DIGITAL signal processing... or just Signal Processing?
|
|
- Sydney Skinner
- 5 years ago
- Views:
Transcription
1 ELECTRICAL AND SYSTEMS ENGINEERING DRAFT DECEMBER 3, ESE 482. Digital Signal Processing R. Martin Arthur Abstract Introduction to analysis and synthesis of discretetime linear shift-invariant (LSI) systems. Discrete-time convolution, discrete-time Fourier transform, z-transform, rational function descriptions of discrete-time LSI systems. Sampling, analog-to-digital conversion, and digital processing of analog signals. Techniques for the design of finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Hardware implementation of digital filters and finite-register effects. The Discrete Fourier Transform and the Fast Fourier Transform (FFT) algorithm. Prerequisite: ESE 351. I. Lecture #1 TAKE THE ROLL on WEDNESDAY A. Introduction DIGITAL signal processing... or just Signal Processing? cf., food processing 1) Objective: To develop quantitative methods to sample, characterize, compress, analyze, interpolate, and recover signals and to design discrete-time systems. That objective does not mean we abandon our judgment and experience in evaluating and interpreting the results of those methods. 2) Prerequisite: Introduction to signals and systems. Topics include Characterization of signals. Example std08n.pdf Solution of differential equations B. Website Show intro-351.a7.ppt in /demo Show algebra.ppt in /demo 1) Catalog description (changes). 2) Signals: two-tone suppression, maury-cheveau maneuver, us thermometry, rma ecg work with mpg 3) rma website 4) Syllabus 5) Handouts: key expressions, etc. 6) Homework will be posted here. Be sure to check for assignments and DUE dates. 7) Office hours, test, final 8) Ethics 9) Matlab Run demosine.m in ese482/mfls R. M. Arthur is with the Department of Electrical and Systems Engineering, Washington University School of Engineering. rma@ese.wustl.edu C. Signal Characteristics Signals: Continuous x(t) and discrete x[n] Run rampstairs.m in ese482/mfls Sample (S/H) Continuous to Discrete Interpolate, Low-Pass Filter Discrete to Continuous Representation in a computer Quantize (A/D) Discrete to Digital Convert (D/A) Digital to Discrete Time Signal-to-noise ratio (SNR): We need to know What s signal? What s noise? Run rnsmplsfn.m in ese482/mfls Source of the signals, noise Gaussian and Poisson (PET, Google) signals? D. Prerequisite Quiz Go over solution to the prerequisite quiz A. Prerequisite Examples 1) Convolution: II. LECTURE #2 System Output Fast convolution using the Fourier transform 2) Transforms: Frequency content of signals Run pltrmadipx.m in ese482/mfls Solution of differential equations RLC circuit with sinusoidal excitation (source) Solve using matrix algebra & the Fourier transform Run lpfcheb.asc in ese482/mfls B. Input/Output Model Input System Output In general there may be many levels of abstraction for a problem. Specifically, in our context there may be many subsystems, i.e., multiple transfer functions that apply to the same problem (state space?). What other signal characteristics would you like to add? Bounded signal? Stable system? What s the difference? NONE for linear signals and systems!
2 2 ELECTRICAL AND SYSTEMS ENGINEERING DRAFT DECEMBER 3, ) Specific Signals: Sinusoids? Exponentials? e jωt e jωn e jωt = cos(ωt) + j sin(ωt) Impulse? δ(t) Unit-Sample? δ[n] 1) Signal Processing: Definition of a Signal Domain & Range 2) Definition of a sequence. Examples: Unit-sample sequence Unit-step sequence 3) Basic definitions Linearity Shift Invariance Unit-Sample Response 4) Examples: Run in /mfls thismom.m demosine.m demontrs.m demontrr.m C. Homework #1 Go over Homework assignment * Go over Quiz on Homework #1 on 3 September The form of the solutions and Matlab figure labeling and program documentation. PREPARE DETAILED, SELF-CONTAINED SOLUTIONS, NOT ANSWERS! (The answers only certify the process & are worth <50%.) Solution to Homework Problem 1.10 as example A digital communication link carries binary-coded words representing samples of an input signal x a (t) = 3 cos 600πt + 2 cos 1800πt (1) The link is operated at 10,000 bits/s and each input sample is quantized into 1024 different voltage levels a) What are the sampling and folding frequencies? b) What is the Nyquist rate for the signal x a (t)? c) What are the frequencies in the resulting discrete-time signal x[n]? d) What is the resolution? SOLUTION Problem Statement: Given a 10kbit link carrying 10-bit samples, find the sample frequency F s, the folding frequency, and the Nyquist rate for x a (t). Find the frequencies in x[n]. Find the distance between quantization levels. Basic definitions Convolution Properties Stability Causality III. LECTURE #3 Sampling: Let x(t) = A cos(ωt) for t = nt, then ω = ΩT Run samsine.m in /mfls Solve homework problems Problem 8. PS: Find the Nyq. Rate for 100 Hz signal. Find the folding frequency for a sample rate of 250s/s Problem 11. PS: Find the output of a discrete-time system that is a 5:1 interpolator of an aliased signal obtained by sampling x a (t) = 3 cos 100πt + 2 sin 250πt at 200 s/s Problem 12. worked in Example Problem 13. PS: Find the number of bits of quantization required to obtain 0.1 and 0.02 resolutions for a ± 6.35 amplitude signal. Administer Quiz 1 IV. LECTURE #4 Go over Quiz #1 Solution and scores Run q1b4.m in /qz1 Comment on Homework #2 and the Answers LTI and LSI system descriptions N th order constant-coefficient differential equations N th order constant-coefficient difference equations Fully documented Matlab scripts and functions Go over contents of demosine.m in /mfls and on website V. LECTURE #5 Go over Homework assignment #3 demosine.m The form of the solutions Matlab problem with fully documented mfile Matlab figure labeling and program documentation Demonstrate genexpt.m in /mfls Run demodeqn.m in /mfls Solution of DEs 1) Direct method: Find the homogeneous and particular solutions y[n] = y h [n] + y p [n] (2) 2) Homogenous solution is always an exponential: y h [n] = λ n (3) Substitute y h [n] into the DE to find the roots of the characteristic equation y h [n] = C 1 λ n 1 + C 2 λ n 2 + C 3 λ n (4) 3) The particular solution y p [n] has the form of the forcing function 4) Combine y h [n] and y p [n] to form the complete solution 5) Use the initial conditions to find the C i s Example solving difference equations Problem 2.49 solving difference equations: build h[n] for S from unit-sample response alone by superposition Administer Quiz 2
3 ARTHUR: ESE 482. DIGITAL SIGNAL PROCESSING DECEMBER 3, VI. LECTURE #6 Quiz #2 Scores on website Run qz2482fb4.m in /quizzes/qz2 Questions on Homework #3? the Matlab exercise? Revisit problem Solve the difference equation, which describes S, by building h[n] from the unit-sample response alone by applying linearity, i.e., using superposition, proportionality and shift invariance. Given y[n] 0.8y[n 1] = 2x[n] + 3x[n 1], then y h [n] = c(0.8) n. Consider simpler system S 1 y[n] 0.8y[n 1] = x 1 [n] = δ[n]. Because y[0] = 1, c = 1 for y 1 [n] = (0.8) n u[n] Consider simpler system S 2 and use shift invariance, y[n] 0.8y[n 1] = x 2 [n 1] = δ[n 1]. Because y[1] = 1, c = 1 for y 2 [n] = (0.8) n 1 u[n 1]. Scale and add y 1 [n] and y 2 [n] to get h[n]. Z transform definition, sampling the Laplace transform X(z) = x[n]z n, for z = e st (5) Inverse Z transforms Power series Long division Partial-fraction expansion Residue theorem VII. LECTURE #7 Review Matlab exercise requirements Go over Homework assignment #4 Z transform properties. See Table 3.2 Describe Figure in /lecture Run pmfig335.m in /mfls Questions on Homework #3 problems Inverse Z transforms Administer Quiz 3 VIII. LECTURE #8 Go over Quiz #3 Solution and scores Run qz3482fb4.m in /quizzes/qz3 Inverse Z transforms Power series Long division Partial-fraction expansion Residue theorem Run invac.m in /mfls IX. LECTURE #9 Go over Homework assignment #5 DUE 1 October Matlab exercise #2 requirements Direct forms I and II and their equivalence Relation of poles & zeros to the frequency response Causality and Stability One-sided z-transform; Solve Problem 3.49 part a Solve problem 3.42: Find h[n] and ZS s[n] z z 2 H(z) = 1 0.6z z 2 (6) Run pmprb342.m in /mfls Run pmprb345.m in /mfls Run pmprb349.m with IC: y[-2]=1,y[-1]=1 in /mfls Administer Quiz 4 X. LECTURE #10 Go over Quiz #4 Solution and scores Frequency Analysis Run demodtft.m in /mfls to demonstrate zero-phase Run fosysfr.m in /mfls to connect genexpt.m exercise result with first-order system behavior Run pltrmadipx.m in /mfls to characterize an ECG for processing, diagnosis, and instrument design Frequency Response: Fourier Transform 1) Characterize a signal for frequency content instrument design equivalent signal representation 2) Perform convolution Factored H(z) on the unit circle H(e jω ): Frequency response Gain in db Frequency response Phase in radians XI. LECTURE #11 Frequency response of a first-order system Effect of a single pole on H(e jω ) Effect of a single zero on H(e jω ) Run iirfireq.m in /mfls to show equivalent FIR pole & zero plot for a first-order (single pole) IIR system Run demompgd.m in /mfls to show effect of poles on group delay Fourier Series & Transform - continuous & discrete Questions on Chapter 4 Administer Quiz 5
4 4 ELECTRICAL AND SYSTEMS ENGINEERING DRAFT DECEMBER 3, 2014 XVI. LECTURE #16 XII. LECTURE #12 Go over Quiz 5: Run qz5fb4.m in /qz5 Go over Matlab Exercise #2: Run ml2fa9.m in /ml2 1) Fourier Series & Transform - continuous & discrete 2) Frequency-Domain Analysis of LSI Systems 3) Effects of an LSI system on sinusoids XIII. SESSION #13 - TEST 1 Test on Wednesday 8 Oct: 4 problems. Each problem similar to a quiz problem Material discussed in class through Fourier transforms of continuous- & discrete-time systems Homework assignments #1 through #5 Assigned text material through chapter 4 on Fourier transforms for both continuous functions and discrete sequences Appropriate subset of tables from the website to be available during the test XIV. LECTURE #14 Go over Test Go over Homework #6 and Matlab Assignment Properties of the Fourier transform, H(e jω ) Find inverse Fourier transform of an ideal low-pass filter Linear-phase systems, example of H(e jω ) = e jωα. Questions on Homework #6 Go over Homework #7 Minimum Phase Transient and steady-state responses Run samsine.m in /mfls Sample Theorem Sampling Administer Quiz 6 XVII. LECTURE #17 Go over Quiz 6 Run qz6fb4.m in /quizzes/ Sampling Ideal Sampler & Practical Samplers Aliasing Sample & Hold Circuits XVIII. LECTURE #18 Group Delay: [ ] τ(ω) = dθ(ω) j dh(e jω ) d(ω) = Re dω H(e jω ) (7) Run demogdly.m in /mfls All Pass, Non-Minimum Phase, Minimum Phase systems Fig. 1. S/H, D/A, & A/D conversion from Proakis & Manolakis, 4th edition. Dispersive Model for Ultrasound Propagation, Ultrasonic Imaging, 4: , in /handouts Run demomnph.m in /mfls to demonstrate minimum phase systems XV. LECTURE #15 Group Delay in tests, circuits and systems Run lfpcheb.asc in /demo Run democheby1.m in /mfls [B,A]=CHEBY1(N,R,Wp), R pkpass ripple, Wp 0-1 Discrete-Time Signal Processing example Run differentiator.m in /demo System Design Chebyshev polynomials in chebypolys.pdf in /lecture Run chebypolys.m in /mfls Sampling & Reconstuction A/D Converters (See Figure??). D/A and A/D Converters Spectrum replication, p6.11 Run demop611.m in /mfls Linear interpolation system, p6.15 Sinc squared is triangle in time, see p a) h(t) a triangle Run pmprb615.m in /mfls H(f) = e j2πft T ( ) 2 sin(πft ) (8) πf H(f) = T e j2πft sinc(πft ) 2 (9) Scale factor, Delay, Sinc squared function Administer Quiz 7
5 ARTHUR: ESE 482. DIGITAL SIGNAL PROCESSING DECEMBER 3, XIX. LECTURE #19 Go over Quiz 7 Run qz7fb4.m in /quizzes/ Go over handout on key expressions Matlab exercise Go over Homework #8 Description & specifications in /homework Due Wednesday, December 3 Run bpfirpm.m Show fsapap91.pdf in /handouts XX. LECTURE #20 Convolution Linear Circular Discrete Fourier Series Discrete Fourier Transform Convolution with the DFT Run imptrain.m in /mlfs Run demofcon.m in /mfls z[111] 2 conv Run convsfcon.m in /mfls XXI. LECTURE #21 Revisit the exercise description Run demorlft.m in /mfls Run demosysd.m in /mfls Run demozpbt.m in /mfls Convolution with the DFT Linear Block Questions on Homework #8 Problems Administer Quiz 8 XXII. LECTURE #22 Go over Quiz 8 Run qz8fb4.m in /quiz8 Go over project description demobcel.m in /mfls Time Frequency Fast Fourier Transform XXIV. LECTURE #24 Go over the last homework assignment (#10), due 12/1 1) Number representation 2) Quantization A/D, coefficients Arithmetic operations Attenuator Questions on Homework #9 Problems Administer Quiz 9 XXV. LECTURE #25 Go over Quiz 9 Run qz9fb4.m in quizzes/qz9 Problem 9.36 (b) lhe nrsr nv1;; output" u... - v ~. ~ The digital system shown in Fig. P9.36 uses a six-bit (including sign) fixed-point twos-complement AID converter with rounding, and the filter H (z) is implemented using eight-bit (including sign) fixed-point twos-complement fractional arithmetic with rounding. The input x(t) is a zero-mean uniformly distribl:lted random process having autocorrelation YxxCr) = 38(r). Assume that the AID converter can handle input values up to ±1.0 without overflow. (a) What value of attenuation should be applied prior to the AID converter to assure that it does not overflow? (b) With the attenuation above, what is the signal-to-quantization-noise ratio (SQNR) at the AID converter output? _, (c) The six-bit AID samples can be left justified, right justified, or centered in the eight-bit word used as the input to the digital filter. What is the correct strategy to use for maximum SNR at the filter output without overflow? (d) What is the SNR at the output of the filter due to all quantization noise sources? Figure P9.36 Fig. 2. r Attenuator l,.,.. J AID converter 6 bits j Filter H(z) (8 bits) x(n) i---~--i + r y(n) 0.75 ~ ~ Problem 9.36 from Proakis & Manolakis, 4th edition. Quantization: Error propogation IIR first-order dead zone FIR structures DFT algorithm IIR structures XXIII. LECTURE #23 Questions on the Matlab Exercise Administer Bidirection QUIZ!!! FFT for N=2 ν = 8 for ν = 3
6 6 ELECTRICAL AND SYSTEMS ENGINEERING DRAFT DECEMBER 3, 2014 XXVI. LECTURE #26 Questions on homework and final Matlab exercise System Design Specification Approximation Implementation Filter Design 1) Analog filter (polynomial) mapping Impulse Invariant h[n]=h(nt) Run demobtwf.m in /mfls Bilinear (no aliasing) s = 1 T log z; z = est (10) s = 2 z 1 T z + 1 ; Ω = 2 T tan ω (11) 2 Run demosysd.m in /mfls 2) Windows Rectangular Hamming: Run wintst.m & wintstm.m in /mfiles 3) Design via Sampling the Ideal Interpolation functions h[n] = idfth[k], H(ω) = FTh[n] Run demorlft.m /mfls XXVII. LECTURE #27 Questions about the Matlab exercise Zero Phase Bi-directional IIR Run bidirex.m in /mfls Run demozpbt.m in /mfls Run tstbtw.m in /mfls Optimal mini-max systems Chebyshev polynomials Equiripple approximation Lagrange interpolation Run bpfirpm.m in /mfls Run optflt.m /mfls Run idlpfsam.m /mfls Alternation Theorem If P (e jω ) is a linear combination of r cosine functions, then a necessary and sufficient condition that P (e jω ) be the unique, best weighted Chebyshev approximation to a continuous function ˆD(e jω ) on A, a subset of (0, π), is that the weighted error function E(e jω ) exhibit at least r + 1 extremal frequencies in A, i.e., there must be r + 1 points on ω i in A such that ω 1 < ω 2... < ω r+1 and for i = 1, 2,..., r and E(e jωi ) = E(e jωi ); E(e jωi ) = max ω A [E(ejωi )] (12) Design Algorithm 1) Specify the desired response D(e jω ), the weighting function W (e j ω), and the length N 2) Formulate the approximation ˆD(e jω ), Ŵ (e jω ), P (e jω ) 3) Solve the approximation problem 4) Calculate the system s unit-sample response h[n] Find the mini-max (L norm) solution for P (e jω ) (firpm) 1) Guess r+1 extremal frequencies 2) Calculate δ (peak error magnitude) on the extremal set 3) Interpolate through the r points to define P (e jω ) 4) Calculate the error function E(e jω ) and find the local maxima where E(e jω ) δ 5) Retain the r+1 largest extrema 6) If the extremal frequencies have changed, go to step 2 XXVIII. LECTURE #28 Timing Run runrmadip.m in /mfls Run demobtwf.m in /mfls Run demosysd.m in /mfls Run fir12vspm.m in /mfls Run *.m below in /mfiles Matlab exercise dft4mat.m to show dft as matrix multiply (roundoff) optflt.m to investigate minimax behavior tstremez.m to design a minimax filter demobcel.m to compare butter, cheby, ellip, and minimax Auto-Correlation and Power Spectral Density Go over homework problems 10.1, 10.22, and Run prob1016a.m /mfls Run zpex.m in /mfls Run bpfirpm.m in /mfls Administer Quiz 10 XXIX. FINAL Monday 12/15, Whitaker 216, 3:30-5:30PM FINAL: 4 Problems of equal weight Emphasis on material since the test Closed book, notes, aid-memoir Tables from the text, as posted on the class website, will be included with the final Final covers: Material discussed in class Reading assignments and homework (& related) problems from the text
EE 521: Instrumentation and Measurements
Aly El-Osery Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA November 1, 2009 1 / 27 1 The z-transform 2 Linear Time-Invariant System 3 Filter Design IIR Filters FIR Filters
More informationLecture 7 Discrete Systems
Lecture 7 Discrete Systems EE 52: Instrumentation and Measurements Lecture Notes Update on November, 29 Aly El-Osery, Electrical Engineering Dept., New Mexico Tech 7. Contents The z-transform 2 Linear
More informationDiscrete-Time David Johns and Ken Martin University of Toronto
Discrete-Time David Johns and Ken Martin University of Toronto (johns@eecg.toronto.edu) (martin@eecg.toronto.edu) University of Toronto 1 of 40 Overview of Some Signal Spectra x c () t st () x s () t xn
More informationVALLIAMMAI ENGINEERING COLLEGE. SRM Nagar, Kattankulathur DEPARTMENT OF INFORMATION TECHNOLOGY. Academic Year
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur- 603 203 DEPARTMENT OF INFORMATION TECHNOLOGY Academic Year 2016-2017 QUESTION BANK-ODD SEMESTER NAME OF THE SUBJECT SUBJECT CODE SEMESTER YEAR
More informationUNIVERSITY OF OSLO. Faculty of mathematics and natural sciences. Forslag til fasit, versjon-01: Problem 1 Signals and systems.
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences Examination in INF3470/4470 Digital signal processing Day of examination: December 1th, 016 Examination hours: 14:30 18.30 This problem set
More informationFILTER DESIGN FOR SIGNAL PROCESSING USING MATLAB AND MATHEMATICAL
FILTER DESIGN FOR SIGNAL PROCESSING USING MATLAB AND MATHEMATICAL Miroslav D. Lutovac The University of Belgrade Belgrade, Yugoslavia Dejan V. Tosic The University of Belgrade Belgrade, Yugoslavia Brian
More informationDigital Signal Processing Lecture 8 - Filter Design - IIR
Digital Signal Processing - Filter Design - IIR Electrical Engineering and Computer Science University of Tennessee, Knoxville October 20, 2015 Overview 1 2 3 4 5 6 Roadmap Discrete-time signals and systems
More informationReview of Discrete-Time System
Review of Discrete-Time System Electrical & Computer Engineering University of Maryland, College Park Acknowledgment: ENEE630 slides were based on class notes developed by Profs. K.J. Ray Liu and Min Wu.
More information! Introduction. ! Discrete Time Signals & Systems. ! Z-Transform. ! Inverse Z-Transform. ! Sampling of Continuous Time Signals
ESE 531: Digital Signal Processing Lec 25: April 24, 2018 Review Course Content! Introduction! Discrete Time Signals & Systems! Discrete Time Fourier Transform! Z-Transform! Inverse Z-Transform! Sampling
More informationSignals and Systems. Problem Set: The z-transform and DT Fourier Transform
Signals and Systems Problem Set: The z-transform and DT Fourier Transform Updated: October 9, 7 Problem Set Problem - Transfer functions in MATLAB A discrete-time, causal LTI system is described by the
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 05 IIR Design 14/03/04 http://www.ee.unlv.edu/~b1morris/ee482/
More informationE : Lecture 1 Introduction
E85.2607: Lecture 1 Introduction 1 Administrivia 2 DSP review 3 Fun with Matlab E85.2607: Lecture 1 Introduction 2010-01-21 1 / 24 Course overview Advanced Digital Signal Theory Design, analysis, and implementation
More informationQuestion Bank. UNIT 1 Part-A
FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY Senkottai Village, Madurai Sivagangai Main Road, Madurai -625 020 An ISO 9001:2008 Certified Institution Question Bank DEPARTMENT OF ELECTRONICS AND COMMUNICATION
More informationDigital Signal Processing Lecture 10 - Discrete Fourier Transform
Digital Signal Processing - Discrete Fourier Transform Electrical Engineering and Computer Science University of Tennessee, Knoxville November 12, 2015 Overview 1 2 3 4 Review - 1 Introduction Discrete-time
More informationUNIVERSITY OF OSLO. Please make sure that your copy of the problem set is complete before you attempt to answer anything.
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences Examination in INF3470/4470 Digital signal processing Day of examination: December 9th, 011 Examination hours: 14.30 18.30 This problem set
More information/ (2π) X(e jω ) dω. 4. An 8 point sequence is given by x(n) = {2,2,2,2,1,1,1,1}. Compute 8 point DFT of x(n) by
Code No: RR320402 Set No. 1 III B.Tech II Semester Regular Examinations, Apr/May 2006 DIGITAL SIGNAL PROCESSING ( Common to Electronics & Communication Engineering, Electronics & Instrumentation Engineering,
More informationEE 225D LECTURE ON DIGITAL FILTERS. University of California Berkeley
University of California Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences Professors : N.Morgan / B.Gold EE225D Digital Filters Spring,1999 Lecture 7 N.MORGAN
More informationAnalysis of Finite Wordlength Effects
Analysis of Finite Wordlength Effects Ideally, the system parameters along with the signal variables have infinite precision taing any value between and In practice, they can tae only discrete values within
More informationLike bilateral Laplace transforms, ROC must be used to determine a unique inverse z-transform.
Inversion of the z-transform Focus on rational z-transform of z 1. Apply partial fraction expansion. Like bilateral Laplace transforms, ROC must be used to determine a unique inverse z-transform. Let X(z)
More informationGrades will be determined by the correctness of your answers (explanations are not required).
6.00 (Fall 2011) Final Examination December 19, 2011 Name: Kerberos Username: Please circle your section number: Section Time 2 11 am 1 pm 4 2 pm Grades will be determined by the correctness of your answers
More informationMultimedia Signals and Systems - Audio and Video. Signal, Image, Video Processing Review-Introduction, MP3 and MPEG2
Multimedia Signals and Systems - Audio and Video Signal, Image, Video Processing Review-Introduction, MP3 and MPEG2 Kunio Takaya Electrical and Computer Engineering University of Saskatchewan December
More informationDHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EC2314- DIGITAL SIGNAL PROCESSING UNIT I INTRODUCTION PART A
DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EC2314- DIGITAL SIGNAL PROCESSING UNIT I INTRODUCTION PART A Classification of systems : Continuous and Discrete
More informationDigital Signal Processing
COMP ENG 4TL4: Digital Signal Processing Notes for Lecture #24 Tuesday, November 4, 2003 6.8 IIR Filter Design Properties of IIR Filters: IIR filters may be unstable Causal IIR filters with rational system
More informationDFT & Fast Fourier Transform PART-A. 7. Calculate the number of multiplications needed in the calculation of DFT and FFT with 64 point sequence.
SHRI ANGALAMMAN COLLEGE OF ENGINEERING & TECHNOLOGY (An ISO 9001:2008 Certified Institution) SIRUGANOOR,TRICHY-621105. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING UNIT I DFT & Fast Fourier
More informationCourse Name: Digital Signal Processing Course Code: EE 605A Credit: 3
Course Name: Digital Signal Processing Course Code: EE 605A Credit: 3 Prerequisites: Sl. No. Subject Description Level of Study 01 Mathematics Fourier Transform, Laplace Transform 1 st Sem, 2 nd Sem 02
More informationIntroduction to DSP Time Domain Representation of Signals and Systems
Introduction to DSP Time Domain Representation of Signals and Systems Dr. Waleed Al-Hanafy waleed alhanafy@yahoo.com Faculty of Electronic Engineering, Menoufia Univ., Egypt Digital Signal Processing (ECE407)
More informationIT DIGITAL SIGNAL PROCESSING (2013 regulation) UNIT-1 SIGNALS AND SYSTEMS PART-A
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING IT6502 - DIGITAL SIGNAL PROCESSING (2013 regulation) UNIT-1 SIGNALS AND SYSTEMS PART-A 1. What is a continuous and discrete time signal? Continuous
More informationEE 224 Signals and Systems I Review 1/10
EE 224 Signals and Systems I Review 1/10 Class Contents Signals and Systems Continuous-Time and Discrete-Time Time-Domain and Frequency Domain (all these dimensions are tightly coupled) SIGNALS SYSTEMS
More informationDISCRETE-TIME SIGNAL PROCESSING
THIRD EDITION DISCRETE-TIME SIGNAL PROCESSING ALAN V. OPPENHEIM MASSACHUSETTS INSTITUTE OF TECHNOLOGY RONALD W. SCHÄFER HEWLETT-PACKARD LABORATORIES Upper Saddle River Boston Columbus San Francisco New
More informationDigital Signal Processing. Midterm 1 Solution
EE 123 University of California, Berkeley Anant Sahai February 15, 27 Digital Signal Processing Instructions Midterm 1 Solution Total time allowed for the exam is 8 minutes Some useful formulas: Discrete
More informationGATE EE Topic wise Questions SIGNALS & SYSTEMS
www.gatehelp.com GATE EE Topic wise Questions YEAR 010 ONE MARK Question. 1 For the system /( s + 1), the approximate time taken for a step response to reach 98% of the final value is (A) 1 s (B) s (C)
More informationCITY UNIVERSITY LONDON. MSc in Information Engineering DIGITAL SIGNAL PROCESSING EPM746
No: CITY UNIVERSITY LONDON MSc in Information Engineering DIGITAL SIGNAL PROCESSING EPM746 Date: 19 May 2004 Time: 09:00-11:00 Attempt Three out of FIVE questions, at least One question from PART B PART
More informationGrades will be determined by the correctness of your answers (explanations are not required).
6.00 (Fall 20) Final Examination December 9, 20 Name: Kerberos Username: Please circle your section number: Section Time 2 am pm 4 2 pm Grades will be determined by the correctness of your answers (explanations
More informationRadar Systems Engineering Lecture 3 Review of Signals, Systems and Digital Signal Processing
Radar Systems Engineering Lecture Review of Signals, Systems and Digital Signal Processing Dr. Robert M. O Donnell Guest Lecturer Radar Systems Course Review Signals, Systems & DSP // Block Diagram of
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 02 DSP Fundamentals 14/01/21 http://www.ee.unlv.edu/~b1morris/ee482/
More informationThe Laplace Transform
The Laplace Transform Syllabus ECE 316, Spring 2015 Final Grades Homework (6 problems per week): 25% Exams (midterm and final): 50% (25:25) Random Quiz: 25% Textbook M. Roberts, Signals and Systems, 2nd
More informationNAME: ht () 1 2π. Hj0 ( ) dω Find the value of BW for the system having the following impulse response.
University of California at Berkeley Department of Electrical Engineering and Computer Sciences Professor J. M. Kahn, EECS 120, Fall 1998 Final Examination, Wednesday, December 16, 1998, 5-8 pm NAME: 1.
More informationELEG 305: Digital Signal Processing
ELEG 305: Digital Signal Processing Lecture : Design of Digital IIR Filters (Part I) Kenneth E. Barner Department of Electrical and Computer Engineering University of Delaware Fall 008 K. E. Barner (Univ.
More informationLecture 16: Filter Design: Impulse Invariance and Bilinear Transform
EE58 Digital Signal Processing University of Washington Autumn 2 Dept. of Electrical Engineering Lecture 6: Filter Design: Impulse Invariance and Bilinear Transform Nov 26, 2 Prof: J. Bilmes
More informationDigital Signal Processing Lecture 9 - Design of Digital Filters - FIR
Digital Signal Processing - Design of Digital Filters - FIR Electrical Engineering and Computer Science University of Tennessee, Knoxville November 3, 2015 Overview 1 2 3 4 Roadmap Introduction Discrete-time
More informationNAME: 11 December 2013 Digital Signal Processing I Final Exam Fall Cover Sheet
NAME: December Digital Signal Processing I Final Exam Fall Cover Sheet Test Duration: minutes. Open Book but Closed Notes. Three 8.5 x crib sheets allowed Calculators NOT allowed. This test contains four
More informationECGR4124 Digital Signal Processing Exam 2 Spring 2017
ECGR4124 Digital Signal Processing Exam 2 Spring 2017 Name: LAST 4 NUMBERS of Student Number: Do NOT begin until told to do so Make sure that you have all pages before starting NO TEXTBOOK, NO CALCULATOR,
More informationDiscrete-time signals and systems
Discrete-time signals and systems 1 DISCRETE-TIME DYNAMICAL SYSTEMS x(t) G y(t) Linear system: Output y(n) is a linear function of the inputs sequence: y(n) = k= h(k)x(n k) h(k): impulse response of the
More informationDiscrete-Time Fourier Transform (DTFT)
Discrete-Time Fourier Transform (DTFT) 1 Preliminaries Definition: The Discrete-Time Fourier Transform (DTFT) of a signal x[n] is defined to be X(e jω ) x[n]e jωn. (1) In other words, the DTFT of x[n]
More informationDigital Signal Processing. Lecture Notes and Exam Questions DRAFT
Digital Signal Processing Lecture Notes and Exam Questions Convolution Sum January 31, 2006 Convolution Sum of Two Finite Sequences Consider convolution of h(n) and g(n) (M>N); y(n) = h(n), n =0... M 1
More informationLecture 3 - Design of Digital Filters
Lecture 3 - Design of Digital Filters 3.1 Simple filters In the previous lecture we considered the polynomial fit as a case example of designing a smoothing filter. The approximation to an ideal LPF can
More informationFinal Exam January 31, Solutions
Final Exam January 31, 014 Signals & Systems (151-0575-01) Prof. R. D Andrea & P. Reist Solutions Exam Duration: Number of Problems: Total Points: Permitted aids: Important: 150 minutes 7 problems 50 points
More informationLAB 6: FIR Filter Design Summer 2011
University of Illinois at Urbana-Champaign Department of Electrical and Computer Engineering ECE 311: Digital Signal Processing Lab Chandra Radhakrishnan Peter Kairouz LAB 6: FIR Filter Design Summer 011
More informationIT6502 DIGITAL SIGNAL PROCESSING Unit I - SIGNALS AND SYSTEMS Basic elements of DSP concepts of frequency in Analo and Diital Sinals samplin theorem Discrete time sinals, systems Analysis of discrete time
More informationEach problem is worth 25 points, and you may solve the problems in any order.
EE 120: Signals & Systems Department of Electrical Engineering and Computer Sciences University of California, Berkeley Midterm Exam #2 April 11, 2016, 2:10-4:00pm Instructions: There are four questions
More informationEC Signals and Systems
UNIT I CLASSIFICATION OF SIGNALS AND SYSTEMS Continuous time signals (CT signals), discrete time signals (DT signals) Step, Ramp, Pulse, Impulse, Exponential 1. Define Unit Impulse Signal [M/J 1], [M/J
More information6.003 (Fall 2011) Quiz #3 November 16, 2011
6.003 (Fall 2011) Quiz #3 November 16, 2011 Name: Kerberos Username: Please circle your section number: Section Time 2 11 am 3 1 pm 4 2 pm Grades will be determined by the correctness of your answers (explanations
More informationRoll No. :... Invigilator s Signature :.. CS/B.Tech (EE-N)/SEM-6/EC-611/ DIGITAL SIGNAL PROCESSING. Time Allotted : 3 Hours Full Marks : 70
Name : Roll No. :.... Invigilator s Signature :.. CS/B.Tech (EE-N)/SEM-6/EC-611/2011 2011 DIGITAL SIGNAL PROCESSING Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks.
More information-Digital Signal Processing- FIR Filter Design. Lecture May-16
-Digital Signal Processing- FIR Filter Design Lecture-17 24-May-16 FIR Filter Design! FIR filters can also be designed from a frequency response specification.! The equivalent sampled impulse response
More informationUNIT - III PART A. 2. Mention any two techniques for digitizing the transfer function of an analog filter?
UNIT - III PART A. Mention the important features of the IIR filters? i) The physically realizable IIR filters does not have linear phase. ii) The IIR filter specification includes the desired characteristics
More informationRoundoff Noise in Digital Feedback Control Systems
Chapter 7 Roundoff Noise in Digital Feedback Control Systems Digital control systems are generally feedback systems. Within their feedback loops are parts that are analog and parts that are digital. At
More informationECE-314 Fall 2012 Review Questions for Midterm Examination II
ECE-314 Fall 2012 Review Questions for Midterm Examination II First, make sure you study all the problems and their solutions from homework sets 4-7. Then work on the following additional problems. Problem
More informationQUESTION BANK SIGNALS AND SYSTEMS (4 th SEM ECE)
QUESTION BANK SIGNALS AND SYSTEMS (4 th SEM ECE) 1. For the signal shown in Fig. 1, find x(2t + 3). i. Fig. 1 2. What is the classification of the systems? 3. What are the Dirichlet s conditions of Fourier
More informationLab 4: Quantization, Oversampling, and Noise Shaping
Lab 4: Quantization, Oversampling, and Noise Shaping Due Friday 04/21/17 Overview: This assignment should be completed with your assigned lab partner(s). Each group must turn in a report composed using
More informationDiscrete-time Signals and Systems in
Discrete-time Signals and Systems in the Frequency Domain Chapter 3, Sections 3.1-39 3.9 Chapter 4, Sections 4.8-4.9 Dr. Iyad Jafar Outline Introduction The Continuous-Time FourierTransform (CTFT) The
More informationEEL3135: Homework #4
EEL335: Homework #4 Problem : For each of the systems below, determine whether or not the system is () linear, () time-invariant, and (3) causal: (a) (b) (c) xn [ ] cos( 04πn) (d) xn [ ] xn [ ] xn [ 5]
More informationVery useful for designing and analyzing signal processing systems
z-transform z-transform The z-transform generalizes the Discrete-Time Fourier Transform (DTFT) for analyzing infinite-length signals and systems Very useful for designing and analyzing signal processing
More informationCommunications and Signal Processing Spring 2017 MSE Exam
Communications and Signal Processing Spring 2017 MSE Exam Please obtain your Test ID from the following table. You must write your Test ID and name on each of the pages of this exam. A page with missing
More informationECGR4124 Digital Signal Processing Final Spring 2009
ECGR4124 Digital Signal Processing Final Spring 2009 Name: LAST 4 NUMBERS of Student Number: Do NOT begin until told to do so Make sure that you have all pages before starting Open book, 2 sheet front/back
More informationMultidimensional digital signal processing
PSfrag replacements Two-dimensional discrete signals N 1 A 2-D discrete signal (also N called a sequence or array) is a function 2 defined over thex(n set 1 of, n 2 ordered ) pairs of integers: y(nx 1,
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts
More informationLecture 9 Infinite Impulse Response Filters
Lecture 9 Infinite Impulse Response Filters Outline 9 Infinite Impulse Response Filters 9 First-Order Low-Pass Filter 93 IIR Filter Design 5 93 CT Butterworth filter design 5 93 Bilinear transform 7 9
More informationFinal Exam of ECE301, Section 1 (Prof. Chih-Chun Wang) 1 3pm, Friday, December 13, 2016, EE 129.
Final Exam of ECE301, Section 1 (Prof. Chih-Chun Wang) 1 3pm, Friday, December 13, 2016, EE 129. 1. Please make sure that it is your name printed on the exam booklet. Enter your student ID number, and
More informationFrequency-Domain C/S of LTI Systems
Frequency-Domain C/S of LTI Systems x(n) LTI y(n) LTI: Linear Time-Invariant system h(n), the impulse response of an LTI systems describes the time domain c/s. H(ω), the frequency response describes the
More informationIntroduction to Digital Signal Processing
Introduction to Digital Signal Processing 1.1 What is DSP? DSP is a technique of performing the mathematical operations on the signals in digital domain. As real time signals are analog in nature we need
More informationDigital Filters Ying Sun
Digital Filters Ying Sun Digital filters Finite impulse response (FIR filter: h[n] has a finite numbers of terms. Infinite impulse response (IIR filter: h[n] has infinite numbers of terms. Causal filter:
More informationDIGITAL SIGNAL PROCESSING UNIT 1 SIGNALS AND SYSTEMS 1. What is a continuous and discrete time signal? Continuous time signal: A signal x(t) is said to be continuous if it is defined for all time t. Continuous
More informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500 043 Title Code Regulation ELECTRONICS AND COMMUNICATION ENGINEERING TUTORIAL QUESTION BANK DIGITAL SIGNAL PROCESSING A60421 R13 Structure
More informationAnalog vs. discrete signals
Analog vs. discrete signals Continuous-time signals are also known as analog signals because their amplitude is analogous (i.e., proportional) to the physical quantity they represent. Discrete-time signals
More informationX. Chen More on Sampling
X. Chen More on Sampling 9 More on Sampling 9.1 Notations denotes the sampling time in second. Ω s = 2π/ and Ω s /2 are, respectively, the sampling frequency and Nyquist frequency in rad/sec. Ω and ω denote,
More informationQuestion Paper Code : AEC11T02
Hall Ticket No Question Paper Code : AEC11T02 VARDHAMAN COLLEGE OF ENGINEERING (AUTONOMOUS) Affiliated to JNTUH, Hyderabad Four Year B. Tech III Semester Tutorial Question Bank 2013-14 (Regulations: VCE-R11)
More informationDesign of IIR filters
Design of IIR filters Standard methods of design of digital infinite impulse response (IIR) filters usually consist of three steps, namely: 1 design of a continuous-time (CT) prototype low-pass filter;
More informationECSE 512 Digital Signal Processing I Fall 2010 FINAL EXAMINATION
FINAL EXAMINATION 9:00 am 12:00 pm, December 20, 2010 Duration: 180 minutes Examiner: Prof. M. Vu Assoc. Examiner: Prof. B. Champagne There are 6 questions for a total of 120 points. This is a closed book
More informationProblem Value Score No/Wrong Rec
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING QUIZ #2 DATE: 14-Oct-11 COURSE: ECE-225 NAME: GT username: LAST, FIRST (ex: gpburdell3) 3 points 3 points 3 points Recitation
More informationFilter Analysis and Design
Filter Analysis and Design Butterworth Filters Butterworth filters have a transfer function whose squared magnitude has the form H a ( jω ) 2 = 1 ( ) 2n. 1+ ω / ω c * M. J. Roberts - All Rights Reserved
More informationExercises in Digital Signal Processing
Exercises in Digital Signal Processing Ivan W. Selesnick September, 5 Contents The Discrete Fourier Transform The Fast Fourier Transform 8 3 Filters and Review 4 Linear-Phase FIR Digital Filters 5 5 Windows
More informationELEN 4810 Midterm Exam
ELEN 4810 Midterm Exam Wednesday, October 26, 2016, 10:10-11:25 AM. One sheet of handwritten notes is allowed. No electronics of any kind are allowed. Please record your answers in the exam booklet. Raise
More informationDiscrete Time Systems
1 Discrete Time Systems {x[0], x[1], x[2], } H {y[0], y[1], y[2], } Example: y[n] = 2x[n] + 3x[n-1] + 4x[n-2] 2 FIR and IIR Systems FIR: Finite Impulse Response -- non-recursive y[n] = 2x[n] + 3x[n-1]
More informationProblem Value
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL & COMPUTER ENGINEERING FINAL EXAM DATE: 30-Apr-04 COURSE: ECE-2025 NAME: GT #: LAST, FIRST Recitation Section: Circle the date & time when your Recitation
More informationSignals and Systems Laboratory with MATLAB
Signals and Systems Laboratory with MATLAB Alex Palamides Anastasia Veloni @ CRC Press Taylor &. Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa
More informationECE 301 Fall 2010 Division 2 Homework 10 Solutions. { 1, if 2n t < 2n + 1, for any integer n, x(t) = 0, if 2n 1 t < 2n, for any integer n.
ECE 3 Fall Division Homework Solutions Problem. Reconstruction of a continuous-time signal from its samples. Consider the following periodic signal, depicted below: {, if n t < n +, for any integer n,
More informationDigital Signal Processing Module 1 Analysis of Discrete time Linear Time - Invariant Systems
Digital Signal Processing Module 1 Analysis of Discrete time Linear Time - Invariant Systems Objective: 1. To understand the representation of Discrete time signals 2. To analyze the causality and stability
More informationTheory and Problems of Signals and Systems
SCHAUM'S OUTLINES OF Theory and Problems of Signals and Systems HWEI P. HSU is Professor of Electrical Engineering at Fairleigh Dickinson University. He received his B.S. from National Taiwan University
More informationDepartment of Electrical and Telecommunications Engineering Technology TEL (718) FAX: (718) Courses Description:
NEW YORK CITY COLLEGE OF TECHNOLOGY The City University of New York 300 Jay Street Brooklyn, NY 11201-2983 Department of Electrical and Telecommunications Engineering Technology TEL (718) 260-5300 - FAX:
More informationAspects of Continuous- and Discrete-Time Signals and Systems
Aspects of Continuous- and Discrete-Time Signals and Systems C.S. Ramalingam Department of Electrical Engineering IIT Madras C.S. Ramalingam (EE Dept., IIT Madras) Networks and Systems 1 / 45 Scaling the
More informationModule 4. Related web links and videos. 1. FT and ZT
Module 4 Laplace transforms, ROC, rational systems, Z transform, properties of LT and ZT, rational functions, system properties from ROC, inverse transforms Related web links and videos Sl no Web link
More informationAnalog to Digital Converters (ADCs)
Analog to Digital Converters (ADCs) Note: Figures are copyrighted Proakis & Manolakis, Digital Signal Processing, 4 th Edition, Pearson Publishers. Embedded System Design A Unified HW Approach, Vahid/Givargis,
More informationA system that is both linear and time-invariant is called linear time-invariant (LTI).
The Cooper Union Department of Electrical Engineering ECE111 Signal Processing & Systems Analysis Lecture Notes: Time, Frequency & Transform Domains February 28, 2012 Signals & Systems Signals are mapped
More informationA.1 THE SAMPLED TIME DOMAIN AND THE Z TRANSFORM. 0 δ(t)dt = 1, (A.1) δ(t)dt =
APPENDIX A THE Z TRANSFORM One of the most useful techniques in engineering or scientific analysis is transforming a problem from the time domain to the frequency domain ( 3). Using a Fourier or Laplace
More informationIntroduction to Biomedical Engineering
Introduction to Biomedical Engineering Biosignal processing Kung-Bin Sung 6/11/2007 1 Outline Chapter 10: Biosignal processing Characteristics of biosignals Frequency domain representation and analysis
More informationChap 2. Discrete-Time Signals and Systems
Digital Signal Processing Chap 2. Discrete-Time Signals and Systems Chang-Su Kim Discrete-Time Signals CT Signal DT Signal Representation 0 4 1 1 1 2 3 Functional representation 1, n 1,3 x[ n] 4, n 2 0,
More informationReview of Linear System Theory
Review of Linear System Theory The following is a (very) brief review of linear system theory and Fourier analysis. I work primarily with discrete signals. I assume the reader is familiar with linear algebra
More informationChapter 7: Filter Design 7.1 Practical Filter Terminology
hapter 7: Filter Design 7. Practical Filter Terminology Analog and digital filters and their designs constitute one of the major emphasis areas in signal processing and communication systems. This is due
More informationComputer Engineering 4TL4: Digital Signal Processing
Computer Engineering 4TL4: Digital Signal Processing Day Class Instructor: Dr. I. C. BRUCE Duration of Examination: 3 Hours McMaster University Final Examination December, 2003 This examination paper includes
More informationCh. 7: Z-transform Reading
c J. Fessler, June 9, 3, 6:3 (student version) 7. Ch. 7: Z-transform Definition Properties linearity / superposition time shift convolution: y[n] =h[n] x[n] Y (z) =H(z) X(z) Inverse z-transform by coefficient
More information