| Date |
Topic |
Problem sets & course materials |
| 9/8-9/11 |
||
| W |
Overview of time-frequency analysis Section 1.1 Introduction to Fourier series |
|
| Th |
Pendulum Waves and Matlab intro |
Matlab tutorial website |
| F |
Section 1.2-3 Fourier coefficients | Exercises 1.2 (p7), 1.7 (p9), 1.17-18 (p15) due Fri 9/18 |
| 9/14-9/18 |
||
| M |
Section 3.1 Pointwise convergence | |
| W |
Section 3.2 Smoothness vs convergence |
|
| Th |
Lab #1 in Webster |
|
| F |
Section 3.3 More on convergence | Exercises 3.22 (p66), 3.26 (p68) due Fri 9/25 |
| 9/21-9/25 |
||
| M |
Section 4.1 Partial Fourier sums & Dirichlet kernel | Dirichlet kernel demo |
| W |
Section 4.2 Convolution |
Convolution example |
| Th |
Lab #2 in Webster | |
| F |
Section 4.3 Good kernels | Convolution with step function kernel Matlab script for convolution Exercises 4.8 (p83), 4.12 (p86), 4.17-18 (p89) due Fri 10/2 |
| 9/28-10/2 |
||
| M |
Section 4.4 Fejer kernels and Cesaro means | Fejer kernel demo |
| W |
Section 4.5 Poisson kernels and Abel means | Poisson kernel demo |
| Th |
Lab #3 in Webster | |
| F |
Section 5.1 Basic Fourier theorems in L^2 | Exercises 4.30-31 (p97), 4.33 (p98), 4.37 (p100) due Fri 10/9 |
| 10/5-10/9 |
||
| M |
Section 5.2 Geometry of L^2 | |
| W |
Section 5.3 Completeness of trig system | |
| Th |
Lab #4 in Webster | |
| F |
Section 5.4 Orthogonal projection | Exercises 5.13-14 (p112), 5.17 (p113), 5.29 (p121) due Fri 10/16 |
| 10/12-10/16 |
||
| M | Fall break | |
| T | Monday classes held today Section 6.1 Fourier series vs DFT Section 6.2 Dual bases |
Train whistle demo in Matlab |
| W | Section 6.3 DFT and inverse DFT | DFT demo |
| Th |
Lab #5 in Webster | Sunspot data file |
| F |
Section 6.4 FFT | Exercises 6.3 (p132), 6.4 (p133), 6.20 (p138), 6.30 (p146), 6.34-35 (p147) due Fri 10/23 |
| 10/19-10/23 |
( | |
| M |
Section 6.5 Discrete Haar basis | |
| W |
Section 6.6 Discrete Haar transform | |
| Th |
Lab #6 in Webster | |
| F |
Review | Exam 1 Review Sheet (no assigned HW) |
| 10/26-10/30 |
||
| M |
Exam 1 | |
| W |
Section 6.7 Fast Haar transform | |
| Th |
Lab #7 in Webster | Magic square image and car image |
| F |
Section 7.1 Fourier series to transform Section 7.2 Schwartz class |
Calculate DHT of v=[1 1 0 1 2 1 0 2] by hand in two ways (matrix H8 and herringbone algorithm) and do Exercise 7.13 (p170), due Fri 11/6 |
| 11/2-11/6 |
||
| M |
Section 7.3 Fourier transform properties | |
| W |
Section 7.5 Convolution | |
| Th |
Lab #8 in Webster | |
| F |
Section 7.6 Fourier inversion and Plancherel | Exercises 7.20 (p176), 7.26-27 (p180), 7.29 (p181) due Fri 11/13 |
| 11/9-11/13 |
||
| M |
Section 8.4 Delta distribution | Project description |
| W |
Section 8.5 Sampling Theorem | Sampling Theorem demo |
| Th |
Lab #9 in Webster | |
| F |
Section 8.5 Uncertainty Principle | Oversampling exercise due Fri 11/20 |
| 11/16-11/20 |
||
| M |
Section 9.2 Windowed Fourier transform | Email project topic |
| W |
Section 9.3 Wavelet transform | |
| Th |
Lab #10 in Webster | |
| F |
Section 9.4 Haar analysis | Exercises 9.8, 9.13, 9.14, 9.22 due Wed 12/2 |
| 11/21-11/29 | Thanksgiving break | |
| 11/30-12/4 |
||
| M |
Section 10.1 Multiresolution analysis |
|
| W |
Section 10.1 continued | |
| Th |
Lab #11 in Webster | Horizon.mat |
| F |
Review | Exam 2 Review Sheet |
| 12/7-12/11 | ||
| M |
Exam 2 | |
| W |
Section 10.3 Mallat's theorem |
|
| Th |
Lab #12 in Webster | |
| F |
Section 10.3 continued | Final homework will be due Wed 12/16 |
| 12/14-15 |
||
| M |
Section 10.4 How to find suitable MRAs | |
| Project meetings (individual) | Final project report due 4pm Mon Dec 21 |
