# Signals and Systems EE235. Leo Lam

Size: px
Start display at page:

## Transcription

1 Signals and Systems EE235 Leo Lam

2 Today s menu Lab detailed arrangements Homework vacation week From yesterday (Intro: Signals) Intro: Systems More: Describing Common Signals

3 Taking a signal apart Offset (atmospheric pressure) A sound signal Frequency Amplitude st ( ) = Asin(2 π ft) + a 0 0 A+a 0 a 0 T t (seconds)

4 Frequency g( t) = sin(2πf 0t) f = 0 196Hz = t (seconds) 196 f (Hz) time-domain frequency-domain

5 t to f t (seconds) F (Hz)

6 Combining signals

7 Summary: Signals Signals carry information Signals represented by functions over time or space Signals can be represented in both time and frequency domains Signals can be summed in both time and frequency domains

8 Systems A system describes a relationship between input and output Examples? v(t) g(t) y(t)

9 Definition: System A system modifies signals or extracts information. It can be considered a transformation that operates on a signal.

10 Motivation: Complex systems

11 Filters All kinds, and everywhere

12 Surprising high pass

13 Summary: System System transforms an input to an output System can extract information System can shape signals (filters)

14 Signals: Digging in Types of signals Some standard signals (alphabets!)

15 Signals: A signal is a mathematical function x(t) x is the value (real, complex) y-axis t is the independent variable (1D, 2D etc.) x-axis Both can be Continuous or Discrete Examples of x

16 Signal types Continuous time / Discrete time An x-axis relationship Discrete time = indexed time

17 Signals: Notations A continuous time signal is specified at all values of time, when time is a real number. xt ( ), t R

18 Signals: Notations A discrete time signal is specified at only discrete values of time (e.g. only on integers) xn [ ], n Z

19 What types are these? 1) 90.3 FM radio transmitted signal 2) Daily count of orcas in Puget Sound 3) Muscle contraction of your heart over time 4) A capacitor s charge over time ((c)) 5) A picture taken by a digital camera (d) 6) Local news broadcast to your old TV (c) 7) Video on YouTube (d) 8) Your voice (c) (continuous) (discrete) (c)

20 Analog / Digital values (y-axis) An analog signal has amplitude that can take any value in a continuous interval (all Real numbers) xn [ ] R, n Z xt () Rt, R Where Z is a finite set of values

21 Analog / Digital values (y-axis) An digital signal has amplitude that can only take on only a discrete set of values (any arbitrary set). xt () G, t R xn [ ] G, n Z Where Z and G are finite sets of values

22 Nature vs. Artificial Natural signals mostly analog Computers/gadgets usually digital (today) Signal can be continuous in time but discrete in value (a continuous time, digital signal)

23 Brake! X-axis: continuous and discrete Y-axis: continuous (analog) and discrete (digital) Our class: (mostly) Continuous time, analog values (real and complex) Clear so far? Leo Lam

24 Common signals Building blocks to bigger things constant signal a xt () = a t unit step signal unit ramp signal t t u(t)=0 for t<0 u(t)=1 for t 0 t r(t)=0 for t<0 r(t)=t = for t 0 r(t)=t*u(t) u(τ ) d for t 0 τ Leo Lam

25 Sinusoids/Decaying sinusoids Leo Lam

26 Decaying and growing Leo Lam

27 Generalizing the sinusoids General form: x(t)=ce at, a=σ+jω Equivalently: x(t)=ce σt e jωt Remember Euler s Formula? e j ω t = cos( ωt) + j sin( ωt) x(t)=ce σt e jωt amplitude Sinusoidal with frequency ω (in radians) Exponential (3 types) What is the frequency in Hz? Leo Lam

28 Imaginary signals Remember how to convert between the two? imag z r φ b a real z=a+jb real/imaginary z=re jφ magnitude/phase Leo Lam

29 Describing signals Of interest? Peak value +/- time? Complex? Magnitude, phase, real, imaginary parts? Periodic? Total energy? Power? 0 s(t) t Time averaged * s(t)s (t)dt = 2 s(t) dt Leo Lam

30 Periodic signals Definition: x(t) is periodic if there exists a T (time period) such that: x ( t) x( t + nt ) = For all integers n The minimum T is the period Fundamental frequency f 0 =1/T Leo Lam

31 Periodic signals: examples Sinusoids x(t)=a cos(ω 0 t+φ) Complex exponential (non-decaying or increasing) y t Ae A ω t ja ω t jω0t ( ) = = cos( ) + sin( ) 0 0 Infinite sum of shifted signals v(t) (more later) T 0 z() t = v( t kt ) k = 0 Leo Lam

### Outline. Discrete time signals. Impulse sampling z-transform Frequency response Stability INF4420. Jørgen Andreas Michaelsen Spring / 37 2 / 37

INF4420 Discrete time signals Jørgen Andreas Michaelsen Spring 2013 1 / 37 Outline Impulse sampling z-transform Frequency response Stability Spring 2013 Discrete time signals 2 2 / 37 Introduction More

### Sinusoids and Phasors (Chapter 9 - Lecture #1) Dr. Shahrel A. Suandi Room 2.20, PPKEE

Sinusoids and Phasors (Chapter 9 - Lecture #1) Dr. Shahrel A. Suandi Room 2.20, PPKEE Email:shahrel@eng.usm.my 1 Outline of Chapter 9 Introduction Sinusoids Phasors Phasor Relationships for Circuit Elements

### Sinusoids. Lecture #2 Chapter 2. BME 310 Biomedical Computing - J.Schesser

Sinusoids Lecture # Chapter BME 30 Biomedical Computing - 8 What Is this Course All About? To Gain an Appreciation of the Various Types of Signals and Systems To Analyze The Various Types of Systems To

### Fall 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

### 6.02 Fall 2012 Lecture #12

6.02 Fall 2012 Lecture #12 Bounded-input, bounded-output stability Frequency response 6.02 Fall 2012 Lecture 12, Slide #1 Bounded-Input Bounded-Output (BIBO) Stability What ensures that the infinite sum

### Midterm 1. Total. Name of Student on Your Left: Name of Student on Your Right: EE 20N: Structure and Interpretation of Signals and Systems

EE 20N: Structure and Interpretation of Signals and Systems Midterm 1 12:40-2:00, February 19 Notes: There are five questions on this midterm. Answer each question part in the space below it, using the

### Basic 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

### Laboratory 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

### Introduction to Digital Signal Processing (Discrete-time Signal Processing)

Introduction to Digital Signal Processing (Discrete-time Signal Processing) Prof. Chu-Song Chen Research Center for Info. Tech. Innovation, Academia Sinica, Taiwan Dept. CSIE & GINM National Taiwan University

### Digital 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

### Digital 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

### Introduction 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

### Lecture 2: SIGNALS. 1 st semester By: Elham Sunbu

Lecture 2: SIGNALS 1 st semester 1439-2017 1 By: Elham Sunbu OUTLINE Signals and the classification of signals Sine wave Time and frequency domains Composite signals Signal bandwidth Digital signal Signal

### EECS 216 Winter 2008 Lab 2: FM Detector Part I: Intro & Pre-lab Assignment

EECS 216 Winter 2008 Lab 2: Part I: Intro & Pre-lab Assignment c Kim Winick 2008 1 Introduction In the first few weeks of EECS 216, you learned how to determine the response of an LTI system by convolving

### The 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

### Lecture #2. EE 313 Linear Systems and Signals

Lecture #2 EE 313 Linear Systems and Signals Preview of today s lecture What is a signal and what is a system? o Define the concepts of a signal and a system o Why? This is essential for a course on Signals

### Signals A Preliminary Discussion EE442 Analog & Digital Communication Systems Lecture 2

Signals A Preliminary Discussion EE442 Analog & Digital Communication Systems Lecture 2 The Fourier transform of single pulse is the sinc function. EE 442 Signal Preliminaries 1 Communication Systems and

### ECE 201: Introduction to Signal Analysis. Dr. B.-P. Paris Dept. Electrical and Comp. Engineering George Mason University

ECE 201: Introduction to Signal Analysis Dr. B.-P. Paris Dept. Electrical and Comp. Engineering George Mason University Last updated: November 29, 2016 2016, B.-P. Paris ECE 201: Intro to Signal Analysis

### ECE 201: Introduction to Signal Analysis

ECE 201: Introduction to Signal Analysis Prof. Paris Last updated: October 9, 2007 Part I Spectrum Representation of Signals Lecture: Sums of Sinusoids (of different frequency) Introduction Sum of Sinusoidal

### Topic 6. The Digital Fourier Transform. (Based, in part, on The Scientist and Engineer's Guide to Digital Signal Processing by Steven Smith)

Topic 6 The Digital Fourier Transform (Based, in part, on The Scientist and Engineer's Guide to Digital Signal Processing by Steven Smith) 10 20 30 40 50 60 70 80 90 100 0-1 -0.8-0.6-0.4-0.2 0 0.2 0.4

### ECE 201: Introduction to Signal Analysis

ECE 201: Introduction to Signal Analysis Dr. B.-P. Paris Dept. Electrical and Comp. Engineering George Mason University Last updated: November 29, 2016 2016, B.-P. Paris ECE 201: Intro to Signal Analysis

Spectrum Music 7a: Modulation Tamara Smyth, trsmyth@ucsd.edu Department of Music, University of California, San Diego (UCSD) October 3, 7 When sinusoids of different frequencies are added together, the

### Chapter 1. Electronics and Semiconductors

Chapter 1. Electronics and Semiconductors Tong In Oh 1 Objective Understanding electrical signals Thevenin and Norton representations of signal sources Representation of a signal as the sum of sine waves

### Continuous time and Discrete time Signals and Systems

Continuous time and Discrete time Signals and Systems 1. Systems in Engineering A system is usually understood to be an engineering device in the field, and a mathematical representation of this system

### Lab10: FM Spectra and VCO

Lab10: FM Spectra and VCO Prepared by: Keyur Desai Dept. of Electrical Engineering Michigan State University ECE458 Lab 10 What is FM? A type of analog modulation Remember a common strategy in analog modulation?

### The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #1

The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #1 Date: October 18, 2013 Course: EE 445S Evans Name: Last, First The exam is scheduled to last 50 minutes. Open books

### Chapter 2. Signals and Spectra

Chapter 2 Signals and Spectra Outline Properties of Signals and Noise Fourier Transform and Spectra Power Spectral Density and Autocorrelation Function Orthogonal Series Representation of Signals and Noise

### Physics 132 Quiz # 23

Name (please (please print) print) Physics 132 Quiz # 23 I. I. The The current in in an an ac ac circuit is is represented by by a phasor.the value of of the the current at at some time time t t is is

### EE3723 : Digital Communications

EE3723 : Digital Communications Week 8-9: Bandpass Modulation MPSK MASK, OOK MFSK 04-May-15 Muhammad Ali Jinnah University, Islamabad - Digital Communications - EE3723 1 In-phase and Quadrature (I&Q) Representation

### Signal Characteristics

Data Transmission The successful transmission of data depends upon two factors:» The quality of the transmission signal» The characteristics of the transmission medium Some type of transmission medium

### CSE4214 Digital Communications. Bandpass Modulation and Demodulation/Detection. Bandpass Modulation. Page 1

CSE414 Digital Communications Chapter 4 Bandpass Modulation and Demodulation/Detection Bandpass Modulation Page 1 1 Bandpass Modulation n Baseband transmission is conducted at low frequencies n Passband

### E40M Sound and Music. M. Horowitz, J. Plummer, R. Howe 1

E40M Sound and Music M. Horowitz, J. Plummer, R. Howe 1 LED Cube Project #3 In the next several lectures, we ll study Concepts Coding Light Sound Transforms/equalizers Devices LEDs Analog to digital converters

### ECE5713 : Advanced Digital Communications

ECE5713 : Advanced Digital Communications Bandpass Modulation MPSK MASK, OOK MFSK 04-May-15 Advanced Digital Communications, Spring-2015, Week-8 1 In-phase and Quadrature (I&Q) Representation Any bandpass

### Lecture 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

I am very pleased to teach this class again, after last year s course on electronics over the Summer Term. Based on the SOLE survey result, it is clear that the format, style and method I used worked with

### Linear Frequency Modulation (FM) Chirp Signal. Chirp Signal cont. CMPT 468: Lecture 7 Frequency Modulation (FM) Synthesis

Linear Frequency Modulation (FM) CMPT 468: Lecture 7 Frequency Modulation (FM) Synthesis Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University January 26, 29 Till now we

### SAMPLING 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

### 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

### Wireless 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

### Real Analog Chapter 10: Steady-state Sinusoidal Analysis

1300 Henley Court Pullman, WA 99163 509.334.6306 www.store. digilent.com Real Analog Chapter 10: Steadystate Sinusoidal Analysis 10 Introduction and Chapter Objectives We will now study dynamic systems

### Signals. Periodic vs. Aperiodic. Signals

Signals 1 Periodic vs. Aperiodic Signals periodic signal completes a pattern within some measurable time frame, called a period (), and then repeats that pattern over subsequent identical periods R s.

### ELT 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

### CHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION

CHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION Broadly speaking, system identification is the art and science of using measurements obtained from a system to characterize the system. The characterization

### Communication 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

### Signals Arthur Holly Compton

Signals The story is told that young King Solomon was given the choice between wealth and wisdom. When he chose wisdom, God was so pleased that he gave Solomon not only wisdom but wealth also. So it is

### Frequency Division Multiplexing Spring 2011 Lecture #14. Sinusoids and LTI Systems. Periodic Sequences. x[n] = x[n + N]

Frequency Division Multiplexing 6.02 Spring 20 Lecture #4 complex exponentials discrete-time Fourier series spectral coefficients band-limited signals To engineer the sharing of a channel through frequency

### AC Theory and Electronics

AC Theory and Electronics An Alternating Current (AC) or Voltage is one whose amplitude is not constant, but varies with time about some mean position (value). Some examples of AC variation are shown below:

### Introduction to Wavelet Transform. Chapter 7 Instructor: Hossein Pourghassem

Introduction to Wavelet Transform Chapter 7 Instructor: Hossein Pourghassem Introduction Most of the signals in practice, are TIME-DOMAIN signals in their raw format. It means that measured signal is a

### LRC Circuit PHYS 296 Your name Lab section

LRC Circuit PHYS 296 Your name Lab section PRE-LAB QUIZZES 1. What will we investigate in this lab? 2. Figure 1 on the following page shows an LRC circuit with the resistor of 1 Ω, the capacitor of 33

### 10. Introduction and Chapter Objectives

Real Analog - Circuits Chapter 0: Steady-state Sinusoidal Analysis 0. Introduction and Chapter Objectives We will now study dynamic systems which are subjected to sinusoidal forcing functions. Previously,

### Sinusoids and Sinusoidal Correlation

Laboratory 3 May 24, 2002, Release v3.0 EECS 206 Laboratory 3 Sinusoids and Sinusoidal Correlation 3.1 Introduction Sinusoids are important signals. Part of their importance comes from their prevalence

### Outline. EECS 3213 Fall Sebastian Magierowski York University. Review Passband Modulation. Constellations ASK, FSK, PSK.

EECS 3213 Fall 2014 L12: Modulation Sebastian Magierowski York University 1 Outline Review Passband Modulation ASK, FSK, PSK Constellations 2 1 Underlying Idea Attempting to send a sequence of digits through

### Lecture 2 Review of Signals and Systems: Part 1. EE4900/EE6720 Digital Communications

EE4900/EE6420: Digital Communications 1 Lecture 2 Review of Signals and Systems: Part 1 Block Diagrams of Communication System Digital Communication System 2 Informatio n (sound, video, text, data, ) Transducer

### Complex Sounds. Reading: Yost Ch. 4

Complex Sounds Reading: Yost Ch. 4 Natural Sounds Most sounds in our everyday lives are not simple sinusoidal sounds, but are complex sounds, consisting of a sum of many sinusoids. The amplitude and frequency

### Angle Modulated Systems

Angle Modulated Systems Angle of carrier signal is changed in accordance with instantaneous amplitude of modulating signal. Two types Frequency Modulation (FM) Phase Modulation (PM) Use Commercial radio

### Topic 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

### Laboratory 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.

### EE42: Running Checklist of Electronics Terms Dick White

EE42: Running Checklist of Electronics Terms 14.02.05 Dick White Terms are listed roughly in order of their introduction. Most definitions can be found in your text. Terms2 TERM Charge, current, voltage,

### Step Response of RC Circuits

EE 233 Laboratory-1 Step Response of RC Circuits 1 Objectives Measure the internal resistance of a signal source (eg an arbitrary waveform generator) Measure the output waveform of simple RC circuits excited

### zt ( ) = Ae find f(t)=re( zt ( )), g(t)= Im( zt ( )), and r(t), and θ ( t) if z(t)=r(t) e

Homework # Fundamentals Review Homework or EECS 562 (As needed or plotting you can use Matlab or another sotware tool or your choice) π. Plot x ( t) = 2cos(2π5 t), x ( t) = 2cos(2π5( t.25)), and x ( t)

### Music 270a: Modulation

Music 7a: Modulation Tamara Smyth, trsmyth@ucsd.edu Department of Music, University of California, San Diego (UCSD) October 3, 7 Spectrum When sinusoids of different frequencies are added together, the

### POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 5 RC Circuits Frequency Response

POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LORTORY Eperiment 5 RC Circuits Frequency Response Modified for Physics 18, rooklyn College I. Overview of Eperiment In this eperiment

### II. Random Processes Review

II. Random Processes Review - [p. 2] RP Definition - [p. 3] RP stationarity characteristics - [p. 7] Correlation & cross-correlation - [p. 9] Covariance and cross-covariance - [p. 10] WSS property - [p.

### Chapter 2. Fourier Series & Fourier Transform. Updated:2/11/15

Chapter 2 Fourier Series & Fourier Transform Updated:2/11/15 Outline Systems and frequency domain representation Fourier Series and different representation of FS Fourier Transform and Spectra Power Spectral

### Transmission Fundamentals

College of Computer & Information Science Wireless Networks Northeastern University Lecture 1 Transmission Fundamentals Signals Data rate and bandwidth Nyquist sampling theorem Shannon capacity theorem

### Lab 3 SPECTRUM ANALYSIS OF THE PERIODIC RECTANGULAR AND TRIANGULAR SIGNALS 3.A. OBJECTIVES 3.B. THEORY

Lab 3 SPECRUM ANALYSIS OF HE PERIODIC RECANGULAR AND RIANGULAR SIGNALS 3.A. OBJECIVES. he spectrum of the periodic rectangular and triangular signals.. he rejection of some harmonics in the spectrum of

### Final 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,

### Modulation is the process of impressing a low-frequency information signal (baseband signal) onto a higher frequency carrier signal

Modulation is the process of impressing a low-frequency information signal (baseband signal) onto a higher frequency carrier signal Modulation is a process of mixing a signal with a sinusoid to produce

### Digital Communication System

Digital Communication System Purpose: communicate information at required rate between geographically separated locations reliably (quality) Important point: rate, quality spectral bandwidth, power requirements

### DIGITAL 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

### CHAPTER 9. Sinusoidal Steady-State Analysis

CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source

### 332:223 Principles of Electrical Engineering I Laboratory Experiment #2 Title: Function Generators and Oscilloscopes Suggested Equipment:

RUTGERS UNIVERSITY The State University of New Jersey School of Engineering Department Of Electrical and Computer Engineering 332:223 Principles of Electrical Engineering I Laboratory Experiment #2 Title:

### Digital Communication System

Digital Communication System Purpose: communicate information at certain rate between geographically separated locations reliably (quality) Important point: rate, quality spectral bandwidth requirement

### Biomedical 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

### Experiments #6. Convolution and Linear Time Invariant Systems

Experiments #6 Convolution and Linear Time Invariant Systems 1) Introduction: In this lab we will explain how to use computer programs to perform a convolution operation on continuous time systems and

### In Exercises 1-12, graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function.

0.5 Graphs of the Trigonometric Functions 809 0.5. Eercises In Eercises -, graph one ccle of the given function. State the period, amplitude, phase shift and vertical shift of the function.. = sin. = sin.

### GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING. ECE 2025 Fall 1999 Lab #7: Frequency Response & Bandpass Filters

GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Fall 1999 Lab #7: Frequency Response & Bandpass Filters Date: 12 18 Oct 1999 This is the official Lab #7 description;

### Principles 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

### E40M Sound and Music. M. Horowitz, J. Plummer, R. Howe 1

E40M Sound and Music M. Horowitz, J. Plummer, R. Howe 1 LED Cube Project #3 In the next several lectures, we ll study Concepts Coding Light Sound Transforms/equalizers Devices LEDs Analog to digital converters

### EE4512 Analog and Digital Communications Chapter 6. Chapter 6 Analog Modulation and Demodulation

Chapter 6 Analog Modulation and Demodulation Chapter 6 Analog Modulation and Demodulation Amplitude Modulation Pages 306-309 309 The analytical signal for double sideband, large carrier amplitude modulation

### Laboratory Project 4: Frequency Response and Filters

2240 Laboratory Project 4: Frequency Response and Filters K. Durney and N. E. Cotter Electrical and Computer Engineering Department University of Utah Salt Lake City, UT 84112 Abstract-You will build a

### INF4420 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

### CSC475 Music Information Retrieval

CSC475 Music Information Retrieval Sinusoids and DSP notation George Tzanetakis University of Victoria 2014 G. Tzanetakis 1 / 38 Table of Contents I 1 Time and Frequency 2 Sinusoids and Phasors G. Tzanetakis

### 5.1 Graphing Sine and Cosine Functions.notebook. Chapter 5: Trigonometric Functions and Graphs

Chapter 5: Trigonometric Functions and Graphs 1 Chapter 5 5.1 Graphing Sine and Cosine Functions Pages 222 237 Complete the following table using your calculator. Round answers to the nearest tenth. 2

### 6.02 Fall 2012 Lecture #13

6.02 Fall 2012 Lecture #13 Frequency response Filters Spectral content 6.02 Fall 2012 Lecture 13 Slide #1 Sinusoidal Inputs and LTI Systems h[n] A very important property of LTI systems or channels: If

### Chapter-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

### EECS 216 Winter 2008 Lab 2: FM Detector Part II: In-Lab & Post-Lab Assignment

EECS 216 Winter 2008 Lab 2: Part II: In-Lab & Post-Lab Assignment c Kim Winick 2008 1 Background DIGITAL vs. ANALOG communication. Over the past fifty years, there has been a transition from analog to

### 2.1 BASIC CONCEPTS Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal.

1 2.1 BASIC CONCEPTS 2.1.1 Basic Operations on Signals Time Shifting. Figure 2.2 Time shifting of a signal. Time Reversal. 2 Time Scaling. Figure 2.4 Time scaling of a signal. 2.1.2 Classification of Signals

### DSP 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

### II 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

### George Mason University ECE 201: Introduction to Signal Analysis Spring 2017

Assigned: March 7, 017 Due Date: Week of April 10, 017 George Mason University ECE 01: Introduction to Signal Analysis Spring 017 Laboratory Project #7 Due Date Your lab report must be submitted on blackboard

### , answer the next six questions.

Frequency Response Problems Conceptual Questions 1) T/F Given f(t) = A cos (ωt + θ): The amplitude of the output in sinusoidal steady-state increases as K increases and decreases as ω increases. 2) T/F

### INF4420. 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

### Signals 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

### Department of Electronic Engineering NED University of Engineering & Technology. LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202)

Department of Electronic Engineering NED University of Engineering & Technology LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202) Instructor Name: Student Name: Roll Number: Semester: Batch:

### ECE503: Digital Signal Processing Lecture 1

ECE503: Digital Signal Processing Lecture 1 D. Richard Brown III WPI 12-January-2012 WPI D. Richard Brown III 12-January-2012 1 / 56 Lecture 1 Major Topics 1. Administrative details: Course web page. Syllabus

### Lab 9 Fourier Synthesis and Analysis

Lab 9 Fourier Synthesis and Analysis In this lab you will use a number of electronic instruments to explore Fourier synthesis and analysis. As you know, any periodic waveform can be represented by a sum

### The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2

The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2 Date: November 18, 2010 Course: EE 313 Evans Name: Last, First The exam is scheduled to last 75 minutes. Open books