Engineering Physics 3W04 - Acquisition and Analysis of Experimental Information

Engineering Physics 3W04
Acquisition and Analysis of Experimental Information

Term II Fourier Transforms

Announcements

This is the web page for Term II of EP3W04 given January-April, 2000. It does not apply to the current offering of this course.

Course objectives for term II

The overall objective of this course is to provide a background in the acquisition and analysis of experimental information. The first term covered error analysis, estimation, probability and statistics. This second term covers Fourier Transforms, signal processing, sampling, filtering and windowing.

Course description for term II:

The second part of this course is about Fourier Transforms, what they are, why they are useful and how to use them. We set the scene for FTs by first looking at linear systems to show why FTs are useful. To provide a better understanding of this tool, the FT is developed from the Fourier Series which the reader may be more familiar with. Complex number notation will be necessary so we will have to make a side trip there to ensure full understanding. We can then proceed to the FT and study it in some detail, exploring its properties and physical interpretation. This will occupy us for the bulk of the term. Our end goal is the application of FTs to practical signal analysis situations. We will be able to study only a few applications within this course but the hope is that a firm understanding of FTs that should be acquired in the study of the material herein will enable the reader to apply FTs to the various situations that will undoubtedly arise in future work.

Two lectures per week; second term
Prerequisite: Registration in Level III or above of any Engineering or Science Program
Lecturer: Bill Garland, NRB 117, extension 24925
Teaching assistant: Imre Vencel, NRB 117, extension 23191

Course administration for term II

Outline
Schedule
- Week of Jan 3: Admin and course overview
- Week of Jan 10: Chapter 2 Linear Systems
- Week of Jan 17: Chapter 3 Fourier Series
- Week of Jan 24: Chapter 4 Complex Numbers
- Week of Jan 31: Quiz, Chapter 5 Fourier Transforms
- Week of Feb 7: Chapter 5 Fourier Transforms
- Week of Feb 14: Chapter 6 Useful Properties and Theorems
- Week of Feb 21: Spring Break
- Week of Feb 28: Midterm
- Week of Mar 6: Chapter 6 Useful Properties and Theorems
- Week of Mar 13: Chapter 7 Application: Fraunhofer Diffraction, demos
- Week of Mar 20: Chapter 8 Signal Analysis and Filters
- Week of Mar 27: Quiz, Chapter 9 Windows and the Discrete Fourier Transform
- Week of Apr 3: Review

Course notes for term II

These course notes are also available as Courseware in the bookstore.

Chapter 1: Introduction, text (pdf 58kb)
Chapter 2: Linear Systems, text (pdf 245kb)
Chapter 3: Fourier Series, text (pdf 243kb)
Chapter 4: Complex Numbers, text (pdf 177kb)
Chapter 5: Fourier Transforms, text (pdf 426kb)
Chapter 6: Useful Properties and Theorems, text (pdf 623kb)
Chapter 7: Application: Fraunhofer Diffraction, text (pdf 176kb)
Chapter 8: Application: Signal Analysis and Filters, text (pdf 394kb)
Chapter 9: Windows and the Discrete Fourier Transform, text (pdf 275kb)

Assignments and Tests

Please drop your assignments off in the dropbox located in the Engineering Physics hallway (3rd floor of JHEA near the elevators). Your marked solutions can be picked up at the reception area of the Nuclear Research Building. The solutions will be posted here on the web a few days after the assignment is due.

Note: the due dates are subject to change. Check here regularly for changes.

Assignment	Solution	Due Date	Status
Assignment based on Chapter 2 (pdf 16kb)	Solution (pdf 16kb)	Thursday 2000.01.20:1700hrs	Marked and available for pickup
Assignment based on Chapter 3 (pdf 51kb)	Solution (pdf 133kb)	Thursday 2000.01.27:1600hrs	Marked and available for pickup
Assignment based on Chapter 4 (pdf 16kb)	Solution (pdf 61kb)	Thursday 2000.02.03:1600hrs	Marked and available for pickup
Assignment based on Chapter 5 (pdf 46kb)	Solution (pdf 95kb)	Friday 2000.02.18:1600hrs	Marked and available for pickup
Assignment based on Chapter 6 (pdf 26kb)	Solution (pdf 115kb)	Friday 2000.03.17:1600hrs	Marked and available for pickup
Assignment based on Chapter 7 (pdf 5kb)	See the student links below for some possible solutions	Friday 2000.03.31:1600hrs	Marked and available for pickup from my office.
Assignment based on Chapter 8 (pdf 24kb)	Solution (pdf 86kb)	Friday 2000.03.31:1600hrs	Marked and available for pickup
Assignment based on Chapter 9 (pdf 40kb)	Solution (pdf 142kb)	Friday 2000.04.07:1600hrs	Marked and available for pickup
Quiz #1 with solution (pdf 100kb)		Held on 2000.02.03	Marked and available for pickup
Midterm (pdf 14kb) and solution (pdf 161kb)		Held on 2000.03.02	Marked and available for pickup
Quiz #2 (pdf 12kb) and solution (pdf 63kb)		Held on 2000.03.30	Marked and available for pickup
Final (pdf kb) and solution (pdf 240kb)

Matlab Code and Related Information and Links

Matlab tutorial from the University of Michigan.
Example Matlab m-files to generate a pulse in the time domain, calculate the Fourier Transform and plot the result. Download all three files into a working directory. From within Matlab, type help dopulse to see the syntax for the main function, dopulse.
- dopulse.m calls pulse.m and evenft.m, and plots the result.
- pulse.m generates a pulse in the time domain.
- evenft.m calculates the FT of the pulse using the cosine FT, ie, it assumes the pulse is an even and real function.
How Can I Use FFT to Obtain Simple Spectral Analysis Plots? - A note from the support pages of The MathWorks people - for all you Matlab lovers.
The scientific portal for MATLAB and MIDEVA m-files, toolboxes, links and resources. - Comprehensive list of links for Matlab.

Interesting and Informative Links

Teaching matters - helpful general information on teaching and learning for the student and the educator.
FFT Laboratory - Very neat Java version of the FFT. Great fun to play with to visualize FFTs. Highly recommended because it is so cute and instructive.
Download FFT Properties 3.01 from this site. - This is a very useful program for visualizing and analyzing Fourier Transforms. Highly recommended for the course.
The Sonic Spot - Interesting site dealing with sound. Has some utilities and other software, including FFT Properties.
Digital Signal Analysis Software download page. - I tried the FFT program on this page. Not bad but I like FFT Properties (above) better.
An Introduction to Fourier Theory. - Just in case you don't have enough theory to read, here is some material from the University of Tennessee, Department of Physics And Astronomy, UT Complex Systems Laboratory
An FFT Demonstration Program - Some nice links, C code for FFT if you want to roll your own. Worth a look.
DADiSP - The Ultimate Engineering Spreadsheet, according to the DSP Development Corporation - and they may be right. You can download a student version for free. I tried it and I like it alot. Yep, it does FFTs - and a whole lot more. Nice tutorial to get you going.
Responsive Graphs: Understanding Engineering Concepts Through Interactive Experience - Brought to you by HP
- Interactive Amplitude Modulation Model - Nifty on-line illustration of AM
- Interactive Frequency Modulation Model - Nifty on-line illustration of FM
The Scientist and Engineer's Guide to Digital Signal Processing - a complete book on-line!

Contributions from Students

An entertaining and well done report by Karen Owen and Sonia Lala: Infrared Spectroscopy
A good overview by Mehdi Shahideh, Nima Safaian, Nick Torenvliet and Umar Chaudry: Fourier Transform Infrared Spectroscopy
Listen up to a report on the ear as a FT device by John Hudson.
Another nice report on Fourier Transform Infrared Spectroscopy (FTIR) by Greg McMahon.
Link contributed by Ricky Fan: The Scientist and Engineer's Guide to Digital Signal Processing
Links contributed by Lukasz Elman LINKS TO FT AND FFT APPLICATIONS
Link contributed by R. Bains: FT applications