George Mason University Signals and Systems I Spring 2016

Size: px
Start display at page:

Download "George Mason University Signals and Systems I Spring 2016"

Transcription

1 George Mason University Signals and Systems I Spring 2016 Laboratory Project #4 Assigned: Week of March 14, 2016 Due Date: Laboratory Section, Week of April 4, 2016 Report Format and Guidelines for Laboratory Projects Your lab report for each lab is a formal report in the sense that it should be well-prepared, carefully written, and follow the format given below. It must include descriptions and analysis of all parts of the lab that have been assigned. It may help in the preparation of your report to assume that your report is being written for your boss at the place where you now work as a newly-hired engineer, and that this report represents your response to his request for an analysis of a problem that you have been given to work on. General Guidelines Your report should be typewritten, neat and well-organized. The report must be well-organized and follow the format given below. It must include all analytical work, MATLAB plots and code, and relevant explanations. The analytical work and calculations should be complete and clearly explained. It is expected that the report will be grammatically correct with no spelling errors. Part of your grade will be based on the grammatical correctness of your report, and points will be deducted for spelling errors. If you prepare your report in Word, there is a spell checker that you are encouraged to use. Explanations should be given that describe your work, and plots must include properly labeled axes and a title. Each plot should be a figure, with a figure number and a caption. Although it is important to be complete and thorough in your report, points will be deducted if you present too many unnecessary graphs and plots. Within the text of your report, when referring to a particular plot, refer to it by number. For example, you may write something such as The frequency response of the bandstop filter is shown in Figure 2, and from this plot we see that the center frequency of the stop-band is 10 khz and the stop-band width is 2 khz as desired.

2 Detailed Format 1. Title Page: This page contains an identification of the Laboratory by title and number. It also has the name and G-Number of the author as well as the date of submission. 2. Introduction: This section contains a description of the purpose and objectives of the laboratory project. Do not simply copy test from the assignment. It should also summarize the topics covered in the laboratory and a brief summary of the key results obtained. 3. Main body: This section is the most detailed part in your report. Note that it must not contain any MATLAB code. It does contain a description of the results obtained including any figures that were generated with MATLAB or other sources. The report body should contain subsections that are organized in a manner similar to the laboratory assignment. All figures must have a caption that is used when referring to them in the body of the report. If theoretical calculations are required, these should be detailed and used in comparisons with the experimental portion of the lab. 4. Conclusions: Summarize the conclusions that you made once the results were obtained. The conclusions should be tied back to the objectives of the Lab Project. This should be a concise section that focuses on the important results obtained and your conclusions that resulted from these results. Be concise, but be complete in your conclusions. 5. References/Appendices: If you used any references (e.g. web pages) identify them here. You should also include appendices labelled Appendix A, Appendix B, Appendix C, etc. for each experiment for which you wrote MATLAB code. In these appendices, do not list every MATLAB instruction that you typed in the MATLAB command line. Only provide those that would be necessary to repeat any of your experiments or to create the plots that you present in the report. Each MATLAB script file, or sequence of MATLAB commands must be fully documented, and before each listing ini the appendix, you should provide a description of what the script file or MATLAB commands are used for.

3 1 Prelab (a) Background: We have seen that periodic functions can be represented in terms of a Fourier Series expansion in either the sine/cosine form or the complex exponential form. In this lab, we will use the complex exponential form. Thus, if x(t) = x(t + T ) for all t, where T is the smallest value for which this is true, then the complex exponential form of the Fourier Series is given by: x(t) = x n e jnω 0t n= The coefficients x n are complex and given by, where ω 0 = 2π/T x n = 1 T t 0 +T x(t)e jnω0t dt When the input to a linear time-invariant system has the following form, t 0 x(t) = e st where s = σ + jω is a complex number, then the output will be an exponential of exactly the same form, but scaled by a complex number whose value depends on s and the impulse response of the system, h(t). More specifically, the output is where y(t) = H(s)e st H(s) = h(t)e st dt (1) is the system function. Thus, complex exponentials are eigenfunctions of linear timeinvariant systems. In the special case when s = jω, then and x(t) = e jωt y(t) = H(jω)e jωt where H(jω) is the frequency response of the system (filter) that is given by H(jω) = H(s) = s=jω h(t)e jωt dt Note that H(jω) is a complex-valued function of ω, the frequency of the complex exponential.

4 (b) LCCDE s Consider an LTI system whose input x(t) and output y(t) are related by a LCCDE of the form a 3 d 3 y(t) dt 3 + a 2 d 2 y(t) dt 2 + a 1 dy(t) dt + a 0 y(t) = b 2 d 2 x(t) dt 2 + b 1 dx(t) dt In this case, the system function is a ratio of two polynomials in s, + b 0 x(t) (2) H(s) = B(s) A(s) = b 2 s 2 + b 1 s + b 0 a 3 s 3 + a 2 s 2 + a 1 s + a 0 (3) where the coefficients a k and b k are the coefficients of the differential equation. The frequency response is then found by setting s = jω, H(jω) = H(s) s=jω The magnitude of H(jω) at a given frequency ω tells us how much a complex exponential at frequency ω is attenuated or amplified in amplitude. The phase (angle) of H(jω) indicates how much the complex exponential is shifted in phase (delayed or advanced in time). Question 1 for Lab 4 An LTI system is defined by the following LCCDE: d 2 y(t) dt dy(t) dt + y(t) = 0.2 d2 x(t) dt dx(t) dt + x(t) (4) The system function is H(s) = B(s)/A(s) where the polynomials A(s) and B(s) have the form: A(s) = a 2 s 2 + a 1 s + a 0 B(s) = b 2 s 2 + b 1 s + b 0 The coefficients of the polynomials A(s) and B(s) may be represented by vectors a and b as follows: a = [a 2 a 1 a 0 ] b = [b 2 b 1 b 0 ] (a) What are the vectors a and b for this system? (b) Find the roots of the polynomial A(s). These are called the poles of the system. (c) Find the roots of the polynomial B(s). These are called the zeros of the system. (d) Plot the pole/zero locations for this filter using the MATLAB commands: H = tf(b,a); pzmap(h) grid More information on the MATLAB functions tf and pzmap can be found using the MATLAB help function.

5 (e) Find an analytical expression for H(jω) for this system. (f) Write a MATLAB program to plot H(jω) over the range 0 ω 5.0 by evaluating your analytical expression. Use 101 equally-spaced values of ω for the horizontal axis. Note: For this part, you must write your own code, and you may not use existing MATLAB functions. Be sure to label both axes in your plot. Provide a documented listing and description of your program in an Appendix of your lab report. 2 Finding the Frequency Response of LTI Systems MATLAB has a number of useful m-files to find and plot the frequency response of a system and to filter signals. One of these that you will be using in this lab is freqs, which returns the frequency response H(jω) of a continuous-time system that is specified by the coefficients a k and b k in the numerator and denominator polynomials of H(jω). Using the vectors a and b that you found in Question 1(a), demonstrate that the MATLAB code below plots the magnitude of the frequency response, H(jω), for the system given in Eq. 4: w = linspace(0,5,101); H = freqs(b,a,w); plot(w,20*log10(abs(h))) xlabel( Frequency (rad/s) ) ylabel( H(j\omega) in db ) grid Note that the vector H contains the values of the frequency response in rad/s at the frequencies specified by the vector w. In this case, H contains 101 samples of H(jω) within the range 0 ω 5 radians/sec. Question 2 for Lab 4 (a) Verify that the results you obtained using freqs in the MATLAB code above agrees with your analytical results from Question 1. Explain any differences. (b) Use MATLAB to plot the system frequency response H(jω) for the following system: s 2 + ω0 2 H(s) = s 2 + 2ω 0 cos(θ)s + ω0 2 with ω 0 = 2π(60) and θ = 60 o. The result will show that H(s) is a notch filter that eliminates one or more frequency components from the input signal. What frequencies are eliminated? (c) If θ is increased to 85 o, what happens to the notch? Explore the behavior of the notch filter for other values of θ and describe what you observe. There are other ways to use the MATLAB function freqs and these may be found by typing help freqs. Additional useful MATLAB functions that you may find useful include impulse(sys,tfinal,dt), and lsim(sys,u,t,x0). Again, for documentation on any of these use the MATLAB help function.

6 (a) Ideal limiter input and output. (b) Spectra. Figure 1: A unit amplitude sinusoid that is input to an ideal limiter with a clipping value of Amplitude Limiting Effects in LTI Systems In many practical filtering systems, the relationship between the input and the output may be accurately modelled as an LTI system provided that the input does not exceed some maximum value. An amplifier, for example, may be linear for signals that do not exceed some maximum amplitude, but nonlinear for signals that exceed this maximum value. In other cases, it may be important to limit the amplitude of the input to an LTI system to some maximum value, x max in order to prevent damage to sensitive system components. In these cases, one may pass the input through a limiter that clips the amplitude to some maximum value, x max. The model for the overall system thus consists of an ideal limiter followed by an LTI system. An ideal limiter is a nonlinear memoryless system where the output is equal to the input provided that the magnitude of the input signal is less than some specified value, called the clipping level. When the input exceeds this value, the output is clipped to this value. For example, if the clipping value is equal to one, then the output is given by { x(t) ; 0 x(t) 1 y(t) = sign(x(t)) ; 1 < x(t) Figure 1(a) illustrates the clipping process for a unit amplitude sinusoid of frequency ω 0 = 2π500 Hz. and a clipping level of 0.6. As we see, the output y(t) has a maximum value of 0.6. The spectra of the original and clipped waveforms are shown in Fig. 1(b). Note that although the input to the limiter is a pure sinusoid with no harmonics, the ideal limiter is a nonlinear device and, therefore, is capable of producing multiple harmonics in the output signal. Question 3 for Lab 4 This question addresses the issue of the effects of amplitude limiting in systems. Suppose that we have a linear time-invariant system with a frequency response H(jω), but any input to this system is first passed through a limiter that clips the amplitude of the input to some maximum value, x max. (a) Using MATLAB, create a vector a consisting of L = 2 16 = 65, 536 samples of a unit-

7 amplitude sinusoid x(t) with a frequency f 0 = 440 Hz. (This is the musical note A above middle C.) With a sampling frequency f s = 44, 100 Hz., the spacing between samples will be T = 1/f s = seconds. What is the duration of the tone that you have created? Instructor Verification (separate page) (b) Using MATLAB, create a clipped signal y(t) that is equal to the sinusoid x(t) that you created in part (a) when x(t) 0.8, and equal to ±0.8 whenever x(t) exceeds 0.8. Use the hold function in MATLAB to produce a plot similar to Figure 1. (c) Listen to the pure tone x(t) and (separately) the clipped signal y(t) using the soundsc command in MATLAB. The format for this function is soundsc(x,fs). It is important that you include the sampling frequency f s in the MATLAB command. If you type soundsc(x), it will take a very long time to play and the frequency you hear will be very low. Explain what you hear when comparing the clipped and original signals. Are the results of your listening experiment expected? Experiment with other clipping levels such as 0.9 and 0.1 and discuss the results of your comparison. Instructor Verification (separate page) (d) The MATLAB code below will plot the spectrum of a 440 Hz sinusoid x(t). fs = 44100; % Sampling frequency fc = 440; % Sinusoid frequency dt = 1/fs; % Sampling interval L = 2^(16); % Number of points in sinusoid t = [0:L-1]; x = sin(2*pi*fc/fs*t); Fx = 20*log10(abs(fft(x,L))); % Spectrum of signal x ff = fs*linspace(0,1,l); % Frequency values plot(ff,fx) xlim([0 3000]) % Limits frequencies to 0 -> 3,000 Hz. grid Modify this program to compute the spectrum of the clipped signal y(t) that you created in part (b), and plot the spectra of both x(t) and y(t) on the same axis as in Figure 1(b). Provide a documented listing and description of your program in an Appendix of your lab report. (e) Experiment with different clipping levels between zero and one. By varying the clipping level and playing the result, find the lowest value of clipping detectable by the ear when playing the clipped waveforms. (f) Change the frequency of the sinusoid in part (e) and determine whether or not there are any differences in the effects of clipping in low-frequency sinusoids compared to high-frequency sinusoids. For example, does the lowest value of clipping detectable by the ear depend on the frequency of the sinusoid?

8 4 Clipped Trumpet Signals As we have seen, the effect of signal clipping on a sinusoid is primarily to produce harmonics at multiples of the sinusoidal frequency. As we will see later, it is possible to attenuate these harmonics by filtering the clipped signal with a lowpass filter that passes frequencies lower than that of the sinusoid while rejecting the higher frequency harmonics. In this section, we examine the effects of clipping on a trumpet signal. (a) Download the file trump_short.mat into your MATLAB workspace. This file can be found in the Blackboard page for Prof. Griffiths or the course web page for Prof. Hayes. Once the file is in your workspace, use the following MATLAB commands to retrieve the audio file of a trumpet playing the note middle C, which is nominally Hz.: >> load( trump_short.mat ); After loading this file, your workspace will contain the following two files: 1. trumpet 2. fs The file trumpet is the trumpet sound and the variable fs is the sampling rate. (b) Use soundsc to listen to the trumpet with the following format: >> soundsc(trumpet,fs); (c) Compute the spectrum of this signal using the method that you used in part 3(d). Plot this spectrum over the range 0 to 3,000 Hz. More than 10 harmonic peaks should be visible. (d) Using the same approach as in Part 3, apply a clipping level of 0.5 to the trumpet signal and plot the resulting spectrum on the same plot as the original (un-clipped) signal. Discuss the differences that you observe in the spectra of the original and clipped trumpet signals. Again, use soundsc to listen to the clipped trumpet waveform and describe the differences that you hear. (e) Experiment with different clipping levels between 0 and 1. By varying the clipping level and listening to the result, find the lowest value of clipping detectable by ear when you play the clipped waveform. 5 Clipped Music Signals In this section, we will examine the effects of clipping on a recorded song. (a) Download the file River_220.mat into your MATLAB workspace. This file can be found in the Blackboard page for Prof. Griffiths or the course web page for Prof. Hayes. Load River_220.mat into MATLAB. This file contains the following two files: 1. y

9 2. fs where y is a music recording. (b) Use soundsc to listen to the trumpet with the command: >> soundsc(y,fs); (c) Analyze this signal using exactly the same approach as in Part 4, i.e., repeat parts (b) through (e) for the music signal. 6 Conclusions and Observations In this lab, you have studied the effects of clipping on three different types of audio signals: 1. A 440 Hz sinusoidal tone. 2. A trumpet playing one note at Hz. 3. A music track having a continuous music spectrum. Write a one page narrative that summarizes your findings in this lab. As a part of your summary, you must discuss the following issues and answer the following questions in addition to any other conclusions that you find relevant and important: (a) Which signal can be clipped to the lowest level without significantly distorting the sound: the sinusoid, the trumpet, or the music track? Rank the three cases with respect to their susceptibility to clipping. Can you provide any reasons that explain your findings? (b) In Question 3(f), you changed the frequency of the sinusoid that is clipped and determined whether or not there are any differences in the effects of clipping in lowfrequency sinusoids compared to high-frequency sinusoids. Does this provide any insight or explanation for your analysis on the effects of clipping in sinusoids compared to the trumpet and to music? (c) What additional experiments would you want to perform in order to analyze the effects of clipping on signals? Formulate an experimental plan for data collection and analysis. 7 Appendices Use the Appendix section to list the MATLAB code that you generated during this lab. Make sure the code is documented sufficiently using comments so that it can easily be understood by others. Make sure you indicate which portion of the report used the MATLAB code that you are listing. If you used the web to search on various items during the lab, list the pages you used as a result of the search. Again indicate which portion of the lab corresponds to the pages you are listing.

10 Lab #4 ECE 220: Spring 2016 Instructor Verification Sheet For each verification, be prepared to explain your answer and respond to other related questions that the lab TA s or professors might ask. Turn this page in along with your lab report. Name: Date of Lab: Question 3(a): With a sampling frequency f s = 44, 100 Hz., the spacing between the samples of a sinusoid of frequency 44,100 Hz. will be T = 1/f s = seconds. With L = 65, 536 samples, what is the duration of the tone? Tone duration = sec. Explain how you determined this value. Verified: Date/Time: Question 3(c): Explain why the command soundsc(x) takes so long to play when x is the sinusoid you created in this problem.

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

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

More information

Knowledge Integration Module 2 Fall 2016

Knowledge Integration Module 2 Fall 2016 Knowledge Integration Module 2 Fall 2016 1 Basic Information: The knowledge integration module 2 or KI-2 is a vehicle to help you better grasp the commonality and correlations between concepts covered

More information

EE 422G - Signals and Systems Laboratory

EE 422G - Signals and Systems Laboratory EE 422G - Signals and Systems Laboratory Lab 3 FIR Filters Written by Kevin D. Donohue Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 September 19, 2015 Objectives:

More information

EEE - 321: Signals and Systems Lab Assignment 3

EEE - 321: Signals and Systems Lab Assignment 3 BILKENT UNIVERSITY ELECTRICAL AND ELECTRONICS ENGINEERING DEPARTMENT EEE - 321: Signals and Systems Lab Assignment 3 For Section-I report submission is due by 08.11.2017 For Section-II report submission

More information

Electrical & Computer Engineering Technology

Electrical & 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 information

Laboratory Assignment 4. Fourier Sound Synthesis

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

More information

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. 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 information

ECE 203 LAB 2 PRACTICAL FILTER DESIGN & IMPLEMENTATION

ECE 203 LAB 2 PRACTICAL FILTER DESIGN & IMPLEMENTATION Version 1. 1 of 7 ECE 03 LAB PRACTICAL FILTER DESIGN & IMPLEMENTATION BEFORE YOU BEGIN PREREQUISITE LABS ECE 01 Labs ECE 0 Advanced MATLAB ECE 03 MATLAB Signals & Systems EXPECTED KNOWLEDGE Understanding

More information

Lab S-8: Spectrograms: Harmonic Lines & Chirp Aliasing

Lab S-8: Spectrograms: Harmonic Lines & Chirp Aliasing DSP First, 2e Signal Processing First Lab S-8: Spectrograms: Harmonic Lines & Chirp Aliasing Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification:

More information

DSP First Lab 08: Frequency Response: Bandpass and Nulling Filters

DSP 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 information

ECE438 - Laboratory 7a: Digital Filter Design (Week 1) By Prof. Charles Bouman and Prof. Mireille Boutin Fall 2015

ECE438 - 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

MATLAB Assignment. The Fourier Series

MATLAB Assignment. The Fourier Series MATLAB Assignment The Fourier Series Read this carefully! Submit paper copy only. This project could be long if you are not very familiar with Matlab! Start as early as possible. This is an individual

More information

Experiments #6. Convolution and Linear Time Invariant Systems

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

More information

Lab P-4: AM and FM Sinusoidal Signals. We have spent a lot of time learning about the properties of sinusoidal waveforms of the form: ) X

Lab P-4: AM and FM Sinusoidal Signals. We have spent a lot of time learning about the properties of sinusoidal waveforms of the form: ) X DSP First, 2e Signal Processing First Lab P-4: 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

More information

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 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

More information

Laboratory 7: Active Filters

Laboratory 7: Active Filters EGR 224L - Spring 208 7. Introduction Laboratory 7: Active Filters During this lab, you are going to use data files produced by two different low-pass filters to examine MATLAB s ability to predict transfer

More information

Laboratory 5: RC Circuits and Filtering

Laboratory 5: RC Circuits and Filtering 5.1 Introduction Laboratory 5: ircuits and Filtering For this lab, you will be comparing the experimental behavior of a filter with analytical behavior modeled in MATLAB using Bode plots. During the lab

More information

GEORGIA 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 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 information

Fourier Series and Gibbs Phenomenon

Fourier Series and Gibbs Phenomenon Fourier Series and Gibbs Phenomenon University Of Washington, Department of Electrical Engineering This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License

More information

MTE 360 Automatic Control Systems University of Waterloo, Department of Mechanical & Mechatronics Engineering

MTE 360 Automatic Control Systems University of Waterloo, Department of Mechanical & Mechatronics Engineering MTE 36 Automatic Control Systems University of Waterloo, Department of Mechanical & Mechatronics Engineering Laboratory #1: Introduction to Control Engineering In this laboratory, you will become familiar

More information

Spring 2018 EE 445S Real-Time Digital Signal Processing Laboratory Prof. Evans. Homework #1 Sinusoids, Transforms and Transfer Functions

Spring 2018 EE 445S Real-Time Digital Signal Processing Laboratory Prof. Evans. Homework #1 Sinusoids, Transforms and Transfer Functions Spring 2018 EE 445S Real-Time Digital Signal Processing Laboratory Prof. Homework #1 Sinusoids, Transforms and Transfer Functions Assigned on Friday, February 2, 2018 Due on Friday, February 9, 2018, by

More information

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) 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:

More information

BME 3512 Bioelectronics Laboratory Two - Passive Filters

BME 3512 Bioelectronics Laboratory Two - Passive Filters BME 35 Bioelectronics Laboratory Two - Passive Filters Learning Objectives: Understand the basic principles of passive filters. Laboratory Equipment: Agilent Oscilloscope Model 546A Agilent Function Generator

More information

PROBLEM SET 6. Note: This version is preliminary in that it does not yet have instructions for uploading the MATLAB problems.

PROBLEM 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 information

Lab 4 Fourier Series and the Gibbs Phenomenon

Lab 4 Fourier Series and the Gibbs Phenomenon Lab 4 Fourier Series and the Gibbs Phenomenon EE 235: Continuous-Time Linear Systems Department of Electrical Engineering University of Washington This work 1 was written by Amittai Axelrod, Jayson Bowen,

More information

THE 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 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 information

Laboratory Assignment 5 Amplitude Modulation

Laboratory Assignment 5 Amplitude Modulation Laboratory Assignment 5 Amplitude Modulation PURPOSE In this assignment, you will explore the use of digital computers for the analysis, design, synthesis, and simulation of an amplitude modulation (AM)

More information

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 The University of Texas at Austin Dept. of Electrical and Computer Engineering Final Exam Date: December 18, 2017 Course: EE 313 Evans Name: Last, First The exam is scheduled to last three hours. Open

More information

ECE 2006 University of Minnesota Duluth Lab 11. AC Circuits

ECE 2006 University of Minnesota Duluth Lab 11. AC Circuits 1. Objective AC Circuits In this lab, the student will study sinusoidal voltages and currents in order to understand frequency, period, effective value, instantaneous power and average power. Also, the

More information

EGR 111 Audio Processing

EGR 111 Audio Processing EGR 111 Audio Processing This lab shows how to load, play, create, and filter sounds and music with MATLAB. Resources (available on course website): speech1.wav, birds_jet_noise.wav New MATLAB commands:

More information

ECE 201: Introduction 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

More information

SMS045 - DSP Systems in Practice. Lab 1 - Filter Design and Evaluation in MATLAB Due date: Thursday Nov 13, 2003

SMS045 - DSP Systems in Practice. Lab 1 - Filter Design and Evaluation in MATLAB Due date: Thursday Nov 13, 2003 SMS045 - DSP Systems in Practice Lab 1 - Filter Design and Evaluation in MATLAB Due date: Thursday Nov 13, 2003 Lab Purpose This lab will introduce MATLAB as a tool for designing and evaluating digital

More information

Each individual is to report on the design, simulations, construction, and testing according to the reporting guidelines attached.

Each individual is to report on the design, simulations, construction, and testing according to the reporting guidelines attached. EE 352 Design Project Spring 2015 FM Receiver Revision 0, 03-02-15 Interim report due: Friday April 3, 2015, 5:00PM Project Demonstrations: April 28, 29, 30 during normal lab section times Final report

More information

Continuous-Time Analog Filters

Continuous-Time Analog Filters ENGR 4333/5333: Digital Signal Processing Continuous-Time Analog Filters Chapter 2 Dr. Mohamed Bingabr University of Central Oklahoma Outline Frequency Response of an LTIC System Signal Transmission through

More information

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

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

More information

Lab S-1: Complex Exponentials Source Localization

Lab S-1: Complex Exponentials Source Localization DSP First, 2e Signal Processing First Lab S-1: Complex Exponentials Source Localization Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification: The

More information

Signals and Systems Lecture 6: Fourier Applications

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

More information

ECE 4670 Spring 2014 Lab 1 Linear System Characteristics

ECE 4670 Spring 2014 Lab 1 Linear System Characteristics ECE 4670 Spring 2014 Lab 1 Linear System Characteristics 1 Linear System Characteristics The first part of this experiment will serve as an introduction to the use of the spectrum analyzer in making absolute

More information

George Mason University ECE 201: Introduction to Signal Analysis

George 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 information

Signal Processing First Lab 20: Extracting Frequencies of Musical Tones

Signal Processing First Lab 20: Extracting Frequencies of Musical Tones Signal Processing First Lab 20: Extracting Frequencies of Musical Tones 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

More information

ECE 301, final exam of the session of Prof. Chih-Chun Wang Saturday 10:20am 12:20pm, December 20, 2008, STEW 130,

ECE 301, final exam of the session of Prof. Chih-Chun Wang Saturday 10:20am 12:20pm, December 20, 2008, STEW 130, ECE 301, final exam of the session of Prof. Chih-Chun Wang Saturday 10:20am 12:20pm, December 20, 2008, STEW 130, 1. Enter your name, student ID number, e-mail address, and signature in the space provided

More information

EEL 4350 Principles of Communication Project 2 Due Tuesday, February 10 at the Beginning of Class

EEL 4350 Principles of Communication Project 2 Due Tuesday, February 10 at the Beginning of Class EEL 4350 Principles of Communication Project 2 Due Tuesday, February 10 at the Beginning of Class Description In this project, MATLAB and Simulink are used to construct a system experiment. The experiment

More information

DSP First. Laboratory Exercise #7. Everyday Sinusoidal Signals

DSP 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 information

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

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

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY /6.071 Introduction to Electronics, Signals and Measurement Spring 2006

MASSACHUSETTS INSTITUTE OF TECHNOLOGY /6.071 Introduction to Electronics, Signals and Measurement Spring 2006 MASSACHUSETTS INSTITUTE OF TECHNOLOGY.071/6.071 Introduction to Electronics, Signals and Measurement Spring 006 Lab. Introduction to signals. Goals for this Lab: Further explore the lab hardware. The oscilloscope

More information

Project 2 - Speech Detection with FIR Filters

Project 2 - Speech Detection with FIR Filters Project 2 - Speech Detection with FIR Filters ECE505, Fall 2015 EECS, University of Tennessee (Due 10/30) 1 Objective The project introduces a practical application where sinusoidal signals are used to

More information

Laboratory Assignment 2 Signal Sampling, Manipulation, and Playback

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.

More information

Signals and Systems Lecture 6: Fourier Applications

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

More information

SECTION 7: FREQUENCY DOMAIN ANALYSIS. MAE 3401 Modeling and Simulation

SECTION 7: FREQUENCY DOMAIN ANALYSIS. MAE 3401 Modeling and Simulation SECTION 7: FREQUENCY DOMAIN ANALYSIS MAE 3401 Modeling and Simulation 2 Response to Sinusoidal Inputs Frequency Domain Analysis Introduction 3 We ve looked at system impulse and step responses Also interested

More information

Here are some of Matlab s complex number operators: conj Complex conjugate abs Magnitude. Angle (or phase) in radians

Here are some of Matlab s complex number operators: conj Complex conjugate abs Magnitude. Angle (or phase) in radians Lab #2: Complex Exponentials Adding Sinusoids Warm-Up/Pre-Lab (section 2): You may do these warm-up exercises at the start of the lab period, or you may do them in advance before coming to the lab. You

More information

Basic Signals and Systems

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

More information

L 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 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 information

Final Exam Solutions June 14, 2006

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,

More information

THE HONG KONG POLYTECHNIC UNIVERSITY Department of Electronic and Information Engineering. EIE2106 Signal and System Analysis Lab 2 Fourier series

THE HONG KONG POLYTECHNIC UNIVERSITY Department of Electronic and Information Engineering. EIE2106 Signal and System Analysis Lab 2 Fourier series THE HONG KONG POLYTECHNIC UNIVERSITY Department of Electronic and Information Engineering EIE2106 Signal and System Analysis Lab 2 Fourier series 1. Objective The goal of this laboratory exercise is to

More information

CSC475 Music Information Retrieval

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

More information

Lab S-3: Beamforming with Phasors. N r k. is the time shift applied to r k

Lab S-3: Beamforming with Phasors. N r k. is the time shift applied to r k DSP First, 2e Signal Processing First Lab S-3: Beamforming with Phasors Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification: The Exercise section

More information

STATION NUMBER: LAB SECTION: Filters. LAB 6: Filters ELECTRICAL ENGINEERING 43/100 INTRODUCTION TO MICROELECTRONIC CIRCUITS

STATION NUMBER: LAB SECTION: Filters. LAB 6: Filters ELECTRICAL ENGINEERING 43/100 INTRODUCTION TO MICROELECTRONIC CIRCUITS Lab 6: Filters YOUR EE43/100 NAME: Spring 2013 YOUR PARTNER S NAME: YOUR SID: YOUR PARTNER S SID: STATION NUMBER: LAB SECTION: Filters LAB 6: Filters Pre- Lab GSI Sign- Off: Pre- Lab: /40 Lab: /60 Total:

More information

ECE503: Digital Filter Design Lecture 9

ECE503: Digital Filter Design Lecture 9 ECE503: Digital Filter Design Lecture 9 D. Richard Brown III WPI 26-March-2012 WPI D. Richard Brown III 26-March-2012 1 / 33 Lecture 9 Topics Within the broad topic of digital filter design, we are going

More information

SIGNALS AND SYSTEMS: 3C1 LABORATORY 1. 1 Dr. David Corrigan Electronic and Electrical Engineering Dept.

SIGNALS AND SYSTEMS: 3C1 LABORATORY 1. 1 Dr. David Corrigan Electronic and Electrical Engineering Dept. 2012 Signals and Systems: Laboratory 1 1 SIGNALS AND SYSTEMS: 3C1 LABORATORY 1. 1 Dr. David Corrigan Electronic and Electrical Engineering Dept. corrigad@tcd.ie www.mee.tcd.ie/ corrigad The aims of this

More information

EELE503. Modern filter design. Filter Design - Introduction

EELE503. Modern filter design. Filter Design - Introduction EELE503 Modern filter design Filter Design - Introduction A filter will modify the magnitude or phase of a signal to produce a desired frequency response or time response. One way to classify ideal filters

More information

Digital Video and Audio Processing. Winter term 2002/ 2003 Computer-based exercises

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

More information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab Objectives Boise State University Department of Electrical and Computer Engineering ECE L Circuit Analysis and Design Lab Experiment #0: Frequency esponse Measurements The objectives of this laboratory

More information

1. In the command window, type "help conv" and press [enter]. Read the information displayed.

1. 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 information

UNIVERSITY OF WARWICK

UNIVERSITY OF WARWICK UNIVERSITY OF WARWICK School of Engineering ES905 MSc Signal Processing Module (2010) AM SIGNALS AND FILTERING EXERCISE Deadline: This is NOT for credit. It is best done before the first assignment. You

More information

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage

More information

Fall Music 320A Homework #2 Sinusoids, Complex Sinusoids 145 points Theory and Lab Problems Due Thursday 10/11/2018 before class

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

More information

ESE531 Spring University of Pennsylvania Department of Electrical and System Engineering Digital Signal Processing

ESE531 Spring University of Pennsylvania Department of Electrical and System Engineering Digital Signal Processing University of Pennsylvania Department of Electrical and System Engineering Digital Signal Processing ESE531, Spring 2017 Final Project: Audio Equalization Wednesday, Apr. 5 Due: Tuesday, April 25th, 11:59pm

More information

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

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

More information

ELT Receiver Architectures and Signal Processing Fall Mandatory homework exercises

ELT Receiver Architectures and Signal Processing Fall Mandatory homework exercises ELT-44006 Receiver Architectures and Signal Processing Fall 2014 1 Mandatory homework exercises - Individual solutions to be returned to Markku Renfors by email or in paper format. - Solutions are expected

More information

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 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;

More information

Lab 8: Frequency Response and Filtering

Lab 8: Frequency Response and Filtering Lab 8: Frequency Response and Filtering 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 going

More information

EE 470 BIOMEDICAL SIGNALS AND SYSTEMS. Active Learning Exercises Part 2

EE 470 BIOMEDICAL SIGNALS AND SYSTEMS. Active Learning Exercises Part 2 EE 47 BIOMEDICAL SIGNALS AND SYSTEMS Active Learning Exercises Part 2 29. For the system whose block diagram presentation given please determine: The differential equation 2 y(t) The characteristic polynomial

More information

EE 210 Lab Exercise #5: OP-AMPS I

EE 210 Lab Exercise #5: OP-AMPS I EE 210 Lab Exercise #5: OP-AMPS I ITEMS REQUIRED EE210 crate, DMM, EE210 parts kit, T-connector, 50Ω terminator, Breadboard Lab report due at the ASSIGNMENT beginning of the next lab period Data and results

More information

Assignment 1. Regular Problems

Assignment 1. Regular Problems ELEC 260, Fall 2017 1 Assignment 1 the textbook. More specifically, Problem y can be found in the textbook at the end of chapter/appendix A.1 a[convert to Cartesian form] A.2 a c[convert to polar form,

More information

Open Loop Frequency Response

Open Loop Frequency Response TAKE HOME LABS OKLAHOMA STATE UNIVERSITY Open Loop Frequency Response by Carion Pelton 1 OBJECTIVE This experiment will reinforce your understanding of the concept of frequency response. As part of the

More information

Laboratory Project 4: Frequency Response and Filters

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

More information

Lab S-7: Spectrograms of AM and FM Signals. 2. Study the frequency resolution of the spectrogram for two closely spaced sinusoids.

Lab S-7: Spectrograms of AM and FM Signals. 2. Study the frequency resolution of the spectrogram for two closely spaced sinusoids. DSP First, 2e Signal Processing First Lab S-7: Spectrograms of AM and FM Signals Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification: The Exercise

More information

ECE 2201 PRELAB 6 BJT COMMON EMITTER (CE) AMPLIFIER

ECE 2201 PRELAB 6 BJT COMMON EMITTER (CE) AMPLIFIER ECE 2201 PRELAB 6 BJT COMMON EMITTER (CE) AMPLIFIER Hand Analysis P1. Determine the DC bias for the BJT Common Emitter Amplifier circuit of Figure 61 (in this lab) including the voltages V B, V C and V

More information

Concordia University. Discrete-Time Signal Processing. Lab Manual (ELEC442) Dr. Wei-Ping Zhu

Concordia University. Discrete-Time Signal Processing. Lab Manual (ELEC442) Dr. Wei-Ping Zhu Concordia University Discrete-Time Signal Processing Lab Manual (ELEC442) Course Instructor: Dr. Wei-Ping Zhu Fall 2012 Lab 1: Linear Constant Coefficient Difference Equations (LCCDE) Objective In this

More information

ECE 3500: Fundamentals of Signals and Systems (Fall 2015) Lab 4: Binary Phase-Shift Keying Modulation and Demodulation

ECE 3500: Fundamentals of Signals and Systems (Fall 2015) Lab 4: Binary Phase-Shift Keying Modulation and Demodulation ECE 500: Fundamentals of Signals and Systems (Fall 2015) Lab 4: Binary Phase-Shift Keying Modulation and Demodulation Files necessary to complete this assignment: none Deliverables Due: Before Dec. 18th

More information

Laboration Exercises in Digital Signal Processing

Laboration Exercises in Digital Signal Processing Laboration Exercises in Digital Signal Processing Mikael Swartling Department of Electrical and Information Technology Lund Institute of Technology revision 215 Introduction Introduction The traditional

More information

ECEN 325 Lab 5: Operational Amplifiers Part III

ECEN 325 Lab 5: Operational Amplifiers Part III ECEN Lab : Operational Amplifiers Part III Objectives The purpose of the lab is to study some of the opamp configurations commonly found in practical applications and also investigate the non-idealities

More information

PYKC 13 Feb 2017 EA2.3 Electronics 2 Lecture 8-1

PYKC 13 Feb 2017 EA2.3 Electronics 2 Lecture 8-1 In this lecture, I will cover amplitude and phase responses of a system in some details. What I will attempt to do is to explain how would one be able to obtain the frequency response from the transfer

More information

EE 4314 Lab 3 Handout Speed Control of the DC Motor System Using a PID Controller Fall Lab Information

EE 4314 Lab 3 Handout Speed Control of the DC Motor System Using a PID Controller Fall Lab Information EE 4314 Lab 3 Handout Speed Control of the DC Motor System Using a PID Controller Fall 2012 IMPORTANT: This handout is common for all workbenches. 1. Lab Information a) Date, Time, Location, and Report

More information

Signal Processing First Lab 02: Introduction to Complex Exponentials Multipath. x(t) = A cos(ωt + φ) = Re{Ae jφ e jωt }

Signal Processing First Lab 02: Introduction to Complex Exponentials Multipath. x(t) = A cos(ωt + φ) = Re{Ae jφ e jωt } Signal Processing First Lab 02: Introduction to Complex Exponentials Multipath 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

More information

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

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

More information

1 Introduction and Overview

1 Introduction and Overview DSP First, 2e Lab S-0: Complex Exponentials Adding Sinusoids Signal Processing First Pre-Lab: Read the Pre-Lab and do all the exercises in the Pre-Lab section prior to attending lab. Verification: The

More information

Introduction to signals and systems

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

More information

Signal Processing. Introduction

Signal Processing. Introduction 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

More information

Subtractive Synthesis. Describing a Filter. Filters. CMPT 468: Subtractive Synthesis

Subtractive 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 information

Real Analog - Circuits 1 Chapter 11: Lab Projects

Real Analog - Circuits 1 Chapter 11: Lab Projects Real Analog - Circuits 1 Chapter 11: Lab Projects 11.2.1: Signals with Multiple Frequency Components Overview: In this lab project, we will calculate the magnitude response of an electrical circuit and

More information

EE 233 Circuit Theory Lab 2: Amplifiers

EE 233 Circuit Theory Lab 2: Amplifiers EE 233 Circuit Theory Lab 2: Amplifiers Table of Contents 1 Introduction... 1 2 Precautions... 1 3 Prelab Exercises... 2 3.1 LM348N Op-amp Parameters... 2 3.2 Voltage Follower Circuit Analysis... 2 3.2.1

More information

EE Experiment 8 Bode Plots of Frequency Response

EE Experiment 8 Bode Plots of Frequency Response EE16:Exp8-1 EE 16 - Experiment 8 Bode Plots of Frequency Response Objectives: To illustrate the relationship between a system frequency response and the frequency response break frequencies, factor powers,

More information

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 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

More information

Problem Set 1 (Solutions are due Mon )

Problem 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 information

Final Exam Solutions June 7, 2004

Final 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 information

From Fourier Series to Analysis of Non-stationary Signals - VII

From 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 information

EE 233 Circuit Theory Lab 3: First-Order Filters

EE 233 Circuit Theory Lab 3: First-Order Filters EE 233 Circuit Theory Lab 3: First-Order Filters Table of Contents 1 Introduction... 1 2 Precautions... 1 3 Prelab Exercises... 2 3.1 Inverting Amplifier... 3 3.2 Non-Inverting Amplifier... 4 3.3 Integrating

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler EECE 31 Signals & Systems Prof. Mark Fowler Note Set #19 C-T Systems: Frequency-Domain Analysis of Systems Reading Assignment: Section 5.2 of Kamen and Heck 1/17 Course Flow Diagram The arrows here show

More information

Experiment 8 Frequency Response

Experiment 8 Frequency Response Experiment 8 Frequency Response W.T. Yeung, R.A. Cortina, and R.T. Howe UC Berkeley EE 105 Spring 2005 1.0 Objective This lab will introduce the student to frequency response of circuits. The student will

More information