Lecture Schedule: Week Date Lecture Title
|
|
- Alexander Dawson
- 5 years ago
- Views:
Transcription
1 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 Systems Overview 2 9-Mar Signals as Vectors & Systems as Maps 10-Mar [Signals] Sampling & Data Acquisition & 16-Mar Antialiasing Filters 17-Mar [Sampling] 23-Mar System Analysis & Convolution 24-Mar [Convolution & FT] 30-Mar Frequency Response & Filter Analysis 31-Mar [Filters] 13-Apr Discrete Systems & Z-Transforms 14-Apr [Z-Transforms] 20-Apr Introduction to Digital Control 21-Apr [Feedback] 27-Apr Digital Filters 28-Apr [Digital Filters] 4-May Digital Control Design 5-May [Digitial Control] 11-May Stability of Digital Systems 12-May [Stability] 18-May State-Space 19-May Controllability & Observability 25-May PID Control & System Identification 26-May Digitial Control System Hardware 31-May Applications in Industry & Information Theory & Communications 2-Jun Summary and Course Review ELEC 3004: Systems 16 March
2 Interpretations of Systems as Maps ELEC 3004: Systems 16 March Then a System is a MATRIX ELEC 3004: Systems 16 March
3 System Analysis [Chapter 2, Lathi] ELEC 3004: Systems 16 March Linear Differential Systems ELEC 3004: Systems 16 March
4 Linear Differential System Order y(t)=p(d)/q(d) f(t) P(D): M Q(D): N In practice: m n (yes, N is denominator) if m > n: then the system is an (m - n) th -order differentiator of high-frequency signals! Derivatives magnify noise! ELEC 3004: Systems 16 March Derivatives magnify noise! 1 sin(10 t) sin(100 t) cos(10 t) t t) + 2 sin( sin( t) cos(10 t t) + 10 cos(100 t) t t ELEC 3004: Systems 16 March
5 Zero-Input Zero-State Zero Input = The system response when the input f(t) = 0 so that it is the result of internal system conditions (such as energy storages, initial conditions) alone. It is independent of the external input. Zero-State = the system response to the external input f (t) when the system is in zero state, meaning the absence of all internal energy storages; that is, all initial conditions are zero. ELEC 3004: Systems 16 March System Stability Lathi, p. 149 ELEC 3004: Systems 16 March
6 System Stability [II] Lathi, p. 150 ELEC 3004: Systems 16 March System Stability [III] ELEC 3004: Systems 16 March
7 Signals Review ELEC 3004: Systems 16 March Signal: A carrier of (desired) information [1] Need NOT be electrical: Thermometer Clock hands Automobile speedometer Need NOT always being given Abnormal sounds/operations Ex: pitch or engine hum during machining as an indicator for feeds and speeds ELEC 3004: Systems 16 March
8 Signal: A carrier of (desired) information [2] Electrical signals Voltage Current Digital signals Convert analog electrical signals to an appropriate digital electrical message Processing by a microcontroller or microprocessor ELEC 3004: Systems 16 March Ex: Current-to-voltage conversion simple: Precision Resistor better: Use an op amp ELEC 3004: Systems 16 March
9 Sampling! ELEC 3004: Systems 16 March Not this type of sampling ELEC 3004: Systems 16 March
10 This type of sampling Source: Wikipedia: ELEC 3004: Systems 16 March Analog vs Digital Analog Signal: An analog or analogue signal is any variable signal continuous in both time and amplitude Digital Signal: A digital signal is a signal that is both discrete and quantized E.g. Music stored in a CD: 44,100 Samples per second and 16 bits to represent amplitude ELEC 3004: Systems 16 March
11 Expected signal (mv) Expected signal (mv) Digital Signal Representation of a signal against a discrete set The set is fixed in by computing hardware Can be scaled or normalized but is limited Time is also discretized ELEC 3004: Systems 16 March Representation of Signal Time Discretization Digitization 600 Coarse time discretization 600 Coarse signal digitization True signal Discrete time sampled points time (s) 100 True signal Digitization time (s) ELEC 3004: Systems 16 March
12 Mathematics of Sampling and Reconstruction sampling reconstruction x(t) x c (t) DSP Ideal y(t) LPF Impulse train T (t)= (t - n t) t Sampling frequency f s = 1/ t 1 0 Gain f c Freq Cut-off frequency = f c ELEC 3004: Systems 16 March Mathematical Model of Sampling x(t) multiplied by impulse train T(t) x ( t) c x( t) ( t) ( t t) ( t 2 t) x( n t) ( t n t) x c (t) is a train of impulses of height x(t) t=n t n x( t) ( t) T ELEC 3004: Systems 16 March
13 Amplitude x c (t) x(t) 2 Continuous-time t Discrete-time t ELEC 3004: Systems 16 March Discrete Time Signal Image a signal 1 Signal Digitized Signal time (s) ELEC 3004: Systems 16 March
14 Amplitude Amplitude Discrete Time Signals Digitization helps beat the Noise! Signal + 5% Gausian Noise Digitized Noisy Signal time (s) ELEC 3004: Systems 16 March Discrete Time Signals But only so much Signal + 20% Gausian Noise Digitized Noisy Signal time (s) ELEC 3004: Systems 16 March
15 Discrete Time Signals Can make control tricky! ELEC 3004: Systems 16 March Signal Manipulations Shifting Reversal Time Scaling (Down Sampling) (Up Sampling) ELEC 3004: Systems 16 March
16 Frequency Domain Analysis of Sampling Consider the case where the DSP performs no filtering operations i.e., only passes xc(t) to the reconstruction filter To understand we need to look at the frequency domain Sampling: we know multiplication in time convolution in frequency F{x(t)} = X(w) F{ T(t)} = (w - 2 n/ t), i.e., an impulse train in the frequency domain ELEC 3004: Systems 16 March Frequency Domain Analysis of Sampling In the frequency domain we have n X c( w) X ( w)* w 2 t n t 1 2 n X w t n t Remember convolution with an impulse? Same idea for an impulse train Let s look at an example where X(w) is triangular function with maximum frequency w m rad/s being sampled by an impulse train, of frequency w s rad/s ELEC 3004: Systems 16 March
17 Fourier transform of original signal X(ω) (signal spectrum) Fourier transform of impulse train T ( /2 ) (sampling signal) 0 w s = 2 / t 4 / t Fourier transform of sampled signal 1/ t Original Replica 1 Replica 2 w w Original spectrum convolved with spectrum of impulse train ELEC 3004: Systems 16 March Spectrum of sampled signal 1/ t Original Replica 1 Replica 2 Reconstruction filter (ideal lowpass filter) w t -w c w c = w m Spectrum of reconstructed signal w Reconstruction filter removes the replica spectrums & leaves only the original -w m w m ELEC 3004: Systems 16 March w 17
18 Sampling Frequency In this example it was possible to recover the original signal from the discrete-time samples But is this always the case? Consider an example where the sampling frequency w s is reduced i.e., t is increased ELEC 3004: Systems 16 March Original Spectrum -w m w m w Fourier transform of impulse train (sampling signal) 0 2 / t 4 / t 6 / t Amplitude spectrum of sampled signal w Replica spectrums overlap with original (and each other) This is Aliasing w Original Replica 1 Replica 2 16 March ELEC 3004: Systems 49 18
19 Amplitude spectrum of sampled signal Original Replica 1 Replica 2 Reconstruction filter (ideal lowpass filter) sampled signal spectrum w -w c w c = w m Spectrum of reconstructed signal The effect of aliasing is that higher frequencies of alias to (appear as) lower frequencies -w m w m w Due to overlapping replicas (aliasing) the reconstruction filter cannot recover the original spectrum ELEC 3004: Systems 16 March w Sampling Theorem The Nyquist criterion states: To prevent aliasing, a bandlimited signal of bandwidth w B rad/s must be sampled at a rate greater than 2w B rad/s w s > 2w B Note: this is a > sign not a Also note: Most real world signals require band-limiting with a lowpass (anti-aliasing) filter ELEC 3004: Systems 16 March
20 Time Domain Analysis of Sampling Frequency domain analysis of sampling is very useful to understand sampling (X(w)* (w - 2 n/ t) ) reconstruction (lowpass filter removes replicas) aliasing (if w s 2w B ) Time domain analysis can also illustrate the concepts sampling a sinewave of increasing frequency sampling images of a rotating wheel ELEC 3004: Systems 16 March Original signal Discrete-time samples Reconstructed signal A signal of the original frequency is reconstructed ELEC 3004: Systems 16 March
21 signal Original signal Discrete-time samples Reconstructed signal A signal with a reduced frequency is recovered, i.e., the signal is aliased to a lower frequency (we recover a replica) ELEC 3004: Systems 16 March Sampling < Nyquist Aliasing True signal Aliased (under sampled) signal time ELEC 3004: Systems 16 March
22 Normalized magnitude Normalized magnitude Nyquist is not enough 1 1Hz Sin Wave: Sin(2 t) 2 Hz Sampling Time(s) ELEC 3004: Systems 16 March A little more than Nyquist is not enough 1 1Hz Sin Wave: Sin(2 t) 4 Hz Sampling Time(s) ELEC 3004: Systems 16 March
23 Sampled Spectrum w s > 2wm LPF -w m w m w s orignal replica 1 original freq recovered Sampled Spectrum w s < 2w m LPF -w m w m w s w Original and replica spectrums overlap Lower frequency recovered (w s w m ) w orignal replica 1 ELEC 3004: Systems 16 March Temporal Aliasing 90 o clockwise rotation/frame clockwise rotation perceived 270 o clockwise rotation/frame (90 o ) anticlockwise rotation perceived i.e., aliasing Require LPF to blur motion ELEC 3004: Systems 16 March
24 Time Domain Analysis of Reconstruction Frequency domain: multiply by ideal LPF ideal LPF: rect function (gain t, cut off w c ) removes replica spectrums, leaves original Time domain: this is equivalent to convolution with sinc function as F -1 { t rect(w/w c )} = t w c sinc(w c t/ ) i.e., weighted sinc on every sample Normally, w c = w s /2 x ( t) r n x( n t) tw c w sinc c ( t n t) ELEC 3004: Systems 16 March Reconstruction ELEC 3004: Systems 16 March
25 Reconstruction Zero-Order Hold [ZOH] ELEC 3004: Systems 16 March Reconstruction Whittaker Shannon interpolation formula ELEC 3004: Systems 16 March
26 Value Reconstruction Whittaker Shannon interpolation formula ELEC 3004: Systems 16 March Ideal "sinc" Interpolation of sample values [ ] reconstructed signal x r (t) Sample ELEC 3004: Systems 16 March
27 Amplitude (V) Sampling and Reconstruction Theory and Practice Signal is bandlimited to bandwidth WB Problem: real signals are not bandlimited Therefore, require (non-ideal) anti-aliasing filter Signal multiplied by ideal impulse train problems: sample pulses have finite width and not in practice, but sample & hold circuit Samples discrete-time, continuous valued Problem: require discrete values for DSP Therefore, require A/D converter (quantisation) Ideal lowpass reconstruction ( sinc interpolation) problems: ideal lowpass filter not available Therefore, use D/A converter and practical lowpass filter ELEC 3004: Systems 16 March staircase output from D/A converter (ZOH) output samples D/A output Time (sec) ELEC 3004: Systems 16 March
28 Amplitude (V) Amplitude (V) 16 Smooth output from reconstruction filter D/A output Reconstruction filter output Time (sec) ELEC 3004: Systems 16 March Example: error due to signal quantisation original signal x(t) quantised samples x q (t) Sample number ELEC 3004: Systems 16 March
29 Original Signal After Anti-aliasing LPF After Sample & Hold After Reconstruction LPF After D/A After A/D Complete practical DSP system signals DSP ELEC 3004: Systems 16 March Zero Order Hold (ZOH) ZOH impulse response ZOH amplitude response ZOH phase response ELEC 3004: Systems 16 March
30 Finite Width Sampling Impulse train sampling not realisable sample pulses have finite width (say nanosecs) This produces two effects, Impulse train has sinc envelope in frequency domain impulse train is square wave with small duty cycle Reduces amplitude of replica spectrums smaller replicas to remove with reconstruction filter Averaging of signal during sample time effective low pass filter of original signal can reduce aliasing, but can reduce fidelity negligible with most S/H ELEC 3004: Systems 16 March Aliasing: Another view of this ELEC 3004: Systems 16 March
31 Alliasing Aliasing - through sampling, two entirely different analog sinusoids take on the same discrete time identity For f[k]=cosωk, Ω=ωT: The period has to be less than Fh (highest frequency): Thus: ω f : aliased frequency: ELEC 3004: Systems 16 March Practical Anti-aliasing Filter Non-ideal filter wc = ws /2 Filter usually 4th 6th order (e.g., Butterworth) so frequencies > wc may still be present not higher order as phase response gets worse Luckily, most real signals are lowpass in nature signal power reduces with increasing frequency e.g., speech naturally bandlimited (say < 8KHz) Natural signals have a (approx) 1/f spectrum so, in practice aliasing is not (usually) a problem ELEC 3004: Systems 16 March
32 Amplitude spectrum of original signal -w m w m w Fourier transform of sampling signal (pulses have finite width) 0 w s = 2 / t 4 / t Fourier transform of sampled signal 1/ t sinc envelope Zero at harmo 1/duty cycle w Original Replica 1 Replica 2 ELEC 3004: Systems 16 March w Practical Sampling Sample and Hold (S/H) 1. takes a sample every t seconds 2. holds that value constant until next sample Produces staircase waveform, x(n t) sample instant x(n t) x(t) hold for t t ELEC 3004: Systems 16 March
33 Quantisation Analogue to digital converter (A/D) Calculates nearest binary number to x(n t) x q [n] = q(x(n t)), where q() is non-linear rounding fctn output modeled as x q [n] = x(n t) + e[n] Approximation process therefore, loss of information (unrecoverable) known as quantisation noise (e[n]) error reduced as number of bits in A/D increased i.e., x, quantisation step size reduces e[ n] x 2 ELEC 3004: Systems 16 March Input-output for 4-bit quantiser (two s compliment) 2A x m 2 1 where A = max amplitude m = no. quantisation bits Digital x quantisation step size Analogue ELEC 3004: Systems 16 March
34 Signal to Quantisation Noise To estimate SQNR we assume e[n] is uncorrelated to signal and is a uniform random process assumptions not always correct! not the only assumptions we could make Also known a Dynamic range (R D ) expressed in decibels (db) ratio of power of largest signal to smallest (noise) P R D 10log10 P signal noise ELEC 3004: Systems 16 March Dynamic Range Need to estimate: 1. Noise power uniform random process: P noise = x 2 /12 2. Signal power (at least) two possible assumptions 1. sinusoidal: P signal = A 2 /2 2. zero mean Gaussian process: P signal = 2 Note: as A/3: P signal A 2 /9 where 2 = variance, A = signal amplitude 1 extra bit halves x i.e., 20log10(1/2) = 6dB Regardless of assumptions: R D increases by 6dB for every bit that is added to the quantiser ELEC 3004: Systems 16 March
35 Practical Reconstruction Two stage process: 1. Digital to analogue converter (D/A) zero order hold filter produces staircase analogue output 2. Reconstruction filter non-ideal filter: w c = w s /2 further reduces replica spectrums usually 4 th 6 th order e.g., Butterworth for acceptable phase response ELEC 3004: Systems 16 March D/A Converter Analogue output y(t) is convolution of output samples y(n t) with h ZOH (t) y( t) y( n t) h h H ZOH ZOH n ZOH ( t n t) 1, 0 t t ( t) 0, otherwise jw t sin( w t / 2) ( w) t exp 2 w t / 2 D/A is lowpass filter with sinc type frequency response It does not completely remove the replica spectrums Therefore, additional reconstruction filter required ELEC 3004: Systems 16 March
36 Summary Theoretical model of Sampling bandlimited signal (wb) multiplication by ideal impulse train (ws > 2wB) convolution of frequency spectrums (creates replicas) Ideal lowpass filter to remove replica spectrums wc = ws /2 Sinc interpolation Practical systems Anti-aliasing filter (wc < ws /2) A/D (S/H and quantisation) D/A (ZOH) Reconstruction filter (wc = ws /2) Don t confuse theory and practice! ELEC 3004: Systems 16 March
Signals 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationece 429/529 digital signal processing robin n. strickland ece dept, university of arizona ECE 429/529 RNS
ece 429/529 digital signal processing robin n. strickland ece dept, university of arizona 2007 SPRING 2007 SCHEDULE All dates are tentative. Lesson Day Date Learning outcomes to be Topics Textbook HW/PROJECT
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 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 informationLaboratory Assignment 5 Amplitude Modulation
Laboratory Assignment 5 Amplitude Modulation PURPOSE In this assignment, you will explore the use of digital computers for the analysis, design, synthesis, and simulation of an amplitude modulation (AM)
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 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 informationThank you! Estimation + Information Theory. ELEC 3004: Systems 1 June
http://elec3004.org Estimation + Information Theory 2014 School of Information Technology and Electrical Engineering at The University of Queensland Thank you! ELEC 3004: Systems 1 June 2015 2 1 Schedule
More informationPhysical Layer: Outline
18-345: Introduction to Telecommunication Networks Lectures 3: Physical Layer Peter Steenkiste Spring 2015 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital networking Modulation Characterization
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 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 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 information! Multi-Rate Filter Banks (con t) ! Data Converters. " Anti-aliasing " ADC. " Practical DAC. ! Noise Shaping
Lecture Outline ESE 531: Digital Signal Processing! (con t)! Data Converters Lec 11: February 16th, 2017 Data Converters, Noise Shaping " Anti-aliasing " ADC " Quantization "! Noise Shaping 2! Use filter
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 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 informationSistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2015/16 Aula 3-29 de Setembro
Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 2015/16 Aula 3-29 de Setembro Aliasing Example fsig=101khz fsig=899 khz All sampled signals are equal! fsig=1101 khz 2 How to
More informationSampling, interpolation and decimation issues
S-72.333 Postgraduate Course in Radiocommunications Fall 2000 Sampling, interpolation and decimation issues Jari Koskelo 28.11.2000. Introduction The topics of this presentation are sampling, interpolation
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 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 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 informationAnalogue Interfacing. What is a signal? Continuous vs. Discrete Time. Continuous time signals
Analogue Interfacing What is a signal? Signal: Function of one or more independent variable(s) such as space or time Examples include images and speech Continuous vs. Discrete Time Continuous time signals
More informationSignal Processing for Speech Applications - Part 2-1. Signal Processing For Speech Applications - Part 2
Signal Processing for Speech Applications - Part 2-1 Signal Processing For Speech Applications - Part 2 May 14, 2013 Signal Processing for Speech Applications - Part 2-2 References Huang et al., Chapter
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 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 informationAnalog and Digital Signals
E.M. Bakker LML Audio Processing and Indexing 1 Analog and Digital Signals 1. From Analog to Digital Signal 2. Sampling & Aliasing LML Audio Processing and Indexing 2 1 Analog and Digital Signals Analog
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 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 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 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 informationSAMPLING AND RECONSTRUCTING SIGNALS
CHAPTER 3 SAMPLING AND RECONSTRUCTING SIGNALS Many DSP applications begin with analog signals. In order to process these analog signals, the signals must first be sampled and converted to digital signals.
More informationFinal Exam Practice Questions for Music 421, with Solutions
Final Exam Practice Questions for Music 4, with Solutions Elementary Fourier Relationships. For the window w = [/,,/ ], what is (a) the dc magnitude of the window transform? + (b) the magnitude at half
More informationLecture #6: Analog-to-Digital Converter
Lecture #6: Analog-to-Digital Converter All electrical signals in the real world are analog, and their waveforms are continuous in time. Since most signal processing is done digitally in discrete time,
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 informationSIGNALS AND SYSTEMS LABORATORY 13: Digital Communication
SIGNALS AND SYSTEMS LABORATORY 13: Digital Communication INTRODUCTION Digital Communication refers to the transmission of binary, or digital, information over analog channels. In this laboratory you will
More informationLaboratory Assignment 1 Sampling Phenomena
1 Main Topics Signal Acquisition Audio Processing Aliasing, Anti-Aliasing Filters Laboratory Assignment 1 Sampling Phenomena 2.171 Analysis and Design of Digital Control Systems Digital Filter Design and
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 informationDiscrete-time Signals & Systems
Discrete-time Signals & Systems S Wongsa Dept. of Control Systems and Instrumentation Engineering, KMU JAN, 2010 1 Overview Signals & Systems Continuous & Discrete ime Sampling Sampling in Frequency Domain
More informationELEC 3004: Signals, Systems & Control
Noise & Data Acquisition ELEC 3004: Signals, Systems & Control Dr. Surya Singh, Prof. Brian Lovell & Dr. Paul Pounds Lecture # ## May 3, 2012 elec3004@itee.uq.edu.au http://courses.itee.uq.edu.au/elec3004/2012s1/
More informationModule 3 : Sampling & Reconstruction Lecture 26 : Ideal low pass filter
Module 3 : Sampling & Reconstruction Lecture 26 : Ideal low pass filter Objectives: Scope of this Lecture: We saw that the ideal low pass filter can be used to reconstruct the original Continuous time
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 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 informationIntroduction to Discrete-Time Control Systems
Chapter 1 Introduction to Discrete-Time Control Systems 1-1 INTRODUCTION The use of digital or discrete technology to maintain conditions in operating systems as close as possible to desired values despite
More informationFUNDAMENTALS OF ANALOG TO DIGITAL CONVERTERS: PART I.1
FUNDAMENTALS OF ANALOG TO DIGITAL CONVERTERS: PART I.1 Many of these slides were provided by Dr. Sebastian Hoyos January 2019 Texas A&M University 1 Spring, 2019 Outline Fundamentals of Analog-to-Digital
More informationFinal Exam Solutions June 14, 2006
Name or 6-Digit Code: PSU Student ID Number: Final Exam Solutions June 14, 2006 ECE 223: Signals & Systems II Dr. McNames Keep your exam flat during the entire exam. If you have to leave the exam temporarily,
More informationTE 302 DISCRETE SIGNALS AND SYSTEMS. Chapter 1: INTRODUCTION
TE 302 DISCRETE SIGNALS AND SYSTEMS Study on the behavior and processing of information bearing functions as they are currently used in human communication and the systems involved. Chapter 1: INTRODUCTION
More informationDigital Filters IIR (& Their Corresponding Analog Filters) 4 April 2017 ELEC 3004: Systems 1. Week Date Lecture Title
http://elec3004.com Digital Filters IIR (& Their Corresponding Analog Filters) 4 April 017 ELEC 3004: Systems 1 017 School of Information Technology and Electrical Engineering at The University of Queensland
More informationInterfacing a Microprocessor to the Analog World
Interfacing a Microprocessor to the Analog World In many systems, the embedded processor must interface to the non-digital, analog world. The issues involved in such interfacing are complex, and go well
More informationFFT analysis in practice
FFT analysis in practice Perception & Multimedia Computing Lecture 13 Rebecca Fiebrink Lecturer, Department of Computing Goldsmiths, University of London 1 Last Week Review of complex numbers: rectangular
More informationLab.3. Tutorial : (draft) Introduction to CODECs
Lab.3. Tutorial : (draft) Introduction to CODECs Fig. Basic digital signal processing system Definition A codec is a device or computer program capable of encoding or decoding a digital data stream or
More informationBasic Concepts in Data Transmission
Basic Concepts in Data Transmission EE450: Introduction to Computer Networks Professor A. Zahid A.Zahid-EE450 1 Data and Signals Data is an entity that convey information Analog Continuous values within
More informationMicrocomputer Systems 1. Introduction to DSP S
Microcomputer Systems 1 Introduction to DSP S Introduction to DSP s Definition: DSP Digital Signal Processing/Processor It refers to: Theoretical signal processing by digital means (subject of ECE3222,
More informationCommunications I (ELCN 306)
Communications I (ELCN 306) c Samy S. Soliman Electronics and Electrical Communications Engineering Department Cairo University, Egypt Email: samy.soliman@cu.edu.eg Website: http://scholar.cu.edu.eg/samysoliman
More informationAppendix B. Design Implementation Description For The Digital Frequency Demodulator
Appendix B Design Implementation Description For The Digital Frequency Demodulator The DFD design implementation is divided into four sections: 1. Analog front end to signal condition and digitize the
More information15 Discrete-Time Modulation
15 Discrete-Time Modulation The modulation property is basically the same for continuous-time and discrete-time signals. The principal difference is that since for discrete-time signals the Fourier transform
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 informationBrief Introduction to Signals & Systems. Phani Chavali
Brief Introduction to Signals & Systems Phani Chavali Outline Signals & Systems Continuous and discrete time signals Properties of Systems Input- Output relation : Convolution Frequency domain representation
More informationCommunication Theory II
Communication Theory II Lecture 17: Conversion of Analog Waveforms into Coded Pulses Ahmed Elnakib, PhD Assistant Professor, Mansoura University, Egypt April 16 th, 2015 1 opulse Modulation Analog Pulse
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 informationQUESTION BANK SUBJECT: DIGITAL COMMUNICATION (15EC61)
QUESTION BANK SUBJECT: DIGITAL COMMUNICATION (15EC61) Module 1 1. Explain Digital communication system with a neat block diagram. 2. What are the differences between digital and analog communication systems?
More informationSignal Processing Summary
Signal Processing Summary Jan Černocký, Valentina Hubeika {cernocky,ihubeika}@fit.vutbr.cz DCGM FIT BUT Brno, ihubeika@fit.vutbr.cz FIT BUT Brno Signal Processing Summary Jan Černocký, Valentina Hubeika,
More informationDigital AudioAmplifiers: Methods for High-Fidelity Fully Digital Class D Systems
Digital AudioAmplifiers: Methods for High-Fidelity Fully Digital Class D Systems P. T. Krein, Director Grainger Center for Electric Machinery and Electromechanics Dept. of Electrical and Computer Engineering
More informationThe University of Texas at Austin Dept. of Electrical and Computer Engineering Final Exam
The University of Texas at Austin Dept. of Electrical and Computer Engineering Final Exam Date: December 18, 2017 Course: EE 313 Evans Name: Last, First The exam is scheduled to last three hours. Open
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 informationCHAPTER 4. PULSE MODULATION Part 2
CHAPTER 4 PULSE MODULATION Part 2 Pulse Modulation Analog pulse modulation: Sampling, i.e., information is transmitted only at discrete time instants. e.g. PAM, PPM and PDM Digital pulse modulation: Sampling
More informationDigital Signal Processing (Subject Code: 7EC2)
CIITM, JAIPUR (DEPARTMENT OF ELECTRONICS & COMMUNICATION) Notes Digital Signal Processing (Subject Code: 7EC2) Prepared Class: B. Tech. IV Year, VII Semester Syllabus UNIT 1: SAMPLING - Discrete time processing
More informationINF4420 Switched capacitor circuits Outline
INF4420 Switched capacitor circuits Spring 2012 1 / 54 Outline Switched capacitor introduction MOSFET as an analog switch z-transform Switched capacitor integrators 2 / 54 Introduction Discrete time analog
More information10. Chapter: A/D and D/A converter principles
Punčochář, Mohylová: TELO, Chapter 10: A/D and D/A converter principles 1 10. Chapter: A/D and D/A converter principles Time of study: 6 hours Goals: the student should be able to define basic principles
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 informationSignals and Systems Lecture 9 Communication Systems Frequency-Division Multiplexing and Frequency Modulation (FM)
Signals and Systems Lecture 9 Communication Systems Frequency-Division Multiplexing and Frequency Modulation (FM) April 11, 2008 Today s Topics 1. Frequency-division multiplexing 2. Frequency modulation
More informationVoice Transmission --Basic Concepts--
Voice Transmission --Basic Concepts-- Voice---is analog in character and moves in the form of waves. 3-important wave-characteristics: Amplitude Frequency Phase Telephone Handset (has 2-parts) 2 1. Transmitter
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 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 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 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 informationToday s menu. Last lecture. Series mode interference. Noise and interferences R/2 V SM Z L. E Th R/2. Voltage transmission system
Last lecture Introduction to statistics s? Random? Deterministic? Probability density functions and probabilities? Properties of random signals. Today s menu Effects of noise and interferences in measurement
More informationIntroduction to Discrete-Time Control Systems
TU Berlin Discrete-Time Control Systems 1 Introduction to Discrete-Time Control Systems Overview Computer-Controlled Systems Sampling and Reconstruction A Naive Approach to Computer-Controlled Systems
More informationBiomedical Instrumentation B2. Dealing with noise
Biomedical Instrumentation B2. Dealing with noise B18/BME2 Dr Gari Clifford Noise & artifact in biomedical signals Ambient / power line interference: 50 ±0.2 Hz mains noise (or 60 Hz in many data sets)
More informationINF4420. Switched capacitor circuits. Spring Jørgen Andreas Michaelsen
INF4420 Switched capacitor circuits Spring 2012 Jørgen Andreas Michaelsen (jorgenam@ifi.uio.no) Outline Switched capacitor introduction MOSFET as an analog switch z-transform Switched capacitor integrators
More information