syde252

linear systems & signals

 

Term and Year of Offering: Fall 2015

Course Number and Title: SYDE 252, Linear Systems & Signals (Section 02)

Lecture Times, Building and Room Number:

lectures:                            T [lecture] 10:30 to 11:20;  MC 1085

                                            W  [lecture] 11:30 to 12:20;  EV3 1408

                                            F  [lecture] 11:30 to 12:20;  MC2065

tutorials:                       R  1.30-2.20 ; MC-4063

                                  R  2.30-3.20 ; MC-4063

                                            exception: Oct 8, 15, 22, Nov. 19, 26, Dec. 3. From 1:30-3:30pm, we will be in e3-3164 for working on the projects

                            extra lectures   (DWE2402)

                                            Thursday Oct. 2 8.30-9.20 am

                                             Tuesday Oct. 28  11.30-12.20 am

                                             Thursday Nov. 13, 8.30-9.20 am

Instructor’s Name, Office Location, Office Hours, Contact:

                 John Zelek,  E5 6122, 11:30 am to 12:30  pm Friday, jzelek.syde252@gmail.com ; ext 32567  (except Friday Oct. 23rd, will be on Thursday Oct 22nd at 10.30 instead)

TA’s Name, Office, Office Hours, Contact;

                  Mechatronics students  (Section 02)

                        Jeremy Pinto ,  Wednesdays 5-6 pm in E5 6009

                          Shahid Haider, Wednesdays 5-6 pm in E5 6009             

Course Description:

This Systems and Signals course is  about signals which essentially are functions that describe measurements on real world phenomena.  Systems are methods by which we transform one signal into another signal.  The signal transformation can be for various reasons; for example to remove the noise, or to get at a particular measurement that is not explicit or hidden in the signal of interest.

“The concepts of signals and systems arise in a variety of fields and the techniques associated with these notions play a central role in many areas of science and technology such as, for example, communications, aeronautics, bio-engineering, energy, circuit design, ect. Although the physical nature of the signals and systems involved in these various disciplines are different, they all have basic features in common. The aim of the course is to provide the fundamental and universal tools for the analysis of signals, and for the analysis and design of basic systems and this independently of the domain of application.”


Course Learning Objectives:

At the end of the course you should be able to:

  1. be comfortable with signals in both the continuous and discrete domains.

  2. be able to sample a continuous signal into a discrete signal,

  3. be comfortable with a signals representation in both the time and frequency domains,

  4. be able to represent a system as a differential equation or convolution filter.

  5. be able to go from the time to frequency domain (and vice versa) for discrete signals using the z-transform, and using the laplace or fourier transforms for continuous signals.

Required Text: B.P. Lathi, “Linear Systems and  Signals”, 2nd Ed., Oxford University Press

Note:  Material, including lecture slides, tutorials and assignments are heavily borrowed from material from other similar courses.

Topics to be Covered in Lectures:

Date                                 Lecture Topic                                                                   Textbook Chapter

WEEK 1:

Sept. 15,16, 21               Signals                                                                                 1.1->1.5

                                        Systems                                                                                1.6->1.7

                                         Review material (e.g., complex numbers)                   Appendix B


WEEK 2:

Sept. 22,23,25         Time domain analysis: Zero-input response                2.1->2.2

                                      


WEEK 3:

Sept. 29,30                   Time domain analysis: Zero-state response                2.3->2.4.1

Oct. 2


WEEK 4:

Oct.  6,7, 9                  Time domain analysis: convolution                 2.4

                                         Time-domain analysis:Discrete systems       3.1->3.7                                                 


WEEK 5:                                     

Oct. 13, 14, 16         Time-domain analysis:Discrete systems (2)                   3.1->3.7

                                         Discrete  time filtering                                                      extra notes                                  

WEEK 6:

Oct. 20, 21, 23           Frequency-domain analysis: Laplace Transform         4.1->4.2

                                   


WEEK 7:

Oct. 26-30        Midterm week, midterm on thursday

                                      


WEEK 8:

Nov. 3,4, 6            Laplace Transform                                                              4.3->4.4

                                        Frequency Response                  4.8->4.9


WEEK 9:

Nov. 10, 11, 13              Poles, Zeros & Filters                                                          4.10


WEEK 10:

Nov. 17, 18,20 Fourier Transform                                                     7.1, 7.2

                                   Fourier Series                                                                   6.1

                                Properties of Fourier Transform                                   7.1,7.3, 7.4

                                 Signal Transmission & Windowing Effects                    7.4, 7.6, 7.8


WEEK 11:

Nov. 24 25, 27               Sampling & Discrete Signals                                       Chapter 8.1, 8.2

                                       Discrete Fourier Transform                      Chapters 8.4, 8.5  

                                   

WEEK 12:

Dec. 3,4, 6    Discrete Time Signal (Z-transform)                           5.1

                                      Discrete Time Analysis                                               5.1+    

                                    DTFT                                                                            9 


Evaluation:

The course grade will be based  on:

midterm                    20%

Final exam             40%

Concept Inventory (CI) tests            5%

Assignments        0%  (they are not to be handed in)

2 Projects                                      35%


PROJECTS

NOTE:  Both projects are to be done in groups of 2 (individual submissions are acceptable as well)


Project 1:    TIME DOMAIN ANALYSIS

The objective of the first project is to do time filtering using matlab.

You are provided with the following 3 sound clips.

  1. 1. ClayColoredRobin.wav

  2. 2.tapestry.wav

  3. 3. drumloop1.wav

Task ONE:

Low pass each of the 3 signals with appropriate parameter settings using ALL of the following three types of low pass filter implementations:

  1. i)averaging, essentially take an average of the signal around the signal of interest,

  2. ii) weighted average (try Gaussian, triangle) and

  3. iii) median filter

The role of low pass filtering is to remove noise.  Define what noise is present in each signal and how it can be modelled as a mathematical signal.  Determine the window size of the various filters sufficient for removing noise.   Which one worked the best and why?  Show your results by properly labelled & annotated graphs and supporting texts.  Provide suggestions on how to express each of these systems (i.e., filters) as difference and differential equations;  provide a rationale.  Also describe each system as an appropriate impulse response function in the discrete and continuous domain.

Task TWO:

In the time domain, devise techniques (i.e., algorithms) that can perform the following functions.

  1. (i)Determine the number of syllables in the tapestry clip.

  2. (ii) Detect the beats per minute in the drum solo clip.

  3. (iii) In the robin clip, count the number of whistle sounds.

DUE:   October 23, 2015 11.30 pm in the LEARN class dropbox

GRADING: 

The report is to be uploaded as 2 files: (1) pdf document in standard engineering report document (e.g., use work report style guide) and (2) a zip file of all matlab files used with a readme text file describing all the files and how to use them.  Note that the pdf document will also include a listing of all matlab code in the Appendix.  An introductory section and concluding section must be included.  The introductory section will just be the descriptions of the project as written above with a description of how to follow the report.  The concluding section will present conclusions and recommendations.  The grading scheme and associated marking is indicated in the following list:

  1. (i) Graphs [5 marks]:   are properly labelled, self communicating, well annotated and clearly communicate findings and are supported by a description in the text.

  2. (ii)  Task One [10 marks]:  correctness, all aspects tackled and cross referenced with graphs and references.

  3. (iii) Task Two [10 marks]:  correctness, all aspects tackled and cross referenced with graphs and references.

  4. (iv) Matlab code [10 marks]:  all code easy to follow, cross referenced, can replicate results, self explanatory from readme file.

  5. (v)Appearance [5 marks]:  report is well written (spelling, grammar), report is well organized, formatting is consistent, headings, texts and graph labels are concise & self explanatory.  If colour is used in graphics, the presentation choices help follow the material.  Students communicate the scope and key points clearly, accurately and confidently.

  6. (vi)  Findings [10 marks]:  conclusions and recommendations are clearly presented and are cross referenced to the report.

The report will be graded out of 50 (see above).


Project 2:  FREQUENCY DOMAIN ANALYSIS

For this project, you will work in groups of 3 and 4, 3 is the minimum and 4 is the maximum.  Please let the TAs know your groups assignments ASAP.  It is not necessary for each group member to be in the same tutorial slot.

The objective of this project is to transcribe and then re-synthesize a piano composition.   I have selected 3 piano compositions from the following site.  You will all be required to do this for the first ONE minute of the following pre-selected piano pieces:

  1. 1. Bach Prelude and Fugue in D major BWV 850

  2. 2.Chopin  Mazurkas, Opus 7  No. 1

  3. 3.Beethoven  For Elise

  The tasks you will be required to perform are as follows:

Task One:  Determine the number of beats per second for each piece.  If you play a musical instrument, you will realize what a metronome is, this sounds off clicks that correspond to the beat, which can be anywhere form 40 to 210 beats per minute, or usually about 2 beats a second.  Beat information can be obtained via analysis software such as  Ellis’ software .  I do not expect you to develop your complicated beat analysis software however I do expect some analysis into the strengths and weaknesses of the method chosen.

Task Two: Transcribe each of the 3 music pieces into piano notes including the note and amplitude.  The transcription’s purpose is not to create sheet music (which is interesting) but it is to identify what notes and at what amplitude are being played at a particular point of time.  This data can be represented in a table (array) format or visually in graphical form.  What is interesting about the piano is that each note is at a particular frequency.  Beware that each note will also produce harmonics as well.  You will have to decide how you deal with harmonics.

Task Three:   The next  part of this project is to take the transcribed music and resynthesize it into a mp3 file.  Some notes on synthesizing are linked here

Task Four: Derive statistics on how accurate your re-synthesized  signal is.  The suggestion on how to do this is that for each sampling time interval, determine the difference in amplitude in the time domain between the original sound file provided and the newly recreated sound file.  Make sure that the total energy in the two signals you are comparing are equal.  For each of the 3 musical pieces, you should be able to get a mean and standard deviation of the difference.  Do a comparison in the frequency domain as well.  Beware that in the frequency domain, you will have to compare for each frequency at each time sample.

DUE:   December 4, 2015 11.45 pm in the LEARN class dropbox

GRADING: 

The report is to be uploaded as 3 files: (1) pdf document in standard engineering report document (e.g., use work report style guide); (2) a zip file of all matlab files used with a readme text file describing all the files and how to use them; and (3) a zip file that contains the 3 one minute synthesized files in mp3 format.   Note that the pdf document will also include a listing of all matlab code in the Appendix.  An introductory section and concluding section must be included.  The introductory section will just be the descriptions of the project as written above with a description of how to follow the report.  The concluding section will present conclusions and recommendations.  The grading scheme and associated marking is indicated in the following list:

  1. (i) Graphs & Tables [5 marks]:   are properly labelled, self communicating, well annotated and clearly communicate findings and are supported by a description in the text.

  2. (ii)  Task One to Four  [20 marks (5 marks each)]:  correctness, all aspects tackled and cross referenced with graphs and references.

  3. (iii) Matlab code [10 marks]:  all code easy to follow, cross referenced, can replicate results, self explanatory from readme file.

  4. (iv)Appearance [5 marks]:  report is well written (spelling, grammar), report is well organized, formatting is consistent, headings, texts and graph labels are concise & self explanatory.  If colour is used in graphics, the presentation choices help follow the material.  Students communicate the scope and key points clearly, accurately and confidently.

  5. (v)  Findings [10 marks]:  conclusions and recommendations are clearly presented and are cross referenced to the report.

The report will be graded out of 50 (see above).


For those of you that are interested in this area, some interesting links to dig deeper (beyond the project) are as follows

  1. vi. signal processing for music analysis paper

  2. vii.  time frequency analysis of musical instruments paper

  3. viii. sound processing in matlab

  4. ix. some matlab audio processing examples

  5. x. IPEM toolbox (perceptual analysis of music)


C.I. test

Wednesday Oct. 21, 2015 11.30 a.m. EV3 -1408

[solutions will be taken up Thursday Oct. 22, 2015 9.30 a.m. MC1085]

Midterm

SYDE252 (02)  Thursday Oct. 29, 2015;    8-10 pm E5 3101, E5 3102 E5 2004


EXAM

SYDE252 (02)  tbd


Late Submissions:  Late submissions will be penalized 50% immediately and 100% at the end of the tutorial.

Pick up Marked Material: Marked projects and the midterm will be available from your TA during your lab section.

Academic Integrity, Grievance, Discipline, Appeals and Note for Students with Disabilities: see www.uwaterloo.ca/accountability/documents/courseoutlinestmts.pdf   The text for this web site is listed below:

Academic Integrity: In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. [Check www.uwaterloo.ca/academicintegrity/ for more information.]

Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, www.adm.uwaterloo.ca/infosec/Policies/policy70.htm.  When in doubt please be certain to contact the department’s administrative assistant who will provide further assistance.

Discipline: A student is expected to know what constitutes academic integrity [check www.uwaterloo.ca/academicintegrity/] to avoid committing an academic offence, and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offence, or who needs help in learning how to avoid offences (e.g., plagiarism, cheating) or about “rules” for group work/collaboration should seek guidance from the course instructor, academic advisor, or the undergraduate Associate Dean. For information on categories of offences and types of penalties, students should refer to Policy 71, Student Discipline, www.adm.uwaterloo.ca/infosec/Policies/policy71.htm. For typical penalties check Guidelines for the Assessment of Penalties,  www.adm.uwaterloo.ca/infosec/guidelines/penaltyguidelines.htm.


Appeals: A decision made or penalty imposed under Policy 70 (Student Petitions and Grievances) (other than a petition) or Policy 71 (Student Discipline) may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72 (Student Appeals)  www.adm.uwaterloo.ca/infosec/Policies/policy72.htm.


Note for Students with Disabilities: The Office for persons with Disabilities (OPD), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the OPD at the beginning of each academic term.


Turnitin.com and alternatives: Plagiarism detection software (Turnitin) will be used to screen assignments in this course.  This is being done to verify that use of all material and sources in assignments is documented.  Students will be given an option if they do not want to have their assignment screened by Turnitin.  In the first week of the term, details will be provided about the arrangements for the use of Turnitin and alternatives in this course.

Note: students must be given a reasonable option if they do not want to have their assignment screened by Turnitin.  See: http://uwaterloo.ca/academicintegrity/Turnitin/index.html for more information.


John Zelek

Sept. 13, 2015 (revised)