Signal Processing. Introduction
|
|
- Terence Morton
- 5 years ago
- Views:
Transcription
1 Signal Processing 0 Introduction One of the premiere uses of MATLAB is in the analysis of signal processing and control systems. In this chapter we consider signal processing. The final chapter of the text considers control systems. To efficiently support signal processing and control system problem solving in MATLAB requires the Signal Processing Toolbox and Control System Toolbox respectively. The student edition of MATLAB 5.0 fully supports both of these toolboxes. Two forms of signal processing are: Analog or continuous-time signal processing (ASP), using analog electronic circuits Digital signal processing (DSP), using discrete-time algorithms running on computers In this chapter of the notes we will deviate from the text Chapter 0 and focus more on specific applications of signal processing Chapter 0: Introduction 0
2 Sinusoidal Signals One of the simplest signals that we deal with in both the continuous and discrete time domains is the cosine function x c () t = A cos( 2πf t + φ ), t (0.) A signal composed of a single sinusoid has three specific attributes: The sinusoid has amplitude A (units of voltage or current) The sinusoid oscillates with frequency f (units of cycles per second or Hz if t has units of seconds) The sinusoid is phase shifted by φ (units of radians or degrees) x c () t is known as a time-domain representation of a signal A second, and equally useful representation of a signal, is the frequency domain Frequency Domain The frequency domain representation of a single sinusoid consists of both an amplitude spectrum and a phase spectrum The amplitude spectrum is a plot of signal amplitude versus frequency The phase spectrum is a plot of signal phase versus frequency Chapter 0: Sinusoidal Signals 0 2
3 Formally, the spectrum of x c () t, denoted X c () f, is obtained by taking the Fourier transform, i.e., X c () f = x c t ()e j2πft dt (0.2) For a sinusoid the complexity of (0.2) is not really needed Intuitively, the spectrum of a single sinusoid is as shown below A x c () t cos φ t X c () f A Amplitude Spectrum A Period T = --- f Time Domain Freq. Domain 0 f f, Hz Chapter 0: Sinusoidal Signals 0 3
4 We now extend the above frequency domain intuition to a signal composed of two sinusoids x c () t = A cos( 2πf t + φ ) + A 2 cos ( 2πf 2 t + φ 2 ) (0.3) # A # T = --- A f 2 x c () t T 2 = --- f 2 t t t X c () f Amplitude Spectrum A A 2 Time Domain Freq. Domain f, Hz 0 f f 2 Chapter 0: Sinusoidal Signals 0 4
5 Discrete-Time Sinusoids Digital signal processing of a continuous-time or analog signals can be accomplished by uniformly sampling x c () t every T seconds, e.g., xn [ ] = x c ( nt) = A cos( 2πf nt+ φ ), n (0.4) A discrete-time or digital signal is just a sampled version of a corresponding analog signal A single sinuoid is again characterized by three attributes Actually there is now a fourth attribute, T, the sampling period or its inverse, the sampling frequency = T To avoid aliasing, a condition that occurs when analog signals are sampled, we must have the sampling frequency, f s, greater than twice the highest frequency component contained in x c () t If we violate this condition the higher frequencies of the signal, those exceeding f s 2, will alias as lower frequencies in the frequency range 0 to f s 2 Typically a digital signal is stored on memory as a data record or processed in real-time following analog-to-digital conversion An N-point data record is typically stored with starting index 0 and ending index N, e.g., when captured from an analog signal we might have xn [ ] = x c ( nt), n = 0,,, N f s (0.5) Chapter 0: Sinusoidal Signals 0 5
6 In MATLAB we typically display a discrete-time or digital signal using the stem() function Popular sampling frequencies used in PC sound systems are submultiples of the compact disc (CD) audio standard which has f s = 44.kHz Example: Discrete-time Sinusoid Generation Suppose we wish to created a sampled sinusoid which has a frequency of 000 Hz, is sampled at 44,00/4 =,025 Hz, and has duration of approximately 2 seconds A 2 second record will contain = samples MATLAB Code to Generate the sinusoid:» % Create a signal index first» N = 22050;» n = 0:N-;» x = cos(2*pi*000*n/025);» % Plot a small of portion of the signal» stem(n(:50),x(:50))» title(' khz Sinusoid with fs =.025 khz',... 'fontsize',8)» ylabel('amplitude','fontsize',4)» xlabel('sequence Index - n','fontsize',4) Assuming your computer is equipped with a sound card, this 2 second record can be played using the MATLAB function sound(x,fs)» Play the sound vector x with fs = 025 Hz» sound(x,025) Chapter 0: Sinusoidal Signals 0 6
7 khz Sinusoid with fs =.025 khz Amplitude Sequence Index - n Note: Each sample in the above signal is spaced by T = / 025 sec with respect to the underlying analog signal Discrete-Time Sinusoids in the Frequency Domain A frequency domain representation of a discrete-time signal can be obtained through the use of the fast Fourier transform (FFT), formally defined for an N-point data record as N j2πkn N Xk [ ] = xn [ ]e, k = 0,,, N n = 0 (0.6) Chapter 0: Sinusoidal Signals 0 7
8 In MATLAB this is accomplished using fft(n) or fft(x,n) where N is the number of points used in the FFT If the vector x has length greater than N points, the record x is truncated to N points If the vector x has length less than N points, the record is zero padded (zeros are appended to x) to length N The function X=fft(x,N) returns a length N complex vector, X, whose magnitude is proportional to the amplitude spectrum of xn [ ] and whose angle is the phase spectrum of xn [ ] Each index of X corresponds to an analog frequency of f k = in the spectrum of k ---f N s, 0 k N x c () t, that is X c () f Example: Continuation of the single sinusoid example (0.7) Using MATLAB the spectrum of the vector x used in the previous example is» X = fft(x(:28),024); % N=28pts padded to 024pts» % Create a frequency axis vector on 0 to fs/2» f = [0:52]*025/024;» plot(f,abs(x(:53)))» grid» title(' khz Sinusoid Spectrum (fs =.025 khz)',... 'fontsize',8)» ylabel(' X(k) ','fontsize',4)» xlabel('index k Scaled to Frequency in Hz',... 'fontsize',4) Chapter 0: Sinusoidal Signals 0 8
9 70 khz Sinusoid Spectrum (fs =.025 khz) 60 X[k] A Single Spectral Line at 000 Hz as Expected Index k Scaled to Frequency in Hz Note: The amplitude is scaling does not match the singlesided spectrum of a sinusoid shown earlier unless we divide by the record length over two, i.e., plot Xk [ ] 2 N Transfer Functions and Filters Both analog and digital signals can be processed by filters to produce modified signals. The MATLAB signal processing toolbox contains a vast array of filter design functions. Chapter 0: Transfer Functions and Filters 0 9
10 Analog Frequency Response (Transfer) Functions Consider a sinusoid passing through an analog filter Acos( 2πf o t + θ) Analog Bcos ( 2πf o t + θ + φ ) x c () t Filter y c () t A sinusoid is returned at the output, but the amplitude and phase are modified by the filters frequency response function A B θ θ + φ In the frequency domain a filter is described as having a frequency response function (a complex function of frequency) which tells us the amplitude gain and phase shift imparted to a sinusoidal signal at a particular frequency If the analog filter depicted above has frequency response function H c () f, then the output sinusoid is related to the input sinuoid and H c () f as follows y c () t = AH c ( f o ) cos [ 2πf o t + θ + H c () f ] (0.8) The four main filter types are lowpass, highpass, bandpass, and bandstop f c f c Lowpass f Highpass f B f o f o Bandpass f Bandstop f Chapter 0: Transfer Functions and Filters 0 0
11 Analog lowpass filters are usually designed to meet a set of amplitude response requirements in the frequency domain Lowpass Filter A p Transition Band H c () f A s 0 0 Passband f p f s Stopband f The actual filter amplitude response, H c () f, just needs to fall within the white space A p is the minimum filter gain in the passband A s is the maximum filter gain in the stopband MATLAB has a collection of functions in the signal processing toolbox that designs analog filters in transfer function form, i.e., Hf () = b 0 s n + b s n + + b n a 0 s n + a s n + + a n Digital Frequency Response Functions In the discrete-time domain filters can also be designed The same basic concepts apply (0.9) When a discrete-time sinusoid is applied to a linear filter, s = j2πf Chapter 0: Transfer Functions and Filters 0
12 the output is a sinusoid of the same frequency, but amplitude attenuated and phase shifted Given a digital filter has frequency response Hf () we can write for xn [ ] = Acos ( 2πf o nt) that yn [ ] = AHf ( o ) cos [ 2πf o nt + θ + Hf ( o ) ] Applications Compact Disc Digital Audio (0.0) Digital audio, CD digital audio, relies on real-time digital signal processing, coding theory, and control theory to function CD recording frame format CD sync subcode Data (96 bits) Data (96 bits) Parity (32 bits) The raw input rate for stereo is.4 Mb/s ( ), but with overhead this is increased to Mb/s An hour of music requires about 5.5 Billion bits Parity (32 bits) Maximum playing time is about 74 minutes, enough for Beethoven s 9th symphony Chapter 0: Applications 0 2
13 Communication Systems Consider the commercial broadcast frequency spectrum Frequency Spectrum AM Radio FM stereo receiver TV khz MHz FM Radio MHz TV MHz Spectrum at Discriminator Output L + R 9 khz Pilot ( L R ) cos ( 2πf sc ) LPF 0-5 khz L + R + Σ + L Limiter Discriminator BPF ~9 khz BPF 23-53kHz Demodulator + - Σ L R R Chapter 0: Applications 0 3
14 Bat Echo Location Signal Processing Bat echo-locate using frequency chirps above the human hearing range To allow humans to listen to bat echo location we must first frequency translate the bat chirp frequency spectrum down to the human hearing range Bat Echo Location Human Hearing f, khz Frequency Translate a Portion into Human Range The front-end to a system for processing bat chirps is a microphone array The output is an audio signal that can be recorded on magnetic tape (a cassette) and later digitized using a PC audio system Chapter 0: Applications 0 4
Lecture 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 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 informationSignal Processing. Naureen Ghani. December 9, 2017
Signal Processing Naureen Ghani December 9, 27 Introduction Signal processing is used to enhance signal components in noisy measurements. It is especially important in analyzing time-series data in neuroscience.
More informationECE 3793 Matlab Project 4
ECE 3793 Matlab Project 4 Spring 2017 Dr. Havlicek DUE: 5/3/2017, 11:59 PM What to Turn In: Make one file that contains your solution for this assignment. It can be an MS WORD file or a PDF file. For Problem
More informationOutline. Communications Engineering 1
Outline Introduction Signal, random variable, random process and spectra Analog modulation Analog to digital conversion Digital transmission through baseband channels Signal space representation Optimal
More information1. In the command window, type "help conv" and press [enter]. Read the information displayed.
ECE 317 Experiment 0 The purpose of this experiment is to understand how to represent signals in MATLAB, perform the convolution of signals, and study some simple LTI systems. Please answer all questions
More informationLaboratory Assignment 4. Fourier Sound Synthesis
Laboratory Assignment 4 Fourier Sound Synthesis PURPOSE This lab investigates how to use a computer to evaluate the Fourier series for periodic signals and to synthesize audio signals from Fourier series
More 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 informationGEORGIA INSTITUTE OF TECHNOLOGY. SCHOOL of ELECTRICAL and COMPUTER ENGINEERING. ECE 2026 Summer 2018 Lab #8: Filter Design of FIR Filters
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2026 Summer 2018 Lab #8: Filter Design of FIR Filters Date: 19. Jul 2018 Pre-Lab: You should read the Pre-Lab section of
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 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 informationSignal Processing Toolbox
Signal Processing Toolbox Perform signal processing, analysis, and algorithm development Signal Processing Toolbox provides industry-standard algorithms for analog and digital signal processing (DSP).
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 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 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 informationECE438 - Laboratory 7a: Digital Filter Design (Week 1) By Prof. Charles Bouman and Prof. Mireille Boutin Fall 2015
Purdue University: ECE438 - Digital Signal Processing with Applications 1 ECE438 - Laboratory 7a: Digital Filter Design (Week 1) By Prof. Charles Bouman and Prof. Mireille Boutin Fall 2015 1 Introduction
More information(i) Understanding of the characteristics of linear-phase finite impulse response (FIR) filters
FIR Filter Design Chapter Intended Learning Outcomes: (i) Understanding of the characteristics of linear-phase finite impulse response (FIR) filters (ii) Ability to design linear-phase FIR filters according
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 informationECE 2713 Design Project Solution
ECE 2713 Design Project Solution Spring 218 Dr. Havlicek 1. (a) Matlab code: ---------------------------------------------------------- P1a Make a 2 second digital audio signal that contains a pure cosine
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 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 informationTopic 2. Signal Processing Review. (Some slides are adapted from Bryan Pardo s course slides on Machine Perception of Music)
Topic 2 Signal Processing Review (Some slides are adapted from Bryan Pardo s course slides on Machine Perception of Music) Recording Sound Mechanical Vibration Pressure Waves Motion->Voltage Transducer
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 information(i) Understanding of the characteristics of linear-phase finite impulse response (FIR) filters
FIR Filter Design Chapter Intended Learning Outcomes: (i) Understanding of the characteristics of linear-phase finite impulse response (FIR) filters (ii) Ability to design linear-phase FIR filters according
More informationArmstrong Atlantic State University Engineering Studies MATLAB Marina Sound Processing Primer
Armstrong Atlantic State University Engineering Studies MATLAB Marina Sound Processing Primer Prerequisites The Sound Processing Primer assumes knowledge of the MATLAB IDE, MATLAB help, arithmetic operations,
More informationProblem Set 1 (Solutions are due Mon )
ECEN 242 Wireless Electronics for Communication Spring 212 1-23-12 P. Mathys Problem Set 1 (Solutions are due Mon. 1-3-12) 1 Introduction The goals of this problem set are to use Matlab to generate and
More informationDiscrete Fourier Transform (DFT)
Amplitude Amplitude Discrete Fourier Transform (DFT) DFT transforms the time domain signal samples to the frequency domain components. DFT Signal Spectrum Time Frequency DFT is often used to do frequency
More informationSTANFORD UNIVERSITY. DEPARTMENT of ELECTRICAL ENGINEERING. EE 102B Spring 2013 Lab #05: Generating DTMF Signals
STANFORD UNIVERSITY DEPARTMENT of ELECTRICAL ENGINEERING EE 102B Spring 2013 Lab #05: Generating DTMF Signals Assigned: May 3, 2013 Due Date: May 17, 2013 Remember that you are bound by the Stanford University
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 informationDSP First. Laboratory Exercise #2. Introduction to Complex Exponentials
DSP First Laboratory Exercise #2 Introduction to Complex Exponentials The goal of this laboratory is gain familiarity with complex numbers and their use in representing sinusoidal signals as complex exponentials.
More informationPROBLEM SET 5. Reminder: Quiz 1will be on March 6, during the regular class hour. Details to follow. z = e jω h[n] H(e jω ) H(z) DTFT.
PROBLEM SET 5 Issued: 2/4/9 Due: 2/22/9 Reading: During the past week we continued our discussion of the impact of pole/zero locations on frequency response, focusing on allpass systems, minimum and maximum-phase
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 informationECE 2713 Homework 7 DUE: 05/1/2018, 11:59 PM
Spring 2018 What to Turn In: ECE 2713 Homework 7 DUE: 05/1/2018, 11:59 PM Dr. Havlicek Submit your solution for this assignment electronically on Canvas by uploading a file to ECE-2713-001 > Assignments
More informationLaboratory Assignment 2 Signal Sampling, Manipulation, and Playback
Laboratory Assignment 2 Signal Sampling, Manipulation, and Playback PURPOSE This lab will introduce you to the laboratory equipment and the software that allows you to link your computer to the hardware.
More informationFourier Transform Analysis of Signals and Systems
Fourier Transform Analysis of Signals and Systems Ideal Filters Filters separate what is desired from what is not desired In the signals and systems context a filter separates signals in one frequency
More informationCG401 Advanced Signal Processing. Dr Stuart Lawson Room A330 Tel: January 2003
CG40 Advanced Dr Stuart Lawson Room A330 Tel: 23780 e-mail: ssl@eng.warwick.ac.uk 03 January 2003 Lecture : Overview INTRODUCTION What is a signal? An information-bearing quantity. Examples of -D and 2-D
More informationENGR 210 Lab 12: Sampling and Aliasing
ENGR 21 Lab 12: Sampling and Aliasing In the previous lab you examined how A/D converters actually work. In this lab we will consider some of the consequences of how fast you sample and of the signal processing
More informationTeam proposals are due tomorrow at 6PM Homework 4 is due next thur. Proposal presentations are next mon in 1311EECS.
Lecture 8 Today: Announcements: References: FIR filter design IIR filter design Filter roundoff and overflow sensitivity Team proposals are due tomorrow at 6PM Homework 4 is due next thur. Proposal presentations
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 Signal Processing Lecture 1 - Introduction
Digital Signal Processing - Electrical Engineering and Computer Science University of Tennessee, Knoxville August 20, 2015 Overview 1 2 3 4 Basic building blocks in DSP Frequency analysis Sampling Filtering
More informationLABORATORY - FREQUENCY ANALYSIS OF DISCRETE-TIME SIGNALS
LABORATORY - FREQUENCY ANALYSIS OF DISCRETE-TIME SIGNALS INTRODUCTION The objective of this lab is to explore many issues involved in sampling and reconstructing signals, including analysis of the frequency
More informationContents. Introduction 1 1 Suggested Reading 2 2 Equipment and Software Tools 2 3 Experiment 2
ECE363, Experiment 02, 2018 Communications Lab, University of Toronto Experiment 02: Noise Bruno Korst - bkf@comm.utoronto.ca Abstract This experiment will introduce you to some of the characteristics
More informationSpeech, music, images, and video are examples of analog signals. Each of these signals is characterized by its bandwidth, dynamic range, and the
Speech, music, images, and video are examples of analog signals. Each of these signals is characterized by its bandwidth, dynamic range, and the nature of the signal. For instance, in the case of audio
More informationDSP Laboratory (EELE 4110) Lab#10 Finite Impulse Response (FIR) Filters
Islamic University of Gaza OBJECTIVES: Faculty of Engineering Electrical Engineering Department Spring-2011 DSP Laboratory (EELE 4110) Lab#10 Finite Impulse Response (FIR) Filters To demonstrate the concept
More informationTHE CITADEL THE MILITARY COLLEGE OF SOUTH CAROLINA. Department of Electrical and Computer Engineering. ELEC 423 Digital Signal Processing
THE CITADEL THE MILITARY COLLEGE OF SOUTH CAROLINA Department of Electrical and Computer Engineering ELEC 423 Digital Signal Processing Project 2 Due date: November 12 th, 2013 I) Introduction In ELEC
More informationAliasing. Consider an analog sinusoid, representing perhaps a carrier in a radio communications system,
Aliasing Digital spectrum analyzers work differently than analog spectrum analyzers. If you place an analog sinusoid at the input to an analog spectrum analyzer and if the frequency range displayed by
More 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 informationELEC3104: Digital Signal Processing Session 1, 2013
ELEC3104: Digital Signal Processing Session 1, 2013 The University of New South Wales School of Electrical Engineering and Telecommunications LABORATORY 1: INTRODUCTION TO TIMS AND MATLAB INTRODUCTION
More informationWaveshaping Synthesis. Indexing. Waveshaper. CMPT 468: Waveshaping Synthesis
Waveshaping Synthesis CMPT 468: Waveshaping Synthesis Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University October 8, 23 In waveshaping, it is possible to change the spectrum
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 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 Channels
Communication Channels wires (PCB trace or conductor on IC) optical fiber (attenuation 4dB/km) broadcast TV (50 kw transmit) voice telephone line (under -9 dbm or 110 µw) walkie-talkie: 500 mw, 467 MHz
More informationFFT Analyzer. Gianfranco Miele, Ph.D
FFT Analyzer Gianfranco Miele, Ph.D www.eng.docente.unicas.it/gianfranco_miele g.miele@unicas.it Introduction It is a measurement instrument that evaluates the spectrum of a time domain signal applying
More informationLab 0: Introduction to TIMS AND MATLAB
TELE3013 TELECOMMUNICATION SYSTEMS 1 Lab 0: Introduction to TIMS AND MATLAB 1. INTRODUCTION The TIMS (Telecommunication Instructional Modelling System) system was first developed by Tim Hooper, then a
More informationF I R Filter (Finite Impulse Response)
F I R Filter (Finite Impulse Response) Ir. Dadang Gunawan, Ph.D Electrical Engineering University of Indonesia The Outline 7.1 State-of-the-art 7.2 Type of Linear Phase Filter 7.3 Summary of 4 Types FIR
More informationDSP First Lab 03: AM and FM Sinusoidal Signals. We have spent a lot of time learning about the properties of sinusoidal waveforms of the form: k=1
DSP First Lab 03: AM and FM Sinusoidal Signals Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up sections of this lab assignment and go over all exercises in the Pre-Lab section before
More informationSubtractive Synthesis. Describing a Filter. Filters. CMPT 468: Subtractive Synthesis
Subtractive Synthesis CMPT 468: Subtractive Synthesis Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University November, 23 Additive synthesis involves building the sound 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 informationWireless Communication
ECEN 242 Wireless Electronics for Communication Spring 22-3-2 P. Mathys Wireless Communication Brief History In 893 Nikola Tesla (Serbian-American, 856 943) gave lectures in Philadelphia before the Franklin
More informationCharan Langton, Editor
Charan Langton, Editor SIGNAL PROCESSING & SIMULATION NEWSLETTER Baseband, Passband Signals and Amplitude Modulation The most salient feature of information signals is that they are generally low frequency.
More informationEBU5375 Signals and Systems: Filtering and sampling in Matlab. Dr Jesús Requena Carrión
EBU5375 Signals and Systems: Filtering and sampling in Matlab Dr Jesús Requena Carrión Background: Ideal filters We have learnt three types of filters: lowpass, highpass and bandpass filters. We represent
More informationMultirate Digital Signal Processing
Multirate Digital Signal Processing Basic Sampling Rate Alteration Devices Up-sampler - Used to increase the sampling rate by an integer factor Down-sampler - Used to increase the sampling rate by an integer
More informationL A B 3 : G E N E R A T I N G S I N U S O I D S
L A B 3 : G E N E R A T I N G S I N U S O I D S NAME: DATE OF EXPERIMENT: DATE REPORT SUBMITTED: 1/7 1 THEORY DIGITAL SIGNAL PROCESSING LABORATORY 1.1 GENERATION OF DISCRETE TIME SINUSOIDAL SIGNALS IN
More informationChapter 9. Chapter 9 275
Chapter 9 Chapter 9: Multirate Digital Signal Processing... 76 9. Decimation... 76 9. Interpolation... 8 9.. Linear Interpolation... 85 9.. Sampling rate conversion by Non-integer factors... 86 9.. Illustration
More informationPrinciples of Communications ECS 332
Principles of Communications ECS 332 Asst. Prof. Dr. Prapun Suksompong prapun@siit.tu.ac.th 5. Angle Modulation Office Hours: BKD, 6th floor of Sirindhralai building Wednesday 4:3-5:3 Friday 4:3-5:3 Example
More informationDigital Signal Processing +
Digital Signal Processing + Nikil Dutt UC Irvine ICS 212 Winter 2005 + Material adapted from Tony Givargis & Rajesh Gupta Templates from Prabhat Mishra ICS212 WQ05 (Dutt) DSP 1 Introduction Any interesting
More informationBasic Signals and Systems
Chapter 2 Basic Signals and Systems A large part of this chapter is taken from: C.S. Burrus, J.H. McClellan, A.V. Oppenheim, T.W. Parks, R.W. Schafer, and H. W. Schüssler: Computer-based exercises for
More informationDSP First. Laboratory Exercise #7. Everyday Sinusoidal Signals
DSP First Laboratory Exercise #7 Everyday Sinusoidal Signals This lab introduces two practical applications where sinusoidal signals are used to transmit information: a touch-tone dialer and amplitude
More informationLECTURER NOTE SMJE3163 DSP
LECTURER NOTE SMJE363 DSP (04/05-) ------------------------------------------------------------------------- Week3 IIR Filter Design -------------------------------------------------------------------------
More informationECE 5650/4650 MATLAB Project 1
This project is to be treated as a take-home exam, meaning each student is to due his/her own work. The project due date is 4:30 PM Tuesday, October 18, 2011. To work the project you will need access to
More informationELT COMMUNICATION THEORY
ELT 41307 COMMUNICATION THEORY Matlab Exercise #1 Sampling, Fourier transform, Spectral illustrations, and Linear filtering 1 SAMPLING The modeled signals and systems in this course are mostly analog (continuous
More informationMultirate DSP, part 3: ADC oversampling
Multirate DSP, part 3: ADC oversampling Li Tan - May 04, 2008 Order this book today at www.elsevierdirect.com or by calling 1-800-545-2522 and receive an additional 20% discount. Use promotion code 92562
More informationLecture 3 Complex Exponential Signals
Lecture 3 Complex Exponential Signals Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/3/1 1 Review of Complex Numbers Using Euler s famous formula for the complex exponential The
More informationFilter Banks I. Prof. Dr. Gerald Schuller. Fraunhofer IDMT & Ilmenau University of Technology Ilmenau, Germany. Fraunhofer IDMT
Filter Banks I Prof. Dr. Gerald Schuller Fraunhofer IDMT & Ilmenau University of Technology Ilmenau, Germany 1 Structure of perceptual Audio Coders Encoder Decoder 2 Filter Banks essential element of most
More informationDigital Video and Audio Processing. Winter term 2002/ 2003 Computer-based exercises
Digital Video and Audio Processing Winter term 2002/ 2003 Computer-based exercises Rudolf Mester Institut für Angewandte Physik Johann Wolfgang Goethe-Universität Frankfurt am Main 6th November 2002 Chapter
More informationSignals and Filtering
FILTERING OBJECTIVES The objectives of this lecture are to: Introduce signal filtering concepts Introduce filter performance criteria Introduce Finite Impulse Response (FIR) filters Introduce Infinite
More informationFall Music 320A Homework #2 Sinusoids, Complex Sinusoids 145 points Theory and Lab Problems Due Thursday 10/11/2018 before class
Fall 2018 2019 Music 320A Homework #2 Sinusoids, Complex Sinusoids 145 points Theory and Lab Problems Due Thursday 10/11/2018 before class Theory Problems 1. 15 pts) [Sinusoids] Define xt) as xt) = 2sin
More informationECEGR Lab #8: Introduction to Simulink
Page 1 ECEGR 317 - Lab #8: Introduction to Simulink Objective: By: Joe McMichael This lab is an introduction to Simulink. The student will become familiar with the Help menu, go through a short example,
More information5650 chapter4. November 6, 2015
5650 chapter4 November 6, 2015 Contents Sampling Theory 2 Starting Point............................................. 2 Lowpass Sampling Theorem..................................... 2 Principle Alias Frequency..................................
More informationMultirate DSP, part 1: Upsampling and downsampling
Multirate DSP, part 1: Upsampling and downsampling Li Tan - April 21, 2008 Order this book today at www.elsevierdirect.com or by calling 1-800-545-2522 and receive an additional 20% discount. Use promotion
More informationDSP First Lab 08: Frequency Response: Bandpass and Nulling Filters
DSP First Lab 08: Frequency Response: Bandpass and Nulling Filters Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up sections of this lab assignment and go over all exercises in the
More informationInstruction Manual for Concept Simulators. Signals and Systems. M. J. Roberts
Instruction Manual for Concept Simulators that accompany the book Signals and Systems by M. J. Roberts March 2004 - All Rights Reserved Table of Contents I. Loading and Running the Simulators II. Continuous-Time
More informationECE 429 / 529 Digital Signal Processing
ECE 429 / 529 Course Policy & Syllabus R. N. Strickland SYLLABUS ECE 429 / 529 Digital Signal Processing SPRING 2009 I. Introduction DSP is concerned with the digital representation of signals and the
More informationIntroduction to signals and systems
CHAPTER Introduction to signals and systems Welcome to Introduction to Signals and Systems. This text will focus on the properties of signals and systems, and the relationship between the inputs and outputs
More 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 informationDIGITAL FILTERS. !! Finite Impulse Response (FIR) !! Infinite Impulse Response (IIR) !! Background. !! Matlab functions AGC DSP AGC DSP
DIGITAL FILTERS!! Finite Impulse Response (FIR)!! Infinite Impulse Response (IIR)!! Background!! Matlab functions 1!! Only the magnitude approximation problem!! Four basic types of ideal filters with magnitude
More informationFilters. Phani Chavali
Filters Phani Chavali Filters Filtering is the most common signal processing procedure. Used as echo cancellers, equalizers, front end processing in RF receivers Used for modifying input signals by passing
More informationSound synthesis with Pure Data
Sound synthesis with Pure Data 1. Start Pure Data from the programs menu in classroom TC307. You should get the following window: The DSP check box switches sound output on and off. Getting sound out First,
More informationA102 Signals and Systems for Hearing and Speech: Final exam answers
A12 Signals and Systems for Hearing and Speech: Final exam answers 1) Take two sinusoids of 4 khz, both with a phase of. One has a peak level of.8 Pa while the other has a peak level of. Pa. Draw the spectrum
More informationIIR Filter Design Chapter Intended Learning Outcomes: (i) Ability to design analog Butterworth filters
IIR Filter Design Chapter Intended Learning Outcomes: (i) Ability to design analog Butterworth filters (ii) Ability to design lowpass IIR filters according to predefined specifications based on analog
More informationWindow Method. designates the window function. Commonly used window functions in FIR filters. are: 1. Rectangular Window:
Window Method We have seen that in the design of FIR filters, Gibbs oscillations are produced in the passband and stopband, which are not desirable features of the FIR filter. To solve this problem, window
More information1. Clearly circle one answer for each part.
TB 1-9 / Exam Style Questions 1 EXAM STYLE QUESTIONS Covering Chapters 1-9 of Telecommunication Breakdown 1. Clearly circle one answer for each part. (a) TRUE or FALSE: Absolute bandwidth is never less
More informationLab S-5: DLTI GUI and Nulling Filters. Please read through the information below prior to attending your lab.
DSP First, 2e Signal Processing First Lab S-5: DLTI GUI and Nulling Filters Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification: The Exercise
More informationFrom Fourier Series to Analysis of Non-stationary Signals - VII
From Fourier Series to Analysis of Non-stationary Signals - VII prof. Miroslav Vlcek November 23, 2010 Contents Short Time Fourier Transform 1 Short Time Fourier Transform 2 Contents Short Time Fourier
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 informationDIGITAL SIGNAL PROCESSING. Chapter 1 Introduction to Discrete-Time Signals & Sampling
DIGITAL SIGNAL PROCESSING Chapter 1 Introduction to Discrete-Time Signals & Sampling by Dr. Norizam Sulaiman Faculty of Electrical & Electronics Engineering norizam@ump.edu.my OER Digital Signal Processing
More informationGeorge Mason University ECE 201: Introduction to Signal Analysis
Due Date: Week of May 01, 2017 1 George Mason University ECE 201: Introduction to Signal Analysis Computer Project Part II Project Description Due to the length and scope of this project, it will be broken
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 informationLecture 4 Frequency Response of FIR Systems (II)
EE3054 Signals and Systems Lecture 4 Frequency Response of FIR Systems (II Yao Wang Polytechnic University Most of the slides included are extracted from lecture presentations prepared by McClellan and
More informationFourier Theory & Practice, Part I: Theory (HP Product Note )
Fourier Theory & Practice, Part I: Theory (HP Product Note 54600-4) By: Robert Witte Hewlett-Packard Co. Introduction: This product note provides a brief review of Fourier theory, especially the unique
More information