Pass 17
18 How to reconstruct the analog signal from its samples? Frequency Domain: F a (W ) F a (W ) F a (W )... 2 w... LP Filter w = w x a (t) = T f(t) = x[n] (t nt ) n= O Time Domain: To reconstruct the Original Signal we require ALL samples x[n], past and future... x r (t) = x a (t) h P B = n= = x[n] (t nt ) h P B (t) n= x[n] h P B (t nt ) t Filter LP 18
19 Impulse Response of the Ideal L.P. Filter -WT/2 T H(w) WT/2 H P B (w) = T u(w + 2 ) u( 2 w T 2 1 it (ei 2 t T 2 h P B (t) = T e iwt dw = T 2 e i 2 t ) = T 2 w) 1 it 2i sin( 2 H P B (w)e iwt dw = 1 e iwt 2 WT it 2 = t) = sin( t T ) t T 5-4T -3T -2T -1T 0 T 1T 2T 3T 4T 5 t Ideal LPF is NON- CAUSAL!!! It is Not physically possible to build as a LTI 19
20 Causal Reconstruction Filter Translate & Truncate the Impulse Response (Introduce a Delay in Time) T ) (t t 0 ) T h c P B(t) = sin( (t t 0), para t > 0 T1 2T 3T 4T 5T 6T 7T 8T 9T NOTE: Translation in time t t t 0 is equivalent of multiplying the FT by e iwt 0 20
21 D-to-A Conversion (DAC) Ideal DAC Zero hold DAC 21
22 Zero-Hold Equalisation Problem Solutions a) b) 22
23 DAC Conversion Unary conversion Resistor Ladders 23
24 DAC Conversion R-2R Ladders 24
25 DAC Conversion Binary conversion Voltage Converters 25
26 Digital-to-Analog Conversion in the Charge Domain Unary Conversion Binary Conversion 26
27 Digital-to-Analog Conversion in the Time Domain 27
28 Bibliografia Data Conversion Handbook, Chapter 2 Analog Devices Inc., data_conversion_handbook.html Analog-to-Digital Conversion, Second Edition, Marcel J.M. Pelgrom, Springer 2013, Chapter 3 Data Acquisition and Control Handbook, A Guide to Hardware and Software for Computer-Based Measurement and Control, Keithley 28
Sistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2016/17 Class 6, 31st October
Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 2016/17 Class 6, 31st October Digital Signal Processing Applications Audio and speech signal processing, Sonar, Radar Telecommunications,
More informationANALOGUE AND DIGITAL COMMUNICATION
ANALOGUE AND DIGITAL COMMUNICATION Syed M. Zafi S. Shah Umair M. Qureshi Lecture xxx: Analogue to Digital Conversion Topics Pulse Modulation Systems Advantages & Disadvantages Pulse Code Modulation Pulse
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 informationIn The Name of Almighty. Lec. 2: Sampling
In The Name of Almighty Lec. 2: Sampling Lecturer: Hooman Farkhani Department of Electrical Engineering Islamic Azad University of Najafabad Feb. 2016. Email: H_farkhani@yahoo.com A/D and D/A Conversion
More informationSampling and Signal Processing
Sampling and Signal Processing Sampling Methods Sampling is most commonly done with two devices, the sample-and-hold (S/H) and the analog-to-digital-converter (ADC) The S/H acquires a continuous-time signal
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 informationII Year (04 Semester) EE6403 Discrete Time Systems and Signal Processing
Class Subject Code Subject II Year (04 Semester) EE6403 Discrete Time Systems and Signal Processing 1.CONTENT LIST: Introduction to Unit I - Signals and Systems 2. SKILLS ADDRESSED: Listening 3. OBJECTIVE
More informationFundamentals of Data Converters. DAVID KRESS Director of Technical Marketing
Fundamentals of Data Converters DAVID KRESS Director of Technical Marketing 9/14/2016 Analog to Electronic Signal Processing Sensor (INPUT) Amp Converter Digital Processor Actuator (OUTPUT) Amp Converter
More informationSystem on a Chip. Prof. Dr. Michael Kraft
System on a Chip Prof. Dr. Michael Kraft Lecture 5: Data Conversion ADC Background/Theory Examples Background Physical systems are typically analogue To apply digital signal processing, the analogue signal
More informationFrequency Domain Representation of Signals
Frequency Domain Representation of Signals The Discrete Fourier Transform (DFT) of a sampled time domain waveform x n x 0, x 1,..., x 1 is a set of Fourier Coefficients whose samples are 1 n0 X k X0, X
More informationChapter-2 SAMPLING PROCESS
Chapter-2 SAMPLING PROCESS SAMPLING: A message signal may originate from a digital or analog source. If the message signal is analog in nature, then it has to be converted into digital form before it can
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 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 informationFYS3240 PC-based instrumentation and microcontrollers. Signal sampling. Spring 2015 Lecture #5
FYS3240 PC-based instrumentation and microcontrollers Signal sampling Spring 2015 Lecture #5 Bekkeng, 29.1.2015 Content Aliasing Nyquist (Sampling) ADC Filtering Oversampling Triggering Analog Signal Information
More informationCyber-Physical Systems ADC / DAC
Cyber-Physical Systems ADC / DAC ICEN 553/453 Fall 2018 Prof. Dola Saha 1 Analog-to-Digital Converter (ADC) Ø ADC is important almost to all application fields Ø Converts a continuous-time voltage signal
More informationDigital Signal Processing
Digital Signal Processing Lecture 9 Discrete-Time Processing of Continuous-Time Signals Alp Ertürk alp.erturk@kocaeli.edu.tr Analog to Digital Conversion Most real life signals are analog signals These
More information6 Sampling. Sampling. The principles of sampling, especially the benefits of coherent sampling
Note: Printed Manuals 6 are not in Color Objectives This chapter explains the following: The principles of sampling, especially the benefits of coherent sampling How to apply sampling principles in a test
More informationMSK has three important properties. However, the PSD of the MSK only drops by 10log 10 9 = 9.54 db below its midband value at ft b = 0.
Gaussian MSK MSK has three important properties Constant envelope (why?) Relatively narrow bandwidth Coherent detection performance equivalent to that of QPSK However, the PSD of the MSK only drops by
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 informationRecall. Sampling. Why discrete time? Why discrete time? Many signals are continuous-time signals Light Object wave CCD
Recall Many signals are continuous-time signals Light Object wave CCD Sampling mic Lens change of voltage change of voltage 2 Why discrete time? With the advance of computer technology, we want to process
More informationChapter 2: Digitization of Sound
Chapter 2: Digitization of Sound Acoustics pressure waves are converted to electrical signals by use of a microphone. The output signal from the microphone is an analog signal, i.e., a continuous-valued
More informationSampling and Reconstruction
Sampling and Reconstruction Peter Rautek, Eduard Gröller, Thomas Theußl Institute of Computer Graphics and Algorithms Vienna University of Technology Motivation Theory and practice of sampling and reconstruction
More informationAdvanced Digital Signal Processing Part 2: Digital Processing of Continuous-Time Signals
Advanced Digital Signal Processing Part 2: Digital Processing of Continuous-Time Signals Gerhard Schmidt Christian-Albrechts-Universität zu Kiel Faculty of Engineering Institute of Electrical Engineering
More informationFYS3240 PC-based instrumentation and microcontrollers. Signal sampling. Spring 2017 Lecture #5
FYS3240 PC-based instrumentation and microcontrollers Signal sampling Spring 2017 Lecture #5 Bekkeng, 30.01.2017 Content Aliasing Sampling Analog to Digital Conversion (ADC) Filtering Oversampling Triggering
More informationSystem Identification & Parameter Estimation
System Identification & Parameter Estimation Wb2301: SIPE lecture 4 Perturbation signal design Alfred C. Schouten, Dept. of Biomechanical Engineering (BMechE), Fac. 3mE 3/9/2010 Delft University of Technology
More informationECE 484 Digital Image Processing Lec 09 - Image Resampling
ECE 484 Digital Image Processing Lec 09 - Image Resampling Zhu Li Dept of CSEE, UMKC Office: FH560E, Email: lizhu@umkc.edu, Ph: x 2346. http://l.web.umkc.edu/lizhu slides created with WPS Office Linux
More informationModule 3 : Sampling and Reconstruction Problem Set 3
Module 3 : Sampling and Reconstruction Problem Set 3 Problem 1 Shown in figure below is a system in which the sampling signal is an impulse train with alternating sign. The sampling signal p(t), the Fourier
More informationECE 6560 Multirate Signal Processing Chapter 13
Multirate Signal Processing Chapter 13 Dr. Bradley J. Bazuin Western Michigan University College of Engineering and Applied Sciences Department of Electrical and Computer Engineering 1903 W. Michigan Ave.
More informationSampling and Pulse Trains
Sampling and Pulse Trains Sampling and interpolation Practical interpolation Pulse trains Analog multiplexing Sampling Theorem Sampling theorem: a signal g(t) with bandwidth B can be reconstructed exactly
More informationSIGMA-DELTA CONVERTER
SIGMA-DELTA CONVERTER (1995: Pacífico R. Concetti Western A. Geophysical-Argentina) The Sigma-Delta A/D Converter is not new in electronic engineering since it has been previously used as part of many
More informationPulse Code Modulation (PCM)
Project Title: e-laboratories for Physics and Engineering Education Tempus Project: contract # 517102-TEMPUS-1-2011-1-SE-TEMPUS-JPCR 1. Experiment Category: Electrical Engineering >> Communications 2.
More informationCT111 Introduction to Communication Systems Lecture 9: Digital Communications
CT111 Introduction to Communication Systems Lecture 9: Digital Communications Yash M. Vasavada Associate Professor, DA-IICT, Gandhinagar 31st January 2018 Yash M. Vasavada (DA-IICT) CT111: Intro to Comm.
More informationAdvantages of Analog Representation. Varies continuously, like the property being measured. Represents continuous values. See Figure 12.
Analog Signals Signals that vary continuously throughout a defined range. Representative of many physical quantities, such as temperature and velocity. Usually a voltage or current level. Digital Signals
More informationMusic 270a: Fundamentals of Digital Audio and Discrete-Time Signals
Music 270a: Fundamentals of Digital Audio and Discrete-Time Signals Tamara Smyth, trsmyth@ucsd.edu Department of Music, University of California, San Diego October 3, 2016 1 Continuous vs. Discrete signals
More informationPrinciples of Baseband Digital Data Transmission
Principles of Baseband Digital Data Transmission Prof. Wangrok Oh Dept. of Information Communications Eng. Chungnam National University Prof. Wangrok Oh(CNU) / 3 Overview Baseband Digital Data Transmission
More informationLecture 9, ANIK. Data converters 1
Lecture 9, ANIK Data converters 1 What did we do last time? Noise and distortion Understanding the simplest circuit noise Understanding some of the sources of distortion 502 of 530 What will we do today?
More informationEE 230 Lecture 39. Data Converters. Time and Amplitude Quantization
EE 230 Lecture 39 Data Converters Time and Amplitude Quantization Review from Last Time: Time Quantization How often must a signal be sampled so that enough information about the original signal is available
More informationElectronics A/D and D/A converters
Electronics A/D and D/A converters Prof. Márta Rencz, Gábor Takács, Dr. György Bognár, Dr. Péter G. Szabó BME DED December 1, 2014 1 / 26 Introduction The world is analog, signal processing nowadays is
More informationWaveform Encoding - PCM. BY: Dr.AHMED ALKHAYYAT. Chapter Two
Chapter Two Layout: 1. Introduction. 2. Pulse Code Modulation (PCM). 3. Differential Pulse Code Modulation (DPCM). 4. Delta modulation. 5. Adaptive delta modulation. 6. Sigma Delta Modulation (SDM). 7.
More informationBased with permission on lectures by John Getty Laboratory Electronics II (PHSX262) Spring 2011 Lecture 9 Page 1
Today 3// Lecture 9 Analog Digital Conversion Sampled Data Acquisition Systems Discrete Sampling and Nyquist Digital to Analog Conversion Analog to Digital Conversion Homework Study for Exam next week
More informationLecture 3 Review of Signals and Systems: Part 2. EE4900/EE6720 Digital Communications
EE4900/EE6720: Digital Communications 1 Lecture 3 Review of Signals and Systems: Part 2 Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer
More information!"!#"#$% Lecture 2: Media Creation. Some materials taken from Prof. Yao Wang s slides RECAP
Lecture 2: Media Creation Some materials taken from Prof. Yao Wang s slides RECAP #% A Big Umbrella Content Creation: produce the media, compress it to a format that is portable/ deliverable Distribution:
More information2.1 BASIC CONCEPTS Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal.
1 2.1 BASIC CONCEPTS 2.1.1 Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal. 2 Time Scaling. Figure 2.4 Time scaling of a signal. 2.1.2 Classification of Signals
More informationAnnex. 1.3 Measuring information
Annex This appendix discusses the interrelated concepts of information, information source, channel capacity, and bandwidth. The first three concepts relate to a digital channel, while bandwidth concerns
More informationData Acquisition Systems. Signal DAQ System The Answer?
Outline Analysis of Waveforms and Transforms How many Samples to Take Aliasing Negative Spectrum Frequency Resolution Synchronizing Sampling Non-repetitive Waveforms Picket Fencing A Sampled Data System
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 informationLinear Time-Invariant Systems
Linear Time-Invariant Systems Modules: Wideband True RMS Meter, Audio Oscillator, Utilities, Digital Utilities, Twin Pulse Generator, Tuneable LPF, 100-kHz Channel Filters, Phase Shifter, Quadrature Phase
More informationCS3291: Digital Signal Processing
CS39 Exam Jan 005 //08 /BMGC University of Manchester Department of Computer Science First Semester Year 3 Examination Paper CS39: Digital Signal Processing Date of Examination: January 005 Answer THREE
More informationESE 531: Digital Signal Processing
ESE 531: Digital Signal Processing Lec 11: February 20, 2018 Data Converters, Noise Shaping Lecture Outline! Review: Multi-Rate Filter Banks " Quadrature Mirror Filters! Data Converters " Anti-aliasing
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 informationCMPT 318: Lecture 4 Fundamentals of Digital Audio, Discrete-Time Signals
CMPT 318: Lecture 4 Fundamentals of Digital Audio, Discrete-Time Signals Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University January 16, 2006 1 Continuous vs. Discrete
More informationDIGITAL FILTERING OF MULTIPLE ANALOG CHANNELS
DIGITAL FILTERING OF MULTIPLE ANALOG CHANNELS Item Type text; Proceedings Authors Hicks, William T. Publisher International Foundation for Telemetering Journal International Telemetering Conference Proceedings
More informationContinuous vs. Discrete signals. Sampling. Analog to Digital Conversion. CMPT 368: Lecture 4 Fundamentals of Digital Audio, Discrete-Time Signals
Continuous vs. Discrete signals CMPT 368: Lecture 4 Fundamentals of Digital Audio, Discrete-Time Signals Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University January 22,
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 informationDigital Processing of Continuous-Time Signals
Chapter 4 Digital Processing of Continuous-Time Signals 清大電機系林嘉文 cwlin@ee.nthu.edu.tw 03-5731152 Original PowerPoint slides prepared by S. K. Mitra 4-1-1 Digital Processing of Continuous-Time Signals Digital
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 informationMoving from continuous- to discrete-time
Moving from continuous- to discrete-time Sampling ideas Uniform, periodic sampling rate, e.g. CDs at 44.1KHz First we will need to consider periodic signals in order to appreciate how to interpret discrete-time
More informationPROBLEM SET 6. Note: This version is preliminary in that it does not yet have instructions for uploading the MATLAB problems.
PROBLEM SET 6 Issued: 2/32/19 Due: 3/1/19 Reading: During the past week we discussed change of discrete-time sampling rate, introducing the techniques of decimation and interpolation, which is covered
More informationDigital Processing of
Chapter 4 Digital Processing of Continuous-Time Signals 清大電機系林嘉文 cwlin@ee.nthu.edu.tw 03-5731152 Original PowerPoint slides prepared by S. K. Mitra 4-1-1 Digital Processing of Continuous-Time Signals Digital
More informationTelecommunication Electronics
Politecnico di Torino ICT School Telecommunication Electronics C5 - Special A/D converters» Logarithmic conversion» Approximation, A and µ laws» Differential converters» Oversampling, noise shaping Logarithmic
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 informationIntuitive Guide to Fourier Analysis. Charan Langton Victor Levin
Intuitive Guide to Fourier Analysis Charan Langton Victor Levin Much of this book relies on math developed by important persons in the field over the last 2 years. When known or possible, the authors have
More informationAnalog and Telecommunication Electronics
Politecnico di Torino - ICT School Analog and Telecommunication Electronics D5 - Special A/D converters» Differential converters» Oversampling, noise shaping» Logarithmic conversion» Approximation, A and
More informationSignals and Systems. Lecture 13 Wednesday 6 th December 2017 DR TANIA STATHAKI
Signals and Systems Lecture 13 Wednesday 6 th December 2017 DR TANIA STATHAKI READER (ASSOCIATE PROFFESOR) IN SIGNAL PROCESSING IMPERIAL COLLEGE LONDON Continuous time versus discrete time Continuous time
More informationElectrical & Computer Engineering Technology
Electrical & Computer Engineering Technology EET 419C Digital Signal Processing Laboratory Experiments by Masood Ejaz Experiment # 1 Quantization of Analog Signals and Calculation of Quantized noise Objective:
More informationSampling of Continuous-Time Signals. Reference chapter 4 in Oppenheim and Schafer.
Sampling of Continuous-Time Signals Reference chapter 4 in Oppenheim and Schafer. Periodic Sampling of Continuous Signals T = sampling period fs = sampling frequency when expressing frequencies in radians
More informationSignal Processing. Level IV/V CITE, BTS/DUT/Licence. i_5. i_6 LOWPASS. 5 in2. w0 =6000rad/s xi =.8; G =3 lp2a1. mul0. Filtre passe-bas.
Signal Processing Level IV/V CITE, BTS/DUT/Licence. Modulation FSK à phase continue i_8 Tension de commande V1 Interrupt SCOPE AD-DA EVENT Fs = 1E5 Hz 1:1.15 i_4 Modulation FSK à phase continue LOWPASS
More informationCommunications IB Paper 6 Handout 3: Digitisation and Digital Signals
Communications IB Paper 6 Handout 3: Digitisation and Digital Signals Jossy Sayir Signal Processing and Communications Lab Department of Engineering University of Cambridge jossy.sayir@eng.cam.ac.uk Lent
More informationQUESTION BANK. SUBJECT CODE / Name: EC2301 DIGITAL COMMUNICATION UNIT 2
QUESTION BANK DEPARTMENT: ECE SEMESTER: V SUBJECT CODE / Name: EC2301 DIGITAL COMMUNICATION UNIT 2 BASEBAND FORMATTING TECHNIQUES 1. Why prefilterring done before sampling [AUC NOV/DEC 2010] The signal
More informationAnalog and Telecommunication Electronics
Politecnico di Torino Electronic Eng. Master Degree Analog and Telecommunication Electronics D1 - A/D/A conversion systems» Sampling, spectrum aliasing» Quantization error» SNRq vs signal type and level»
More informationThe Fundamentals of Mixed Signal Testing
The Fundamentals of Mixed Signal Testing Course Information The Fundamentals of Mixed Signal Testing course is designed to provide the foundation of knowledge that is required for testing modern mixed
More informationMultipath can be described in two domains: time and frequency
Multipath can be described in two domains: and frequency Time domain: Impulse response Impulse response Frequency domain: Frequency response f Sinusoidal signal as input Frequency response Sinusoidal signal
More informationDesign IV. E232 Spring 07
Design IV Spring 07 Class 8 Bruce McNair bmcnair@stevens.edu 8-1/38 Computerized Data Acquisition Measurement system architecture System under test sensor sensor sensor sensor signal conditioning signal
More informationfor amateur radio applications and beyond...
for amateur radio applications and beyond... Table of contents Numerically Controlled Oscillator (NCO) Basic implementation Optimization for reduced ROM table sizes Achievable performance with FPGA implementations
More informationOverview ta3520 Introduction to seismics
Overview ta3520 Introduction to seismics Fourier Analysis Basic principles of the Seismic Method Interpretation of Raw Seismic Records Seismic Instrumentation Processing of Seismic Reflection Data Vertical
More informationTheoretical 1 Bit A/D Converter
Acquisition 16.1 Chapter 4 - Acquisition D/A converter (or DAC): Digital to Analog converters are used to map a finite number of values onto a physical output range (usually a ) A/D converter (or ADC):
More informationUnderstanding Data Converters SLAA013 July 1995
Understanding Data Converters SLAA03 July 995 Printed on Recycled Paper IMPORTANT NOTICE Texas Instruments (TI) reserves the right to make changes to its products or to discontinue any semiconductor product
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 informationCS4495/6495 Introduction to Computer Vision. 2C-L3 Aliasing
CS4495/6495 Introduction to Computer Vision 2C-L3 Aliasing Recall: Fourier Pairs (from Szeliski) Fourier Transform Sampling Pairs FT of an impulse train is an impulse train Sampling and Aliasing Sampling
More informationEE482: Digital Signal Processing Applications
Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu EE482: Digital Signal Processing Applications Spring 2014 TTh 14:30-15:45 CBC C222 Lecture 01 Introduction 14/01/21 http://www.ee.unlv.edu/~b1morris/ee482/
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 informationPULSE SHAPING AND RECEIVE FILTERING
PULSE SHAPING AND RECEIVE FILTERING Pulse and Pulse Amplitude Modulated Message Spectrum Eye Diagram Nyquist Pulses Matched Filtering Matched, Nyquist Transmit and Receive Filter Combination adaptive components
More informationChapter 3 Data Transmission COSC 3213 Summer 2003
Chapter 3 Data Transmission COSC 3213 Summer 2003 Courtesy of Prof. Amir Asif Definitions 1. Recall that the lowest layer in OSI is the physical layer. The physical layer deals with the transfer of raw
More informationThe Real Facts of Life
The Real Facts of Life Phil Karn, karn@ka9q.net June 13, 2001 The problems in Harold Walker s latest essay, amusingly titled The Facts of Life, start with his very first line: Digital Modulation is usually
More informationFinal Exam Solutions June 7, 2004
Name: Final Exam Solutions June 7, 24 ECE 223: Signals & Systems II Dr. McNames Write your name above. Keep your exam flat during the entire exam period. If you have to leave the exam temporarily, close
More informationFlatten DAC frequency response EQUALIZING TECHNIQUES CAN COPE WITH THE NONFLAT FREQUENCY RESPONSE OF A DAC.
BY KEN YANG MAXIM INTEGRATED PRODUCTS Flatten DAC frequency response EQUALIZING TECHNIQUES CAN COPE WITH THE NONFLAT OF A DAC In a generic example a DAC samples a digital baseband signal (Figure 1) The
More informationFinal Exam. EE313 Signals and Systems. Fall 1999, Prof. Brian L. Evans, Unique No
Final Exam EE313 Signals and Systems Fall 1999, Prof. Brian L. Evans, Unique No. 14510 December 11, 1999 The exam is scheduled to last 50 minutes. Open books and open notes. You may refer to your homework
More information2) How fast can we implement these in a system
Filtration Now that we have looked at the concept of interpolation we have seen practically that a "digital filter" (hold, or interpolate) can affect the frequency response of the overall system. We need
More informationEEE 309 Communication Theory
EEE 309 Communication Theory Semester: January 2017 Dr. Md. Farhad Hossain Associate Professor Department of EEE, BUET Email: mfarhadhossain@eee.buet.ac.bd Office: ECE 331, ECE Building Types of Modulation
More informationSignals and Systems Lecture 6: Fourier Applications
Signals and Systems Lecture 6: Fourier Applications Farzaneh Abdollahi Department of Electrical Engineering Amirkabir University of Technology Winter 2012 arzaneh Abdollahi Signal and Systems Lecture 6
More informationSignals and Systems Lecture 6: Fourier Applications
Signals and Systems Lecture 6: Fourier Applications Farzaneh Abdollahi Department of Electrical Engineering Amirkabir University of Technology Winter 2012 arzaneh Abdollahi Signal and Systems Lecture 6
More informationDigital Filters IIR (& Their Corresponding Analog Filters) Week Date Lecture Title
http://elec3004.com Digital Filters IIR (& Their Corresponding Analog Filters) 2017 School of Information Technology and Electrical Engineering at The University of Queensland Lecture Schedule: Week Date
More informationSpectrum Analysis - Elektronikpraktikum
Spectrum Analysis Introduction Why measure a spectra? In electrical engineering we are most often interested how a signal develops over time. For this time-domain measurement we use the Oscilloscope. Like
More informationDigital Communication (650533) CH 3 Pulse Modulation
Philadelphia University/Faculty of Engineering Communication and Electronics Engineering Digital Communication (650533) CH 3 Pulse Modulation Instructor: Eng. Nada Khatib Website: http://www.philadelphia.edu.jo/academics/nkhatib/
More informationDigital-to-Analog Converter (DAC) Output Response
Digital-to-Analog Converter (DAC) Output Response TIPL 475 Presented by Matt Guibord Prepared by Matt Guibord What is a Digital-to-Analog Converter (DAC)? xff3 x355a x5 xf23e x546 xcc4 x5f6 xab Reconstruction
More informationOutline / Wireless Networks and Applications Lecture 3: Physical Layer Signals, Modulation, Multiplexing. Cartoon View 1 A Wave of Energy
Outline 18-452/18-750 Wireless Networks and Applications Lecture 3: Physical Layer Signals, Modulation, Multiplexing Peter Steenkiste Carnegie Mellon University Spring Semester 2017 http://www.cs.cmu.edu/~prs/wirelesss17/
More informationConcordia University. Discrete-Time Signal Processing. Lab Manual (ELEC442) Dr. Wei-Ping Zhu
Concordia University Discrete-Time Signal Processing Lab Manual (ELEC442) Course Instructor: Dr. Wei-Ping Zhu Fall 2012 Lab 1: Linear Constant Coefficient Difference Equations (LCCDE) Objective In this
More informationMultirate Signal Processing Lecture 7, Sampling Gerald Schuller, TU Ilmenau
Multirate Signal Processing Lecture 7, Sampling Gerald Schuller, TU Ilmenau (Also see: Lecture ADSP, Slides 06) In discrete, digital signal we use the normalized frequency, T = / f s =: it is without a
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 informationAudio /Video Signal Processing. Lecture 1, Organisation, A/D conversion, Sampling Gerald Schuller, TU Ilmenau
Audio /Video Signal Processing Lecture 1, Organisation, A/D conversion, Sampling Gerald Schuller, TU Ilmenau Gerald Schuller gerald.schuller@tu ilmenau.de Organisation: Lecture each week, 2SWS, Seminar
More information