ECE 637 Spring 2009 Exam Prep: Fourier Transforms, Tomography, Discrete Transforms - Prof., Study notes of Electrical and Electronics Engineering

A study guide for students in the ece 637 spring 2009 course, listing recommended homework assignments and their corresponding exam problems. Topics covered include continuous and discrete fourier transforms, tomography and mri, discrete transforms and filters, random processes, neighborhoods, and color spaces. Students are encouraged to work through the problems before checking solutions.

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Homework Study Guide
ECE 637 Spring 2009
It is recommended that students work the problems listed below in order to prepare for exams. However
these homework assignments are not required and will not be counted toward the final course gr ade. The
problems are fro m previous exams, so they can be foun d on the archived web sites. Many (most)
problems also have associated solutions, however, it is a good idea to try working the problems your self
before reviewing the solutions.
Assignment 1 โ€“ due January 23 (Session 5)
Topics: Continuous 1 and 2D Fourier Transform
Spring 2008 Exam 1: Proble m 1 (CSFT)
Spring 2006 Exam 1: Proble m 2 (CSFT)
Assignment 2 โ€“ due January 30 (Session 8)
Topics: Tomography and MRI
Spring 2008 Exam 1: Proble m 2, 3, 4 (tomography)
Spring 2008 Final: Problem 5 (MRI)
Spring 2007 Exam 1: Proble m 3 (tomography)
Spring 2007 Final: Problem 2 (MRI)
Spring 2006 Exam 1: Proble m 3 (MRI)
Spring 2006 Final: Problem 5 (tomography)
Spring 2005 Exam 1: Proble m 2 (tomography)
Spring 2004 Final: Problem 1 (tomography)
Spring 2003 Exam 1: Proble m 1 (tomography)
Spring 2002 Exam 1: Proble m 2 (tomography)
Spring 2002 Exam 1: Proble m 3 (MRI)
Spring 2001 Exam 1: Proble m 4 (tomography)
Spring 2001 Final: Problem 5 (MRI)
Assignment 3 โ€“ due February 6 (Session 11)
Topics: Discrete transforms; 1 and 2D Filters, sampling, and scanning
Spring 2008 Exam 2: Proble m 3 (sampling)
Spring 2008 Final: Problem 1 (DSFT and DTFT)
Spring 2007 Exam 1: Proble m 1, 2 (DSFT and 2D Z-transform)
Spring 2006 Exam 1: Proble m 1 (discrete-time filtering)
Spring 2005 Exam 1: Proble m 3 (DSFT and CSFT)
Spring 2005 Exam 2: Proble m 2 (2D discret e-time filte rs)
Spring 2005 Final: Problem 4 (sampling)
Spring 2004 Final: Problem 3 (2D systems)
Spring 2003 Exam 1: Proble m 2 (2D systems)
Spring 2002 Final: Problem 2 (video scanning and sampling)
Spring 2001 Exam 1: Proble m 1 (2D FIR filtering)
Spring 2001 Exam 1: Proble m 2 (2D IIR filtering)
Assignment 4 โ€“ due February 13
Topics: Random processes, spectral estimation, and edge detection
Spring 2008 Exam 2: Proble m 2 (power spectrum)
Spring 2007 Exam 2: Proble m 3 (edge detection)
Spring 2007 Final: Problem 1 (power spectrum)
Spring 2006 Exam 2: Proble m 3 (edge detection)
Spring 2005 Exam 1: Proble m 1 (2D power spectrum and filtering)
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Homework Study Guide

ECE 637 Spring 2009

It is recommended that students work the problems listed below in order to prepare for exams. However these homework assignments are not required and will not be counted toward the final course grade. The problems are from previous exams, so they can be found on the archived web sites. Many (most) problems also have associated solutions, however, it is a good idea to try working the problems your self before reviewing the solutions. Assignment 1 โ€“ due January 23 (Session 5) Topics: Continuous 1 and 2D Fourier Transform Spring 2008 Exam 1: Problem 1 (CSFT) Spring 2006 Exam 1: Problem 2 (CSFT) Assignment 2 โ€“ due January 30 (Session 8) Topics: Tomography and MRI Spring 2008 Exam 1: Problem 2, 3, 4 (tomography) Spring 2008 Final: Problem 5 (MRI) Spring 2007 Exam 1: Problem 3 (tomography) Spring 2007 Final: Problem 2 (MRI) Spring 2006 Exam 1: Problem 3 (MRI) Spring 2006 Final: Problem 5 (tomography) Spring 2005 Exam 1: Problem 2 (tomography) Spring 2004 Final: Problem 1 (tomography) Spring 2003 Exam 1: Problem 1 (tomography) Spring 2002 Exam 1: Problem 2 (tomography) Spring 2002 Exam 1: Problem 3 (MRI) Spring 2001 Exam 1: Problem 4 (tomography) Spring 2001 Final: Problem 5 (MRI) Assignment 3 โ€“ due February 6 (Session 11) Topics: Discrete transforms; 1 and 2D Filters, sampling, and scanning Spring 2008 Exam 2: Problem 3 (sampling) Spring 2008 Final: Problem 1 (DSFT and DTFT) Spring 2007 Exam 1: Problem 1, 2 (DSFT and 2D Z-transform) Spring 2006 Exam 1: Problem 1 (discrete-time filtering) Spring 2005 Exam 1: Problem 3 (DSFT and CSFT) Spring 2005 Exam 2: Problem 2 (2D discrete-time filters) Spring 2005 Final: Problem 4 (sampling) Spring 2004 Final: Problem 3 (2D systems) Spring 2003 Exam 1: Problem 2 (2D systems) Spring 2002 Final: Problem 2 (video scanning and sampling) Spring 2001 Exam 1: Problem 1 (2D FIR filtering) Spring 2001 Exam 1: Problem 2 (2D IIR filtering) Assignment 4 โ€“ due February 13 Topics: Random processes, spectral estimation, and edge detection Spring 2008 Exam 2: Problem 2 (power spectrum) Spring 2007 Exam 2: Problem 3 (edge detection) Spring 2007 Final: Problem 1 (power spectrum) Spring 2006 Exam 2: Problem 3 (edge detection) Spring 2005 Exam 1: Problem 1 (2D power spectrum and filtering)

Spring 2004 Midterm Exam: Problem 1 (2D AR processes) Spring 2003 Exam 1: Problem 3 (power spectrum estimation) Spring 2002 Exam 1: Problem 1 (power spectrum estimation) Spring 2001 Exam 1: Problem 3 (power spectrum) Assignment 5 โ€“ due February 18 Topics: Neighborhoods, connected components, and clustering Spring 2005 Final: Problem 2 (connected component analysis) Spring 2004 Midterm Exam: Problem 2 (connected components) Spring 2003 Exam 2: Problem 1 (clustering) Spring 2001 Exam 2: Problem 1 (clustering) Assignment 6 โ€“ due February 27 Topics: Achromatic Vision, Gamma, and Visual MTF Spring 2008 Final: Problem 3 (gamma correction) Spring 2007 Exam 2: Problem 2 (contrast) Spring 2005 Final: Problem 5 (gamma correction) Spring 2004 Midterm Exam: Problem 4 (MTF and gamma correction) Spring 2002 Exam 2: Problem 1 (image distortion metrics) Spring 2001 Exam 2: Problem 2 (gamma correction) Spring 2001 Final: Problem 4 (gamma correction) Assignment 7 โ€“ due March 6 Topics: Color matching, additive and subtractive color Spring 2008 Exam 2: Problem 1 (color and gamma) Spring 2007 Exam 2: Problem 1 (color and gamma) Spring 2006 Exam 2: Problem 2 (color matching) Spring 2004 Final: Problem 4 (color matching) Spring 2003 Exam 2: Problem 3 (subtractive color) Assignment 8 โ€“ due March 13 Topics: Chromaticity and white point Spring 2005 Exam 2: Problem 1 (chromaticity diagram) Spring 2003 Exam 2: Problem 2 (chromaticity components) Spring 2002 Exam 2: Problem 2 (chromaticity diagram) Spring 2001 Exam 2: Problem 3 (chromaticity and white point) Assignment 9 โ€“ due March 27 Topics: Color spaces, and perceptual uniformity Spring 2006 Exam 2: Problem 1 (Lab space) Spring 2006 Final: Problem 2 (color transformations) Spring 2004 Midterm Exam: Problem 3 (perceptual uniformity) Assignment 10 โ€“ due April 3 Topics: Interpolation, decimation, and optimum linear filtering Spring 2007 Final: Problem 4 (inverse filtering) Spring 2006 Final: Problem 3 (MMSE prediction) Spring 2005 Exam 2: Problem 3 (MMSE prediction) Spring 2004 Final: Problem 5 (MMSE prediction) Spring 2002 Final: Problem 3 (2D interpolation) Spring 2001 Final: Problem 2 (MMSE and MAE filtering) Assignment 11 โ€“ due April 8